Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, D

Percentage Accurate: 58.9% → 97.4%

Time: 5.8s

Alternatives: 16

Speedup: 7.9×

Specification

Math

\[\begin{array}{l} \\ x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (+
  x
  (/
   (*
    y
    (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b))
   (+
    (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z)
    0.607771387771))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return x + ((y * ((((((((z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b)) / (((((((z + 15.234687407) * z) + 31.4690115749) * z) + 11.9400905721) * z) + 0.607771387771));
}

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)
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
    code = x + ((y * ((((((((z * 3.13060547623d0) + 11.1667541262d0) * z) + t) * z) + a) * z) + b)) / (((((((z + 15.234687407d0) * z) + 31.4690115749d0) * z) + 11.9400905721d0) * z) + 0.607771387771d0))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x + ((y * ((((((((z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b)) / (((((((z + 15.234687407) * z) + 31.4690115749) * z) + 11.9400905721) * z) + 0.607771387771));
}

Python

def code(x, y, z, t, a, b):
	return x + ((y * ((((((((z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b)) / (((((((z + 15.234687407) * z) + 31.4690115749) * z) + 11.9400905721) * z) + 0.607771387771))

Julia

function code(x, y, z, t, a, b)
	return Float64(x + Float64(Float64(y * Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b)) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(z + 15.234687407) * z) + 31.4690115749) * z) + 11.9400905721) * z) + 0.607771387771)))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x + ((y * ((((((((z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b)) / (((((((z + 15.234687407) * z) + 31.4690115749) * z) + 11.9400905721) * z) + 0.607771387771));
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x + N[(N[(y * N[(N[(N[(N[(N[(N[(N[(N[(z * 3.13060547623), $MachinePrecision] + 11.1667541262), $MachinePrecision] * z), $MachinePrecision] + t), $MachinePrecision] * z), $MachinePrecision] + a), $MachinePrecision] * z), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(z + 15.234687407), $MachinePrecision] * z), $MachinePrecision] + 31.4690115749), $MachinePrecision] * z), $MachinePrecision] + 11.9400905721), $MachinePrecision] * z), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 58.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (+
  x
  (/
   (*
    y
    (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b))
   (+
    (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z)
    0.607771387771))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return x + ((y * ((((((((z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b)) / (((((((z + 15.234687407) * z) + 31.4690115749) * z) + 11.9400905721) * z) + 0.607771387771));
}

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)
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
    code = x + ((y * ((((((((z * 3.13060547623d0) + 11.1667541262d0) * z) + t) * z) + a) * z) + b)) / (((((((z + 15.234687407d0) * z) + 31.4690115749d0) * z) + 11.9400905721d0) * z) + 0.607771387771d0))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x + ((y * ((((((((z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b)) / (((((((z + 15.234687407) * z) + 31.4690115749) * z) + 11.9400905721) * z) + 0.607771387771));
}

Python

def code(x, y, z, t, a, b):
	return x + ((y * ((((((((z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b)) / (((((((z + 15.234687407) * z) + 31.4690115749) * z) + 11.9400905721) * z) + 0.607771387771))

Julia

function code(x, y, z, t, a, b)
	return Float64(x + Float64(Float64(y * Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b)) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(z + 15.234687407) * z) + 31.4690115749) * z) + 11.9400905721) * z) + 0.607771387771)))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x + ((y * ((((((((z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b)) / (((((((z + 15.234687407) * z) + 31.4690115749) * z) + 11.9400905721) * z) + 0.607771387771));
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x + N[(N[(y * N[(N[(N[(N[(N[(N[(N[(N[(z * 3.13060547623), $MachinePrecision] + 11.1667541262), $MachinePrecision] * z), $MachinePrecision] + t), $MachinePrecision] * z), $MachinePrecision] + a), $MachinePrecision] * z), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(z + 15.234687407), $MachinePrecision] * z), $MachinePrecision] + 31.4690115749), $MachinePrecision] * z), $MachinePrecision] + 11.9400905721), $MachinePrecision] * z), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 97.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z - -15.234687407, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)\\ \mathbf{if}\;x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(y, z \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(3.13060547623, z, 11.1667541262\right), z, t\right), z, a\right)}{t\_1}, \mathsf{fma}\left(b, \frac{y}{t\_1}, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + 3.13060547623 \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (fma
          (fma (fma (- z -15.234687407) z 31.4690115749) z 11.9400905721)
          z
          0.607771387771)))
   (if (<=
        (+
         x
         (/
          (*
           y
           (+
            (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z)
            b))
          (+
           (*
            (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721)
            z)
           0.607771387771)))
        INFINITY)
     (fma
      y
      (* z (/ (fma (fma (fma 3.13060547623 z 11.1667541262) z t) z a) t_1))
      (fma b (/ y t_1) x))
     (+ x (* 3.13060547623 y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(fma(fma((z - -15.234687407), z, 31.4690115749), z, 11.9400905721), z, 0.607771387771);
	double tmp;
	if ((x + ((y * ((((((((z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b)) / (((((((z + 15.234687407) * z) + 31.4690115749) * z) + 11.9400905721) * z) + 0.607771387771))) <= ((double) INFINITY)) {
		tmp = fma(y, (z * (fma(fma(fma(3.13060547623, z, 11.1667541262), z, t), z, a) / t_1)), fma(b, (y / t_1), x));
	} else {
		tmp = x + (3.13060547623 * y);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(fma(fma(Float64(z - -15.234687407), z, 31.4690115749), z, 11.9400905721), z, 0.607771387771)
	tmp = 0.0
	if (Float64(x + Float64(Float64(y * Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b)) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(z + 15.234687407) * z) + 31.4690115749) * z) + 11.9400905721) * z) + 0.607771387771))) <= Inf)
		tmp = fma(y, Float64(z * Float64(fma(fma(fma(3.13060547623, z, 11.1667541262), z, t), z, a) / t_1)), fma(b, Float64(y / t_1), x));
	else
		tmp = Float64(x + Float64(3.13060547623 * y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(z - -15.234687407), $MachinePrecision] * z + 31.4690115749), $MachinePrecision] * z + 11.9400905721), $MachinePrecision] * z + 0.607771387771), $MachinePrecision]}, If[LessEqual[N[(x + N[(N[(y * N[(N[(N[(N[(N[(N[(N[(N[(z * 3.13060547623), $MachinePrecision] + 11.1667541262), $MachinePrecision] * z), $MachinePrecision] + t), $MachinePrecision] * z), $MachinePrecision] + a), $MachinePrecision] * z), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(z + 15.234687407), $MachinePrecision] * z), $MachinePrecision] + 31.4690115749), $MachinePrecision] * z), $MachinePrecision] + 11.9400905721), $MachinePrecision] * z), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(y * N[(z * N[(N[(N[(N[(3.13060547623 * z + 11.1667541262), $MachinePrecision] * z + t), $MachinePrecision] * z + a), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(b * N[(y / t$95$1), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision], N[(x + N[(3.13060547623 * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z #s(literal 313060547623/100000000000 binary64)) #s(literal 55833770631/5000000000 binary64)) z) t) z) a) z) b)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z #s(literal 15234687407/1000000000 binary64)) z) #s(literal 314690115749/10000000000 binary64)) z) #s(literal 119400905721/10000000000 binary64)) z) #s(literal 607771387771/1000000000000 binary64)))) < +inf.0

   1. Initial program 58.9%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

   3. Applied rewrites 63.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, z \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(3.13060547623, z, 11.1667541262\right), z, t\right), z, a\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z - -15.234687407, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}, \mathsf{fma}\left(b, \frac{y}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z - -15.234687407, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}, x\right)\right)} \]

   if +inf.0 < (+.f64 x (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z #s(literal 313060547623/100000000000 binary64)) #s(literal 55833770631/5000000000 binary64)) z) t) z) a) z) b)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z #s(literal 15234687407/1000000000 binary64)) z) #s(literal 314690115749/10000000000 binary64)) z) #s(literal 119400905721/10000000000 binary64)) z) #s(literal 607771387771/1000000000000 binary64))))

   1. Initial program 58.9%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

   2. Taylor expanded in z around inf

      \[\leadsto x + \color{blue}{\frac{313060547623}{100000000000} \cdot y} \]
   3. Step-by-step derivation

      1. lower-*.f64 62.5

         \[\leadsto x + 3.13060547623 \cdot \color{blue}{y} \]

   4. Applied rewrites 62.5%

      \[\leadsto x + \color{blue}{3.13060547623 \cdot y} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 96.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(3.13060547623, z, 11.1667541262\right), z, t\right), z, a\right), z, b\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z - -15.234687407, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + 3.13060547623 \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<=
      (+
       x
       (/
        (*
         y
         (+
          (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z)
          b))
        (+
         (*
          (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721)
          z)
         0.607771387771)))
      INFINITY)
   (fma
    (/
     (fma (fma (fma (fma 3.13060547623 z 11.1667541262) z t) z a) z b)
     (fma
      (fma (fma (- z -15.234687407) z 31.4690115749) z 11.9400905721)
      z
      0.607771387771))
    y
    x)
   (+ x (* 3.13060547623 y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x + ((y * ((((((((z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b)) / (((((((z + 15.234687407) * z) + 31.4690115749) * z) + 11.9400905721) * z) + 0.607771387771))) <= ((double) INFINITY)) {
		tmp = fma((fma(fma(fma(fma(3.13060547623, z, 11.1667541262), z, t), z, a), z, b) / fma(fma(fma((z - -15.234687407), z, 31.4690115749), z, 11.9400905721), z, 0.607771387771)), y, x);
	} else {
		tmp = x + (3.13060547623 * y);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(x + Float64(Float64(y * Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b)) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(z + 15.234687407) * z) + 31.4690115749) * z) + 11.9400905721) * z) + 0.607771387771))) <= Inf)
		tmp = fma(Float64(fma(fma(fma(fma(3.13060547623, z, 11.1667541262), z, t), z, a), z, b) / fma(fma(fma(Float64(z - -15.234687407), z, 31.4690115749), z, 11.9400905721), z, 0.607771387771)), y, x);
	else
		tmp = Float64(x + Float64(3.13060547623 * y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(x + N[(N[(y * N[(N[(N[(N[(N[(N[(N[(N[(z * 3.13060547623), $MachinePrecision] + 11.1667541262), $MachinePrecision] * z), $MachinePrecision] + t), $MachinePrecision] * z), $MachinePrecision] + a), $MachinePrecision] * z), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(z + 15.234687407), $MachinePrecision] * z), $MachinePrecision] + 31.4690115749), $MachinePrecision] * z), $MachinePrecision] + 11.9400905721), $MachinePrecision] * z), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(N[(N[(N[(N[(3.13060547623 * z + 11.1667541262), $MachinePrecision] * z + t), $MachinePrecision] * z + a), $MachinePrecision] * z + b), $MachinePrecision] / N[(N[(N[(N[(z - -15.234687407), $MachinePrecision] * z + 31.4690115749), $MachinePrecision] * z + 11.9400905721), $MachinePrecision] * z + 0.607771387771), $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision], N[(x + N[(3.13060547623 * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z #s(literal 313060547623/100000000000 binary64)) #s(literal 55833770631/5000000000 binary64)) z) t) z) a) z) b)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z #s(literal 15234687407/1000000000 binary64)) z) #s(literal 314690115749/10000000000 binary64)) z) #s(literal 119400905721/10000000000 binary64)) z) #s(literal 607771387771/1000000000000 binary64)))) < +inf.0

   1. Initial program 58.9%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

   3. Applied rewrites 60.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(3.13060547623, z, 11.1667541262\right), z, t\right), z, a\right), z, b\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z - -15.234687407, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}, y, x\right)} \]

   if +inf.0 < (+.f64 x (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z #s(literal 313060547623/100000000000 binary64)) #s(literal 55833770631/5000000000 binary64)) z) t) z) a) z) b)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z #s(literal 15234687407/1000000000 binary64)) z) #s(literal 314690115749/10000000000 binary64)) z) #s(literal 119400905721/10000000000 binary64)) z) #s(literal 607771387771/1000000000000 binary64))))

   1. Initial program 58.9%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

   2. Taylor expanded in z around inf

      \[\leadsto x + \color{blue}{\frac{313060547623}{100000000000} \cdot y} \]
   3. Step-by-step derivation

      1. lower-*.f64 62.5

         \[\leadsto x + 3.13060547623 \cdot \color{blue}{y} \]

   4. Applied rewrites 62.5%

      \[\leadsto x + \color{blue}{3.13060547623 \cdot y} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 95.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z - -15.234687407, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)\\ \mathbf{if}\;z \leq -2.9 \cdot 10^{+51}:\\ \;\;\;\;\mathsf{fma}\left(\frac{3.13060547623}{z} \cdot z, y, \mathsf{fma}\left(\frac{y}{t\_1}, b, x\right)\right)\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+35}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(t, z, a\right), z, b\right), \left(-y\right) \cdot \frac{-1}{t\_1}, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + 3.13060547623 \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (fma
          (fma (fma (- z -15.234687407) z 31.4690115749) z 11.9400905721)
          z
          0.607771387771)))
   (if (<= z -2.9e+51)
     (fma (* (/ 3.13060547623 z) z) y (fma (/ y t_1) b x))
     (if (<= z 5.2e+35)
       (fma (fma (fma t z a) z b) (* (- y) (/ -1.0 t_1)) x)
       (+ x (* 3.13060547623 y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(fma(fma((z - -15.234687407), z, 31.4690115749), z, 11.9400905721), z, 0.607771387771);
	double tmp;
	if (z <= -2.9e+51) {
		tmp = fma(((3.13060547623 / z) * z), y, fma((y / t_1), b, x));
	} else if (z <= 5.2e+35) {
		tmp = fma(fma(fma(t, z, a), z, b), (-y * (-1.0 / t_1)), x);
	} else {
		tmp = x + (3.13060547623 * y);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(fma(fma(Float64(z - -15.234687407), z, 31.4690115749), z, 11.9400905721), z, 0.607771387771)
	tmp = 0.0
	if (z <= -2.9e+51)
		tmp = fma(Float64(Float64(3.13060547623 / z) * z), y, fma(Float64(y / t_1), b, x));
	elseif (z <= 5.2e+35)
		tmp = fma(fma(fma(t, z, a), z, b), Float64(Float64(-y) * Float64(-1.0 / t_1)), x);
	else
		tmp = Float64(x + Float64(3.13060547623 * y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(z - -15.234687407), $MachinePrecision] * z + 31.4690115749), $MachinePrecision] * z + 11.9400905721), $MachinePrecision] * z + 0.607771387771), $MachinePrecision]}, If[LessEqual[z, -2.9e+51], N[(N[(N[(3.13060547623 / z), $MachinePrecision] * z), $MachinePrecision] * y + N[(N[(y / t$95$1), $MachinePrecision] * b + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.2e+35], N[(N[(N[(t * z + a), $MachinePrecision] * z + b), $MachinePrecision] * N[((-y) * N[(-1.0 / t$95$1), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(x + N[(3.13060547623 * y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.8999999999999998e51

   1. Initial program 58.9%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

   2. Taylor expanded in z around 0

      \[\leadsto x + \frac{y \cdot \left(\left(\color{blue}{t} \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]
   3. Step-by-step derivation

   4. Applied rewrites 62.1%

      \[\leadsto x + \frac{y \cdot \left(\left(\color{blue}{t} \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

   6. Applied rewrites 70.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z \cdot y, \frac{\mathsf{fma}\left(t, z, a\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z - -15.234687407, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}, \mathsf{fma}\left(\frac{y}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z - -15.234687407, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}, b, x\right)\right)} \]

   7. Taylor expanded in z around inf

      \[\leadsto \mathsf{fma}\left(z \cdot y, \color{blue}{\frac{\frac{313060547623}{100000000000}}{z}}, \mathsf{fma}\left(\frac{y}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z - \frac{-15234687407}{1000000000}, z, \frac{314690115749}{10000000000}\right), z, \frac{119400905721}{10000000000}\right), z, \frac{607771387771}{1000000000000}\right)}, b, x\right)\right) \]
   8. Step-by-step derivation

      1. lower-/.f64 69.8

         \[\leadsto \mathsf{fma}\left(z \cdot y, \frac{3.13060547623}{\color{blue}{z}}, \mathsf{fma}\left(\frac{y}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z - -15.234687407, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}, b, x\right)\right) \]

   9. Applied rewrites 69.8%

      \[\leadsto \mathsf{fma}\left(z \cdot y, \color{blue}{\frac{3.13060547623}{z}}, \mathsf{fma}\left(\frac{y}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z - -15.234687407, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}, b, x\right)\right) \]
   10. Step-by-step derivation

       1. lift-fma.f64 N/A

          \[\leadsto \color{blue}{\left(z \cdot y\right) \cdot \frac{\frac{313060547623}{100000000000}}{z} + \mathsf{fma}\left(\frac{y}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z - \frac{-15234687407}{1000000000}, z, \frac{314690115749}{10000000000}\right), z, \frac{119400905721}{10000000000}\right), z, \frac{607771387771}{1000000000000}\right)}, b, x\right)} \]

       2. *-commutative N/A

          \[\leadsto \color{blue}{\frac{\frac{313060547623}{100000000000}}{z} \cdot \left(z \cdot y\right)} + \mathsf{fma}\left(\frac{y}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z - \frac{-15234687407}{1000000000}, z, \frac{314690115749}{10000000000}\right), z, \frac{119400905721}{10000000000}\right), z, \frac{607771387771}{1000000000000}\right)}, b, x\right) \]

       3. lift-*.f64 N/A

          \[\leadsto \frac{\frac{313060547623}{100000000000}}{z} \cdot \color{blue}{\left(z \cdot y\right)} + \mathsf{fma}\left(\frac{y}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z - \frac{-15234687407}{1000000000}, z, \frac{314690115749}{10000000000}\right), z, \frac{119400905721}{10000000000}\right), z, \frac{607771387771}{1000000000000}\right)}, b, x\right) \]

       4. associate-*r* N/A

          \[\leadsto \color{blue}{\left(\frac{\frac{313060547623}{100000000000}}{z} \cdot z\right) \cdot y} + \mathsf{fma}\left(\frac{y}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z - \frac{-15234687407}{1000000000}, z, \frac{314690115749}{10000000000}\right), z, \frac{119400905721}{10000000000}\right), z, \frac{607771387771}{1000000000000}\right)}, b, x\right) \]

       5. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{\frac{313060547623}{100000000000}}{z} \cdot z, y, \mathsf{fma}\left(\frac{y}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z - \frac{-15234687407}{1000000000}, z, \frac{314690115749}{10000000000}\right), z, \frac{119400905721}{10000000000}\right), z, \frac{607771387771}{1000000000000}\right)}, b, x\right)\right)} \]

   11. Applied rewrites 79.3%

       \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{3.13060547623}{z} \cdot z, y, \mathsf{fma}\left(\frac{y}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z - -15.234687407, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}, b, x\right)\right)} \]

   if -2.8999999999999998e51 < z < 5.20000000000000013e35

   1. Initial program 58.9%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

   2. Taylor expanded in z around 0

      \[\leadsto x + \frac{y \cdot \left(\left(\color{blue}{t} \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]
   3. Step-by-step derivation

   4. Applied rewrites 62.1%

      \[\leadsto x + \frac{y \cdot \left(\left(\color{blue}{t} \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

   6. Applied rewrites 63.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(t, z, a\right), z, b\right), \left(-y\right) \cdot \frac{-1}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z - -15.234687407, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}, x\right)} \]

   if 5.20000000000000013e35 < z

   1. Initial program 58.9%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

   2. Taylor expanded in z around inf

      \[\leadsto x + \color{blue}{\frac{313060547623}{100000000000} \cdot y} \]
   3. Step-by-step derivation

      1. lower-*.f64 62.5

         \[\leadsto x + 3.13060547623 \cdot \color{blue}{y} \]

   4. Applied rewrites 62.5%

      \[\leadsto x + \color{blue}{3.13060547623 \cdot y} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 4: 95.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z - -15.234687407, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}\\ \mathbf{if}\;z \leq -2.9 \cdot 10^{+51}:\\ \;\;\;\;\mathsf{fma}\left(\frac{3.13060547623}{z} \cdot z, y, \mathsf{fma}\left(t\_1, b, x\right)\right)\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+35}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(t, z, a\right), z, b\right), t\_1, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + 3.13060547623 \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (/
          y
          (fma
           (fma (fma (- z -15.234687407) z 31.4690115749) z 11.9400905721)
           z
           0.607771387771))))
   (if (<= z -2.9e+51)
     (fma (* (/ 3.13060547623 z) z) y (fma t_1 b x))
     (if (<= z 5.2e+35)
       (fma (fma (fma t z a) z b) t_1 x)
       (+ x (* 3.13060547623 y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y / fma(fma(fma((z - -15.234687407), z, 31.4690115749), z, 11.9400905721), z, 0.607771387771);
	double tmp;
	if (z <= -2.9e+51) {
		tmp = fma(((3.13060547623 / z) * z), y, fma(t_1, b, x));
	} else if (z <= 5.2e+35) {
		tmp = fma(fma(fma(t, z, a), z, b), t_1, x);
	} else {
		tmp = x + (3.13060547623 * y);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y / fma(fma(fma(Float64(z - -15.234687407), z, 31.4690115749), z, 11.9400905721), z, 0.607771387771))
	tmp = 0.0
	if (z <= -2.9e+51)
		tmp = fma(Float64(Float64(3.13060547623 / z) * z), y, fma(t_1, b, x));
	elseif (z <= 5.2e+35)
		tmp = fma(fma(fma(t, z, a), z, b), t_1, x);
	else
		tmp = Float64(x + Float64(3.13060547623 * y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y / N[(N[(N[(N[(z - -15.234687407), $MachinePrecision] * z + 31.4690115749), $MachinePrecision] * z + 11.9400905721), $MachinePrecision] * z + 0.607771387771), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.9e+51], N[(N[(N[(3.13060547623 / z), $MachinePrecision] * z), $MachinePrecision] * y + N[(t$95$1 * b + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.2e+35], N[(N[(N[(t * z + a), $MachinePrecision] * z + b), $MachinePrecision] * t$95$1 + x), $MachinePrecision], N[(x + N[(3.13060547623 * y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.8999999999999998e51

   1. Initial program 58.9%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

   2. Taylor expanded in z around 0

      \[\leadsto x + \frac{y \cdot \left(\left(\color{blue}{t} \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]
   3. Step-by-step derivation

   4. Applied rewrites 62.1%

      \[\leadsto x + \frac{y \cdot \left(\left(\color{blue}{t} \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

   6. Applied rewrites 70.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z \cdot y, \frac{\mathsf{fma}\left(t, z, a\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z - -15.234687407, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}, \mathsf{fma}\left(\frac{y}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z - -15.234687407, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}, b, x\right)\right)} \]

   7. Taylor expanded in z around inf

      \[\leadsto \mathsf{fma}\left(z \cdot y, \color{blue}{\frac{\frac{313060547623}{100000000000}}{z}}, \mathsf{fma}\left(\frac{y}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z - \frac{-15234687407}{1000000000}, z, \frac{314690115749}{10000000000}\right), z, \frac{119400905721}{10000000000}\right), z, \frac{607771387771}{1000000000000}\right)}, b, x\right)\right) \]
   8. Step-by-step derivation

      1. lower-/.f64 69.8

         \[\leadsto \mathsf{fma}\left(z \cdot y, \frac{3.13060547623}{\color{blue}{z}}, \mathsf{fma}\left(\frac{y}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z - -15.234687407, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}, b, x\right)\right) \]

   9. Applied rewrites 69.8%

      \[\leadsto \mathsf{fma}\left(z \cdot y, \color{blue}{\frac{3.13060547623}{z}}, \mathsf{fma}\left(\frac{y}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z - -15.234687407, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}, b, x\right)\right) \]
   10. Step-by-step derivation

       1. lift-fma.f64 N/A

          \[\leadsto \color{blue}{\left(z \cdot y\right) \cdot \frac{\frac{313060547623}{100000000000}}{z} + \mathsf{fma}\left(\frac{y}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z - \frac{-15234687407}{1000000000}, z, \frac{314690115749}{10000000000}\right), z, \frac{119400905721}{10000000000}\right), z, \frac{607771387771}{1000000000000}\right)}, b, x\right)} \]

       2. *-commutative N/A

          \[\leadsto \color{blue}{\frac{\frac{313060547623}{100000000000}}{z} \cdot \left(z \cdot y\right)} + \mathsf{fma}\left(\frac{y}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z - \frac{-15234687407}{1000000000}, z, \frac{314690115749}{10000000000}\right), z, \frac{119400905721}{10000000000}\right), z, \frac{607771387771}{1000000000000}\right)}, b, x\right) \]

       3. lift-*.f64 N/A

          \[\leadsto \frac{\frac{313060547623}{100000000000}}{z} \cdot \color{blue}{\left(z \cdot y\right)} + \mathsf{fma}\left(\frac{y}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z - \frac{-15234687407}{1000000000}, z, \frac{314690115749}{10000000000}\right), z, \frac{119400905721}{10000000000}\right), z, \frac{607771387771}{1000000000000}\right)}, b, x\right) \]

       4. associate-*r* N/A

          \[\leadsto \color{blue}{\left(\frac{\frac{313060547623}{100000000000}}{z} \cdot z\right) \cdot y} + \mathsf{fma}\left(\frac{y}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z - \frac{-15234687407}{1000000000}, z, \frac{314690115749}{10000000000}\right), z, \frac{119400905721}{10000000000}\right), z, \frac{607771387771}{1000000000000}\right)}, b, x\right) \]

       5. lower-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{\frac{313060547623}{100000000000}}{z} \cdot z, y, \mathsf{fma}\left(\frac{y}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z - \frac{-15234687407}{1000000000}, z, \frac{314690115749}{10000000000}\right), z, \frac{119400905721}{10000000000}\right), z, \frac{607771387771}{1000000000000}\right)}, b, x\right)\right)} \]

   11. Applied rewrites 79.3%

       \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{3.13060547623}{z} \cdot z, y, \mathsf{fma}\left(\frac{y}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z - -15.234687407, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}, b, x\right)\right)} \]

   if -2.8999999999999998e51 < z < 5.20000000000000013e35

   1. Initial program 58.9%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

   2. Taylor expanded in z around 0

      \[\leadsto x + \frac{y \cdot \left(\left(\color{blue}{t} \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]
   3. Step-by-step derivation

   4. Applied rewrites 62.1%

      \[\leadsto x + \frac{y \cdot \left(\left(\color{blue}{t} \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

   6. Applied rewrites 63.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(t, z, a\right), z, b\right), \frac{y}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z - -15.234687407, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}, x\right)} \]

   if 5.20000000000000013e35 < z

   1. Initial program 58.9%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

   2. Taylor expanded in z around inf

      \[\leadsto x + \color{blue}{\frac{313060547623}{100000000000} \cdot y} \]
   3. Step-by-step derivation

      1. lower-*.f64 62.5

         \[\leadsto x + 3.13060547623 \cdot \color{blue}{y} \]

   4. Applied rewrites 62.5%

      \[\leadsto x + \color{blue}{3.13060547623 \cdot y} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 5: 95.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + 3.13060547623 \cdot y\\ \mathbf{if}\;z \leq -1.7 \cdot 10^{+60}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+35}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(t, z, a\right), z, b\right), \frac{y}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z - -15.234687407, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* 3.13060547623 y))))
   (if (<= z -1.7e+60)
     t_1
     (if (<= z 5.2e+35)
       (fma
        (fma (fma t z a) z b)
        (/
         y
         (fma
          (fma (fma (- z -15.234687407) z 31.4690115749) z 11.9400905721)
          z
          0.607771387771))
        x)
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (3.13060547623 * y);
	double tmp;
	if (z <= -1.7e+60) {
		tmp = t_1;
	} else if (z <= 5.2e+35) {
		tmp = fma(fma(fma(t, z, a), z, b), (y / fma(fma(fma((z - -15.234687407), z, 31.4690115749), z, 11.9400905721), z, 0.607771387771)), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(3.13060547623 * y))
	tmp = 0.0
	if (z <= -1.7e+60)
		tmp = t_1;
	elseif (z <= 5.2e+35)
		tmp = fma(fma(fma(t, z, a), z, b), Float64(y / fma(fma(fma(Float64(z - -15.234687407), z, 31.4690115749), z, 11.9400905721), z, 0.607771387771)), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(3.13060547623 * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.7e+60], t$95$1, If[LessEqual[z, 5.2e+35], N[(N[(N[(t * z + a), $MachinePrecision] * z + b), $MachinePrecision] * N[(y / N[(N[(N[(N[(z - -15.234687407), $MachinePrecision] * z + 31.4690115749), $MachinePrecision] * z + 11.9400905721), $MachinePrecision] * z + 0.607771387771), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.7e60 or 5.20000000000000013e35 < z

   1. Initial program 58.9%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

   2. Taylor expanded in z around inf

      \[\leadsto x + \color{blue}{\frac{313060547623}{100000000000} \cdot y} \]
   3. Step-by-step derivation

      1. lower-*.f64 62.5

         \[\leadsto x + 3.13060547623 \cdot \color{blue}{y} \]

   4. Applied rewrites 62.5%

      \[\leadsto x + \color{blue}{3.13060547623 \cdot y} \]

   if -1.7e60 < z < 5.20000000000000013e35

   1. Initial program 58.9%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

   2. Taylor expanded in z around 0

      \[\leadsto x + \frac{y \cdot \left(\left(\color{blue}{t} \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]
   3. Step-by-step derivation

   4. Applied rewrites 62.1%

      \[\leadsto x + \frac{y \cdot \left(\left(\color{blue}{t} \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

   6. Applied rewrites 63.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(t, z, a\right), z, b\right), \frac{y}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z - -15.234687407, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}, x\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 95.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + 3.13060547623 \cdot y\\ \mathbf{if}\;z \leq -1.7 \cdot 10^{+60}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+35}:\\ \;\;\;\;\mathsf{fma}\left(\frac{\mathsf{fma}\left(\mathsf{fma}\left(t, z, a\right), z, b\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z - -15.234687407, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* 3.13060547623 y))))
   (if (<= z -1.7e+60)
     t_1
     (if (<= z 5.2e+35)
       (fma
        (/
         (fma (fma t z a) z b)
         (fma
          (fma (fma (- z -15.234687407) z 31.4690115749) z 11.9400905721)
          z
          0.607771387771))
        y
        x)
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (3.13060547623 * y);
	double tmp;
	if (z <= -1.7e+60) {
		tmp = t_1;
	} else if (z <= 5.2e+35) {
		tmp = fma((fma(fma(t, z, a), z, b) / fma(fma(fma((z - -15.234687407), z, 31.4690115749), z, 11.9400905721), z, 0.607771387771)), y, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(3.13060547623 * y))
	tmp = 0.0
	if (z <= -1.7e+60)
		tmp = t_1;
	elseif (z <= 5.2e+35)
		tmp = fma(Float64(fma(fma(t, z, a), z, b) / fma(fma(fma(Float64(z - -15.234687407), z, 31.4690115749), z, 11.9400905721), z, 0.607771387771)), y, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(3.13060547623 * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.7e+60], t$95$1, If[LessEqual[z, 5.2e+35], N[(N[(N[(N[(t * z + a), $MachinePrecision] * z + b), $MachinePrecision] / N[(N[(N[(N[(z - -15.234687407), $MachinePrecision] * z + 31.4690115749), $MachinePrecision] * z + 11.9400905721), $MachinePrecision] * z + 0.607771387771), $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.7e60 or 5.20000000000000013e35 < z

   1. Initial program 58.9%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

   2. Taylor expanded in z around inf

      \[\leadsto x + \color{blue}{\frac{313060547623}{100000000000} \cdot y} \]
   3. Step-by-step derivation

      1. lower-*.f64 62.5

         \[\leadsto x + 3.13060547623 \cdot \color{blue}{y} \]

   4. Applied rewrites 62.5%

      \[\leadsto x + \color{blue}{3.13060547623 \cdot y} \]

   if -1.7e60 < z < 5.20000000000000013e35

   1. Initial program 58.9%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

   2. Taylor expanded in z around 0

      \[\leadsto x + \frac{y \cdot \left(\left(\color{blue}{t} \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]
   3. Step-by-step derivation

   4. Applied rewrites 62.1%

      \[\leadsto x + \frac{y \cdot \left(\left(\color{blue}{t} \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

   6. Applied rewrites 63.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\mathsf{fma}\left(t, z, a\right), z, b\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z - -15.234687407, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}, y, x\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 93.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + 3.13060547623 \cdot y\\ \mathbf{if}\;z \leq -8.5 \cdot 10^{+58}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+33}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(t, z, a\right), z, b\right), \frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(31.4690115749, z, 11.9400905721\right), z, 0.607771387771\right)} \cdot y, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* 3.13060547623 y))))
   (if (<= z -8.5e+58)
     t_1
     (if (<= z 1.25e+33)
       (fma
        (fma (fma t z a) z b)
        (*
         (/ 1.0 (fma (fma 31.4690115749 z 11.9400905721) z 0.607771387771))
         y)
        x)
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (3.13060547623 * y);
	double tmp;
	if (z <= -8.5e+58) {
		tmp = t_1;
	} else if (z <= 1.25e+33) {
		tmp = fma(fma(fma(t, z, a), z, b), ((1.0 / fma(fma(31.4690115749, z, 11.9400905721), z, 0.607771387771)) * y), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(3.13060547623 * y))
	tmp = 0.0
	if (z <= -8.5e+58)
		tmp = t_1;
	elseif (z <= 1.25e+33)
		tmp = fma(fma(fma(t, z, a), z, b), Float64(Float64(1.0 / fma(fma(31.4690115749, z, 11.9400905721), z, 0.607771387771)) * y), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(3.13060547623 * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.5e+58], t$95$1, If[LessEqual[z, 1.25e+33], N[(N[(N[(t * z + a), $MachinePrecision] * z + b), $MachinePrecision] * N[(N[(1.0 / N[(N[(31.4690115749 * z + 11.9400905721), $MachinePrecision] * z + 0.607771387771), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -8.50000000000000015e58 or 1.24999999999999993e33 < z

   1. Initial program 58.9%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

   2. Taylor expanded in z around inf

      \[\leadsto x + \color{blue}{\frac{313060547623}{100000000000} \cdot y} \]
   3. Step-by-step derivation

      1. lower-*.f64 62.5

         \[\leadsto x + 3.13060547623 \cdot \color{blue}{y} \]

   4. Applied rewrites 62.5%

      \[\leadsto x + \color{blue}{3.13060547623 \cdot y} \]

   if -8.50000000000000015e58 < z < 1.24999999999999993e33

   1. Initial program 58.9%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

   2. Taylor expanded in z around 0

      \[\leadsto x + \frac{y \cdot \left(\left(\color{blue}{t} \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]
   3. Step-by-step derivation

   4. Applied rewrites 62.1%

      \[\leadsto x + \frac{y \cdot \left(\left(\color{blue}{t} \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

   5. Taylor expanded in z around 0

      \[\leadsto x + \frac{y \cdot \left(\left(t \cdot z + a\right) \cdot z + b\right)}{\left(\color{blue}{\frac{314690115749}{10000000000}} \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]
   6. Step-by-step derivation

   7. Applied rewrites 60.0%

      \[\leadsto x + \frac{y \cdot \left(\left(t \cdot z + a\right) \cdot z + b\right)}{\left(\color{blue}{31.4690115749} \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   8. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \frac{y \cdot \left(\left(t \cdot z + a\right) \cdot z + b\right)}{\left(\frac{314690115749}{10000000000} \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}}} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\frac{y \cdot \left(\left(t \cdot z + a\right) \cdot z + b\right)}{\left(\frac{314690115749}{10000000000} \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} + x} \]

      3. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{y \cdot \left(\left(t \cdot z + a\right) \cdot z + b\right)}{\left(\frac{314690115749}{10000000000} \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}}} + x \]

      4. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{y \cdot \left(\left(t \cdot z + a\right) \cdot z + b\right)}}{\left(\frac{314690115749}{10000000000} \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} + x \]

      5. associate-/l* N/A

         \[\leadsto \color{blue}{y \cdot \frac{\left(t \cdot z + a\right) \cdot z + b}{\left(\frac{314690115749}{10000000000} \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}}} + x \]

   9. Applied rewrites 60.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(t, z, a\right), z, b\right), \frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(31.4690115749, z, 11.9400905721\right), z, 0.607771387771\right)} \cdot y, x\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 8: 92.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + 3.13060547623 \cdot y\\ \mathbf{if}\;z \leq -8.5 \cdot 10^{+58}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+33}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(t, z, a\right), z, b\right), \frac{y}{\mathsf{fma}\left(\mathsf{fma}\left(31.4690115749, z, 11.9400905721\right), z, 0.607771387771\right)}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* 3.13060547623 y))))
   (if (<= z -8.5e+58)
     t_1
     (if (<= z 1.25e+33)
       (fma
        (fma (fma t z a) z b)
        (/ y (fma (fma 31.4690115749 z 11.9400905721) z 0.607771387771))
        x)
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (3.13060547623 * y);
	double tmp;
	if (z <= -8.5e+58) {
		tmp = t_1;
	} else if (z <= 1.25e+33) {
		tmp = fma(fma(fma(t, z, a), z, b), (y / fma(fma(31.4690115749, z, 11.9400905721), z, 0.607771387771)), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(3.13060547623 * y))
	tmp = 0.0
	if (z <= -8.5e+58)
		tmp = t_1;
	elseif (z <= 1.25e+33)
		tmp = fma(fma(fma(t, z, a), z, b), Float64(y / fma(fma(31.4690115749, z, 11.9400905721), z, 0.607771387771)), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(3.13060547623 * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.5e+58], t$95$1, If[LessEqual[z, 1.25e+33], N[(N[(N[(t * z + a), $MachinePrecision] * z + b), $MachinePrecision] * N[(y / N[(N[(31.4690115749 * z + 11.9400905721), $MachinePrecision] * z + 0.607771387771), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -8.50000000000000015e58 or 1.24999999999999993e33 < z

   1. Initial program 58.9%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

   2. Taylor expanded in z around inf

      \[\leadsto x + \color{blue}{\frac{313060547623}{100000000000} \cdot y} \]
   3. Step-by-step derivation

      1. lower-*.f64 62.5

         \[\leadsto x + 3.13060547623 \cdot \color{blue}{y} \]

   4. Applied rewrites 62.5%

      \[\leadsto x + \color{blue}{3.13060547623 \cdot y} \]

   if -8.50000000000000015e58 < z < 1.24999999999999993e33

   1. Initial program 58.9%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

   2. Taylor expanded in z around 0

      \[\leadsto x + \frac{y \cdot \left(\left(\color{blue}{t} \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]
   3. Step-by-step derivation

   4. Applied rewrites 62.1%

      \[\leadsto x + \frac{y \cdot \left(\left(\color{blue}{t} \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

   5. Taylor expanded in z around 0

      \[\leadsto x + \frac{y \cdot \left(\left(t \cdot z + a\right) \cdot z + b\right)}{\left(\color{blue}{\frac{314690115749}{10000000000}} \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]
   6. Step-by-step derivation

   7. Applied rewrites 60.0%

      \[\leadsto x + \frac{y \cdot \left(\left(t \cdot z + a\right) \cdot z + b\right)}{\left(\color{blue}{31.4690115749} \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   8. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \frac{y \cdot \left(\left(t \cdot z + a\right) \cdot z + b\right)}{\left(\frac{314690115749}{10000000000} \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}}} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\frac{y \cdot \left(\left(t \cdot z + a\right) \cdot z + b\right)}{\left(\frac{314690115749}{10000000000} \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} + x} \]

      3. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{y \cdot \left(\left(t \cdot z + a\right) \cdot z + b\right)}{\left(\frac{314690115749}{10000000000} \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}}} + x \]

      4. mult-flip N/A

         \[\leadsto \color{blue}{\left(y \cdot \left(\left(t \cdot z + a\right) \cdot z + b\right)\right) \cdot \frac{1}{\left(\frac{314690115749}{10000000000} \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}}} + x \]

      5. lift-*.f64 N/A

         \[\leadsto \color{blue}{\left(y \cdot \left(\left(t \cdot z + a\right) \cdot z + b\right)\right)} \cdot \frac{1}{\left(\frac{314690115749}{10000000000} \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} + x \]

      6. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(\left(t \cdot z + a\right) \cdot z + b\right) \cdot y\right)} \cdot \frac{1}{\left(\frac{314690115749}{10000000000} \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} + x \]

      7. associate-*l* N/A

         \[\leadsto \color{blue}{\left(\left(t \cdot z + a\right) \cdot z + b\right) \cdot \left(y \cdot \frac{1}{\left(\frac{314690115749}{10000000000} \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}}\right)} + x \]

   9. Applied rewrites 60.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(t, z, a\right), z, b\right), \frac{y}{\mathsf{fma}\left(\mathsf{fma}\left(31.4690115749, z, 11.9400905721\right), z, 0.607771387771\right)}, x\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 92.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + 3.13060547623 \cdot y\\ \mathbf{if}\;z \leq -8.5 \cdot 10^{+58}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+33}:\\ \;\;\;\;\mathsf{fma}\left(\frac{\mathsf{fma}\left(\mathsf{fma}\left(t, z, a\right), z, b\right)}{\mathsf{fma}\left(\mathsf{fma}\left(31.4690115749, z, 11.9400905721\right), z, 0.607771387771\right)}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* 3.13060547623 y))))
   (if (<= z -8.5e+58)
     t_1
     (if (<= z 1.25e+33)
       (fma
        (/
         (fma (fma t z a) z b)
         (fma (fma 31.4690115749 z 11.9400905721) z 0.607771387771))
        y
        x)
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (3.13060547623 * y);
	double tmp;
	if (z <= -8.5e+58) {
		tmp = t_1;
	} else if (z <= 1.25e+33) {
		tmp = fma((fma(fma(t, z, a), z, b) / fma(fma(31.4690115749, z, 11.9400905721), z, 0.607771387771)), y, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(3.13060547623 * y))
	tmp = 0.0
	if (z <= -8.5e+58)
		tmp = t_1;
	elseif (z <= 1.25e+33)
		tmp = fma(Float64(fma(fma(t, z, a), z, b) / fma(fma(31.4690115749, z, 11.9400905721), z, 0.607771387771)), y, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(3.13060547623 * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.5e+58], t$95$1, If[LessEqual[z, 1.25e+33], N[(N[(N[(N[(t * z + a), $MachinePrecision] * z + b), $MachinePrecision] / N[(N[(31.4690115749 * z + 11.9400905721), $MachinePrecision] * z + 0.607771387771), $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -8.50000000000000015e58 or 1.24999999999999993e33 < z

   1. Initial program 58.9%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

   2. Taylor expanded in z around inf

      \[\leadsto x + \color{blue}{\frac{313060547623}{100000000000} \cdot y} \]
   3. Step-by-step derivation

      1. lower-*.f64 62.5

         \[\leadsto x + 3.13060547623 \cdot \color{blue}{y} \]

   4. Applied rewrites 62.5%

      \[\leadsto x + \color{blue}{3.13060547623 \cdot y} \]

   if -8.50000000000000015e58 < z < 1.24999999999999993e33

   1. Initial program 58.9%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

   2. Taylor expanded in z around 0

      \[\leadsto x + \frac{y \cdot \left(\left(\color{blue}{t} \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]
   3. Step-by-step derivation

   4. Applied rewrites 62.1%

      \[\leadsto x + \frac{y \cdot \left(\left(\color{blue}{t} \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

   5. Taylor expanded in z around 0

      \[\leadsto x + \frac{y \cdot \left(\left(t \cdot z + a\right) \cdot z + b\right)}{\left(\color{blue}{\frac{314690115749}{10000000000}} \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]
   6. Step-by-step derivation

   7. Applied rewrites 60.0%

      \[\leadsto x + \frac{y \cdot \left(\left(t \cdot z + a\right) \cdot z + b\right)}{\left(\color{blue}{31.4690115749} \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   8. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{x + \frac{y \cdot \left(\left(t \cdot z + a\right) \cdot z + b\right)}{\left(\frac{314690115749}{10000000000} \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}}} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\frac{y \cdot \left(\left(t \cdot z + a\right) \cdot z + b\right)}{\left(\frac{314690115749}{10000000000} \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} + x} \]

      3. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{y \cdot \left(\left(t \cdot z + a\right) \cdot z + b\right)}{\left(\frac{314690115749}{10000000000} \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}}} + x \]

      4. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{y \cdot \left(\left(t \cdot z + a\right) \cdot z + b\right)}}{\left(\frac{314690115749}{10000000000} \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} + x \]

      5. associate-/l* N/A

         \[\leadsto \color{blue}{y \cdot \frac{\left(t \cdot z + a\right) \cdot z + b}{\left(\frac{314690115749}{10000000000} \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}}} + x \]

   9. Applied rewrites 60.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\mathsf{fma}\left(t, z, a\right), z, b\right)}{\mathsf{fma}\left(\mathsf{fma}\left(31.4690115749, z, 11.9400905721\right), z, 0.607771387771\right)}, y, x\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 10: 92.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + 3.13060547623 \cdot y\\ \mathbf{if}\;z \leq -1.3 \cdot 10^{+27}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+18}:\\ \;\;\;\;\mathsf{fma}\left(1.6453555072203998, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(3.13060547623, z, 11.1667541262\right), z, t\right), z, a\right), z, b\right) \cdot y, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* 3.13060547623 y))))
   (if (<= z -1.3e+27)
     t_1
     (if (<= z 1.3e+18)
       (fma
        1.6453555072203998
        (* (fma (fma (fma (fma 3.13060547623 z 11.1667541262) z t) z a) z b) y)
        x)
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (3.13060547623 * y);
	double tmp;
	if (z <= -1.3e+27) {
		tmp = t_1;
	} else if (z <= 1.3e+18) {
		tmp = fma(1.6453555072203998, (fma(fma(fma(fma(3.13060547623, z, 11.1667541262), z, t), z, a), z, b) * y), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(3.13060547623 * y))
	tmp = 0.0
	if (z <= -1.3e+27)
		tmp = t_1;
	elseif (z <= 1.3e+18)
		tmp = fma(1.6453555072203998, Float64(fma(fma(fma(fma(3.13060547623, z, 11.1667541262), z, t), z, a), z, b) * y), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(3.13060547623 * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.3e+27], t$95$1, If[LessEqual[z, 1.3e+18], N[(1.6453555072203998 * N[(N[(N[(N[(N[(3.13060547623 * z + 11.1667541262), $MachinePrecision] * z + t), $MachinePrecision] * z + a), $MachinePrecision] * z + b), $MachinePrecision] * y), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.30000000000000004e27 or 1.3e18 < z

   1. Initial program 58.9%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

   2. Taylor expanded in z around inf

      \[\leadsto x + \color{blue}{\frac{313060547623}{100000000000} \cdot y} \]
   3. Step-by-step derivation

      1. lower-*.f64 62.5

         \[\leadsto x + 3.13060547623 \cdot \color{blue}{y} \]

   4. Applied rewrites 62.5%

      \[\leadsto x + \color{blue}{3.13060547623 \cdot y} \]

   if -1.30000000000000004e27 < z < 1.3e18

   1. Initial program 58.9%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

   3. Applied rewrites 59.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z - -15.234687407, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(3.13060547623, z, 11.1667541262\right), z, t\right), z, a\right), z, b\right) \cdot y, x\right)} \]

   4. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{1000000000000}{607771387771}}, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{313060547623}{100000000000}, z, \frac{55833770631}{5000000000}\right), z, t\right), z, a\right), z, b\right) \cdot y, x\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 55.5%

      \[\leadsto \mathsf{fma}\left(\color{blue}{1.6453555072203998}, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(3.13060547623, z, 11.1667541262\right), z, t\right), z, a\right), z, b\right) \cdot y, x\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 11: 92.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + 3.13060547623 \cdot y\\ \mathbf{if}\;z \leq -8.5 \cdot 10^{+58}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+18}:\\ \;\;\;\;x + \frac{y \cdot \left(\left(t \cdot z + a\right) \cdot z + b\right)}{0.607771387771}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* 3.13060547623 y))))
   (if (<= z -8.5e+58)
     t_1
     (if (<= z 1.3e+18)
       (+ x (/ (* y (+ (* (+ (* t z) a) z) b)) 0.607771387771))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (3.13060547623 * y);
	double tmp;
	if (z <= -8.5e+58) {
		tmp = t_1;
	} else if (z <= 1.3e+18) {
		tmp = x + ((y * ((((t * z) + a) * z) + b)) / 0.607771387771);
	} 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)
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) :: t_1
    real(8) :: tmp
    t_1 = x + (3.13060547623d0 * y)
    if (z <= (-8.5d+58)) then
        tmp = t_1
    else if (z <= 1.3d+18) then
        tmp = x + ((y * ((((t * z) + a) * z) + b)) / 0.607771387771d0)
    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 t_1 = x + (3.13060547623 * y);
	double tmp;
	if (z <= -8.5e+58) {
		tmp = t_1;
	} else if (z <= 1.3e+18) {
		tmp = x + ((y * ((((t * z) + a) * z) + b)) / 0.607771387771);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (3.13060547623 * y)
	tmp = 0
	if z <= -8.5e+58:
		tmp = t_1
	elif z <= 1.3e+18:
		tmp = x + ((y * ((((t * z) + a) * z) + b)) / 0.607771387771)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(3.13060547623 * y))
	tmp = 0.0
	if (z <= -8.5e+58)
		tmp = t_1;
	elseif (z <= 1.3e+18)
		tmp = Float64(x + Float64(Float64(y * Float64(Float64(Float64(Float64(t * z) + a) * z) + b)) / 0.607771387771));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (3.13060547623 * y);
	tmp = 0.0;
	if (z <= -8.5e+58)
		tmp = t_1;
	elseif (z <= 1.3e+18)
		tmp = x + ((y * ((((t * z) + a) * z) + b)) / 0.607771387771);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(3.13060547623 * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.5e+58], t$95$1, If[LessEqual[z, 1.3e+18], N[(x + N[(N[(y * N[(N[(N[(N[(t * z), $MachinePrecision] + a), $MachinePrecision] * z), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / 0.607771387771), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -8.50000000000000015e58 or 1.3e18 < z

   1. Initial program 58.9%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

   2. Taylor expanded in z around inf

      \[\leadsto x + \color{blue}{\frac{313060547623}{100000000000} \cdot y} \]
   3. Step-by-step derivation

      1. lower-*.f64 62.5

         \[\leadsto x + 3.13060547623 \cdot \color{blue}{y} \]

   4. Applied rewrites 62.5%

      \[\leadsto x + \color{blue}{3.13060547623 \cdot y} \]

   if -8.50000000000000015e58 < z < 1.3e18

   1. Initial program 58.9%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

   2. Taylor expanded in z around 0

      \[\leadsto x + \frac{y \cdot \left(\left(\color{blue}{t} \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]
   3. Step-by-step derivation

   4. Applied rewrites 62.1%

      \[\leadsto x + \frac{y \cdot \left(\left(\color{blue}{t} \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

   5. Taylor expanded in z around 0

      \[\leadsto x + \frac{y \cdot \left(\left(t \cdot z + a\right) \cdot z + b\right)}{\color{blue}{\frac{607771387771}{1000000000000}}} \]
   6. Step-by-step derivation

   7. Applied rewrites 57.8%

      \[\leadsto x + \frac{y \cdot \left(\left(t \cdot z + a\right) \cdot z + b\right)}{\color{blue}{0.607771387771}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 12: 89.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + 3.13060547623 \cdot y\\ \mathbf{if}\;z \leq -4500000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+22}:\\ \;\;\;\;\mathsf{fma}\left(z \cdot y, \frac{a}{0.607771387771}, \mathsf{fma}\left(\frac{y}{0.607771387771}, b, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* 3.13060547623 y))))
   (if (<= z -4500000000000.0)
     t_1
     (if (<= z 2.05e+22)
       (fma (* z y) (/ a 0.607771387771) (fma (/ y 0.607771387771) b x))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (3.13060547623 * y);
	double tmp;
	if (z <= -4500000000000.0) {
		tmp = t_1;
	} else if (z <= 2.05e+22) {
		tmp = fma((z * y), (a / 0.607771387771), fma((y / 0.607771387771), b, x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(3.13060547623 * y))
	tmp = 0.0
	if (z <= -4500000000000.0)
		tmp = t_1;
	elseif (z <= 2.05e+22)
		tmp = fma(Float64(z * y), Float64(a / 0.607771387771), fma(Float64(y / 0.607771387771), b, x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(3.13060547623 * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4500000000000.0], t$95$1, If[LessEqual[z, 2.05e+22], N[(N[(z * y), $MachinePrecision] * N[(a / 0.607771387771), $MachinePrecision] + N[(N[(y / 0.607771387771), $MachinePrecision] * b + x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.5e12 or 2.0499999999999999e22 < z

   1. Initial program 58.9%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

   2. Taylor expanded in z around inf

      \[\leadsto x + \color{blue}{\frac{313060547623}{100000000000} \cdot y} \]
   3. Step-by-step derivation

      1. lower-*.f64 62.5

         \[\leadsto x + 3.13060547623 \cdot \color{blue}{y} \]

   4. Applied rewrites 62.5%

      \[\leadsto x + \color{blue}{3.13060547623 \cdot y} \]

   if -4.5e12 < z < 2.0499999999999999e22

   1. Initial program 58.9%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

   2. Taylor expanded in z around 0

      \[\leadsto x + \frac{y \cdot \left(\left(\color{blue}{t} \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]
   3. Step-by-step derivation

   4. Applied rewrites 62.1%

      \[\leadsto x + \frac{y \cdot \left(\left(\color{blue}{t} \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

   6. Applied rewrites 70.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z \cdot y, \frac{\mathsf{fma}\left(t, z, a\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z - -15.234687407, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}, \mathsf{fma}\left(\frac{y}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z - -15.234687407, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}, b, x\right)\right)} \]

   7. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(z \cdot y, \frac{\mathsf{fma}\left(t, z, a\right)}{\color{blue}{\frac{607771387771}{1000000000000}}}, \mathsf{fma}\left(\frac{y}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z - \frac{-15234687407}{1000000000}, z, \frac{314690115749}{10000000000}\right), z, \frac{119400905721}{10000000000}\right), z, \frac{607771387771}{1000000000000}\right)}, b, x\right)\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 59.2%

      \[\leadsto \mathsf{fma}\left(z \cdot y, \frac{\mathsf{fma}\left(t, z, a\right)}{\color{blue}{0.607771387771}}, \mathsf{fma}\left(\frac{y}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z - -15.234687407, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}, b, x\right)\right) \]

   10. Taylor expanded in z around 0

       \[\leadsto \mathsf{fma}\left(z \cdot y, \frac{\mathsf{fma}\left(t, z, a\right)}{\frac{607771387771}{1000000000000}}, \mathsf{fma}\left(\frac{y}{\color{blue}{\frac{607771387771}{1000000000000}}}, b, x\right)\right) \]
   11. Step-by-step derivation

   12. Applied rewrites 57.9%

       \[\leadsto \mathsf{fma}\left(z \cdot y, \frac{\mathsf{fma}\left(t, z, a\right)}{0.607771387771}, \mathsf{fma}\left(\frac{y}{\color{blue}{0.607771387771}}, b, x\right)\right) \]

   13. Taylor expanded in z around 0

       \[\leadsto \mathsf{fma}\left(z \cdot y, \frac{\color{blue}{a}}{\frac{607771387771}{1000000000000}}, \mathsf{fma}\left(\frac{y}{\frac{607771387771}{1000000000000}}, b, x\right)\right) \]
   14. Step-by-step derivation

   15. Applied rewrites 60.2%

       \[\leadsto \mathsf{fma}\left(z \cdot y, \frac{\color{blue}{a}}{0.607771387771}, \mathsf{fma}\left(\frac{y}{0.607771387771}, b, x\right)\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 13: 83.0% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + 3.13060547623 \cdot y\\ \mathbf{if}\;z \leq -1.7 \cdot 10^{+27}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 750000:\\ \;\;\;\;x + \frac{y \cdot b}{11.9400905721 \cdot z + 0.607771387771}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* 3.13060547623 y))))
   (if (<= z -1.7e+27)
     t_1
     (if (<= z 750000.0)
       (+ x (/ (* y b) (+ (* 11.9400905721 z) 0.607771387771)))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (3.13060547623 * y);
	double tmp;
	if (z <= -1.7e+27) {
		tmp = t_1;
	} else if (z <= 750000.0) {
		tmp = x + ((y * b) / ((11.9400905721 * z) + 0.607771387771));
	} 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)
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) :: t_1
    real(8) :: tmp
    t_1 = x + (3.13060547623d0 * y)
    if (z <= (-1.7d+27)) then
        tmp = t_1
    else if (z <= 750000.0d0) then
        tmp = x + ((y * b) / ((11.9400905721d0 * z) + 0.607771387771d0))
    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 t_1 = x + (3.13060547623 * y);
	double tmp;
	if (z <= -1.7e+27) {
		tmp = t_1;
	} else if (z <= 750000.0) {
		tmp = x + ((y * b) / ((11.9400905721 * z) + 0.607771387771));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (3.13060547623 * y)
	tmp = 0
	if z <= -1.7e+27:
		tmp = t_1
	elif z <= 750000.0:
		tmp = x + ((y * b) / ((11.9400905721 * z) + 0.607771387771))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(3.13060547623 * y))
	tmp = 0.0
	if (z <= -1.7e+27)
		tmp = t_1;
	elseif (z <= 750000.0)
		tmp = Float64(x + Float64(Float64(y * b) / Float64(Float64(11.9400905721 * z) + 0.607771387771)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (3.13060547623 * y);
	tmp = 0.0;
	if (z <= -1.7e+27)
		tmp = t_1;
	elseif (z <= 750000.0)
		tmp = x + ((y * b) / ((11.9400905721 * z) + 0.607771387771));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(3.13060547623 * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.7e+27], t$95$1, If[LessEqual[z, 750000.0], N[(x + N[(N[(y * b), $MachinePrecision] / N[(N[(11.9400905721 * z), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.7e27 or 7.5e5 < z

   1. Initial program 58.9%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

   2. Taylor expanded in z around inf

      \[\leadsto x + \color{blue}{\frac{313060547623}{100000000000} \cdot y} \]
   3. Step-by-step derivation

      1. lower-*.f64 62.5

         \[\leadsto x + 3.13060547623 \cdot \color{blue}{y} \]

   4. Applied rewrites 62.5%

      \[\leadsto x + \color{blue}{3.13060547623 \cdot y} \]

   if -1.7e27 < z < 7.5e5

   1. Initial program 58.9%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

   2. Taylor expanded in z around 0

      \[\leadsto x + \frac{y \cdot \color{blue}{b}}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]
   3. Step-by-step derivation

   4. Applied rewrites 64.5%

      \[\leadsto x + \frac{y \cdot \color{blue}{b}}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

   5. Taylor expanded in z around 0

      \[\leadsto x + \frac{y \cdot b}{\color{blue}{\frac{119400905721}{10000000000}} \cdot z + \frac{607771387771}{1000000000000}} \]
   6. Step-by-step derivation

   7. Applied rewrites 63.0%

      \[\leadsto x + \frac{y \cdot b}{\color{blue}{11.9400905721} \cdot z + 0.607771387771} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 14: 83.0% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + 3.13060547623 \cdot y\\ \mathbf{if}\;z \leq -750000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 750000:\\ \;\;\;\;x + \left(1.6453555072203998 \cdot b\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* 3.13060547623 y))))
   (if (<= z -750000000000.0)
     t_1
     (if (<= z 750000.0) (+ x (* (* 1.6453555072203998 b) y)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (3.13060547623 * y);
	double tmp;
	if (z <= -750000000000.0) {
		tmp = t_1;
	} else if (z <= 750000.0) {
		tmp = x + ((1.6453555072203998 * b) * y);
	} 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)
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) :: t_1
    real(8) :: tmp
    t_1 = x + (3.13060547623d0 * y)
    if (z <= (-750000000000.0d0)) then
        tmp = t_1
    else if (z <= 750000.0d0) then
        tmp = x + ((1.6453555072203998d0 * b) * y)
    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 t_1 = x + (3.13060547623 * y);
	double tmp;
	if (z <= -750000000000.0) {
		tmp = t_1;
	} else if (z <= 750000.0) {
		tmp = x + ((1.6453555072203998 * b) * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (3.13060547623 * y)
	tmp = 0
	if z <= -750000000000.0:
		tmp = t_1
	elif z <= 750000.0:
		tmp = x + ((1.6453555072203998 * b) * y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(3.13060547623 * y))
	tmp = 0.0
	if (z <= -750000000000.0)
		tmp = t_1;
	elseif (z <= 750000.0)
		tmp = Float64(x + Float64(Float64(1.6453555072203998 * b) * y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (3.13060547623 * y);
	tmp = 0.0;
	if (z <= -750000000000.0)
		tmp = t_1;
	elseif (z <= 750000.0)
		tmp = x + ((1.6453555072203998 * b) * y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(3.13060547623 * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -750000000000.0], t$95$1, If[LessEqual[z, 750000.0], N[(x + N[(N[(1.6453555072203998 * b), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -7.5e11 or 7.5e5 < z

   1. Initial program 58.9%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

   2. Taylor expanded in z around inf

      \[\leadsto x + \color{blue}{\frac{313060547623}{100000000000} \cdot y} \]
   3. Step-by-step derivation

      1. lower-*.f64 62.5

         \[\leadsto x + 3.13060547623 \cdot \color{blue}{y} \]

   4. Applied rewrites 62.5%

      \[\leadsto x + \color{blue}{3.13060547623 \cdot y} \]

   if -7.5e11 < z < 7.5e5

   1. Initial program 58.9%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

   2. Taylor expanded in z around 0

      \[\leadsto x + \color{blue}{\frac{1000000000000}{607771387771} \cdot \left(b \cdot y\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto x + \frac{1000000000000}{607771387771} \cdot \color{blue}{\left(b \cdot y\right)} \]

      2. lower-*.f64 60.2

         \[\leadsto x + 1.6453555072203998 \cdot \left(b \cdot \color{blue}{y}\right) \]

   4. Applied rewrites 60.2%

      \[\leadsto x + \color{blue}{1.6453555072203998 \cdot \left(b \cdot y\right)} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto x + \frac{1000000000000}{607771387771} \cdot \color{blue}{\left(b \cdot y\right)} \]

      2. lift-*.f64 N/A

         \[\leadsto x + \frac{1000000000000}{607771387771} \cdot \left(b \cdot \color{blue}{y}\right) \]

      3. associate-*r* N/A

         \[\leadsto x + \left(\frac{1000000000000}{607771387771} \cdot b\right) \cdot \color{blue}{y} \]

      4. lower-*.f64 N/A

         \[\leadsto x + \left(\frac{1000000000000}{607771387771} \cdot b\right) \cdot \color{blue}{y} \]

      5. lower-*.f64 60.2

         \[\leadsto x + \left(1.6453555072203998 \cdot b\right) \cdot y \]

   6. Applied rewrites 60.2%

      \[\leadsto x + \left(1.6453555072203998 \cdot b\right) \cdot \color{blue}{y} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 15: 83.0% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + 3.13060547623 \cdot y\\ \mathbf{if}\;z \leq -750000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 750000:\\ \;\;\;\;x + 1.6453555072203998 \cdot \left(b \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* 3.13060547623 y))))
   (if (<= z -750000000000.0)
     t_1
     (if (<= z 750000.0) (+ x (* 1.6453555072203998 (* b y))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (3.13060547623 * y);
	double tmp;
	if (z <= -750000000000.0) {
		tmp = t_1;
	} else if (z <= 750000.0) {
		tmp = x + (1.6453555072203998 * (b * y));
	} 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)
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) :: t_1
    real(8) :: tmp
    t_1 = x + (3.13060547623d0 * y)
    if (z <= (-750000000000.0d0)) then
        tmp = t_1
    else if (z <= 750000.0d0) then
        tmp = x + (1.6453555072203998d0 * (b * y))
    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 t_1 = x + (3.13060547623 * y);
	double tmp;
	if (z <= -750000000000.0) {
		tmp = t_1;
	} else if (z <= 750000.0) {
		tmp = x + (1.6453555072203998 * (b * y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (3.13060547623 * y)
	tmp = 0
	if z <= -750000000000.0:
		tmp = t_1
	elif z <= 750000.0:
		tmp = x + (1.6453555072203998 * (b * y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(3.13060547623 * y))
	tmp = 0.0
	if (z <= -750000000000.0)
		tmp = t_1;
	elseif (z <= 750000.0)
		tmp = Float64(x + Float64(1.6453555072203998 * Float64(b * y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (3.13060547623 * y);
	tmp = 0.0;
	if (z <= -750000000000.0)
		tmp = t_1;
	elseif (z <= 750000.0)
		tmp = x + (1.6453555072203998 * (b * y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(3.13060547623 * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -750000000000.0], t$95$1, If[LessEqual[z, 750000.0], N[(x + N[(1.6453555072203998 * N[(b * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -7.5e11 or 7.5e5 < z

   1. Initial program 58.9%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

   2. Taylor expanded in z around inf

      \[\leadsto x + \color{blue}{\frac{313060547623}{100000000000} \cdot y} \]
   3. Step-by-step derivation

      1. lower-*.f64 62.5

         \[\leadsto x + 3.13060547623 \cdot \color{blue}{y} \]

   4. Applied rewrites 62.5%

      \[\leadsto x + \color{blue}{3.13060547623 \cdot y} \]

   if -7.5e11 < z < 7.5e5

   1. Initial program 58.9%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

   2. Taylor expanded in z around 0

      \[\leadsto x + \color{blue}{\frac{1000000000000}{607771387771} \cdot \left(b \cdot y\right)} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto x + \frac{1000000000000}{607771387771} \cdot \color{blue}{\left(b \cdot y\right)} \]

      2. lower-*.f64 60.2

         \[\leadsto x + 1.6453555072203998 \cdot \left(b \cdot \color{blue}{y}\right) \]

   4. Applied rewrites 60.2%

      \[\leadsto x + \color{blue}{1.6453555072203998 \cdot \left(b \cdot y\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 16: 62.5% accurate, 7.9× speedup

Math

\[\begin{array}{l} \\ x + 3.13060547623 \cdot y \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (+ x (* 3.13060547623 y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return x + (3.13060547623 * 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)
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
    code = x + (3.13060547623d0 * y)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x + (3.13060547623 * y);
}

Python

def code(x, y, z, t, a, b):
	return x + (3.13060547623 * y)

Julia

function code(x, y, z, t, a, b)
	return Float64(x + Float64(3.13060547623 * y))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x + (3.13060547623 * y);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x + N[(3.13060547623 * y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 58.9%

   \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

2. Taylor expanded in z around inf

   \[\leadsto x + \color{blue}{\frac{313060547623}{100000000000} \cdot y} \]
3. Step-by-step derivation

   1. lower-*.f64 62.5

      \[\leadsto x + 3.13060547623 \cdot \color{blue}{y} \]

4. Applied rewrites 62.5%

   \[\leadsto x + \color{blue}{3.13060547623 \cdot y} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2025156 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, D"
  :precision binary64
  (+ x (/ (* y (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b)) (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))))