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

Percentage Accurate: 59.7% → 97.4%

Time: 8.3s

Alternatives: 20

Speedup: 1.8×

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: 59.7% 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, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z \cdot z}\\ t_2 := \left(\mathsf{fma}\left(3.13060547623, y, x\right) + \mathsf{fma}\left(\frac{y}{z}, 11.1667541262, t \cdot t\_1\right)\right) - \mathsf{fma}\left(\frac{y \cdot -36.52704169880642}{z \cdot z}, 15.234687407, \mathsf{fma}\left(t\_1, 98.5170599679272, 47.69379582500642 \cdot \frac{y}{z}\right)\right)\\ \mathbf{if}\;z \leq -2.4 \cdot 10^{+28}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+48}:\\ \;\;\;\;x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ y (* z z)))
        (t_2
         (-
          (+ (fma 3.13060547623 y x) (fma (/ y z) 11.1667541262 (* t t_1)))
          (fma
           (/ (* y -36.52704169880642) (* z z))
           15.234687407
           (fma t_1 98.5170599679272 (* 47.69379582500642 (/ y z)))))))
   (if (<= z -2.4e+28)
     t_2
     (if (<= z 2.5e+48)
       (+
        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)))
       t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y / (z * z);
	double t_2 = (fma(3.13060547623, y, x) + fma((y / z), 11.1667541262, (t * t_1))) - fma(((y * -36.52704169880642) / (z * z)), 15.234687407, fma(t_1, 98.5170599679272, (47.69379582500642 * (y / z))));
	double tmp;
	if (z <= -2.4e+28) {
		tmp = t_2;
	} else if (z <= 2.5e+48) {
		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));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y / Float64(z * z))
	t_2 = Float64(Float64(fma(3.13060547623, y, x) + fma(Float64(y / z), 11.1667541262, Float64(t * t_1))) - fma(Float64(Float64(y * -36.52704169880642) / Float64(z * z)), 15.234687407, fma(t_1, 98.5170599679272, Float64(47.69379582500642 * Float64(y / z)))))
	tmp = 0.0
	if (z <= -2.4e+28)
		tmp = t_2;
	elseif (z <= 2.5e+48)
		tmp = 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)));
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y / N[(z * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(3.13060547623 * y + x), $MachinePrecision] + N[(N[(y / z), $MachinePrecision] * 11.1667541262 + N[(t * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(y * -36.52704169880642), $MachinePrecision] / N[(z * z), $MachinePrecision]), $MachinePrecision] * 15.234687407 + N[(t$95$1 * 98.5170599679272 + N[(47.69379582500642 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.4e+28], t$95$2, If[LessEqual[z, 2.5e+48], 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], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.39999999999999981e28 or 2.49999999999999987e48 < z

   1. Initial program 8.1%

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

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\left(x + \left(\frac{313060547623}{100000000000} \cdot y + \left(\frac{55833770631}{5000000000} \cdot \frac{y}{z} + \frac{t \cdot y}{{z}^{2}}\right)\right)\right) - \left(\frac{15234687407}{1000000000} \cdot \frac{\frac{55833770631}{5000000000} \cdot y - \frac{4769379582500641883561}{100000000000000000000} \cdot y}{{z}^{2}} + \left(\frac{4769379582500641883561}{100000000000000000000} \cdot \frac{y}{z} + \frac{98517059967927196814627}{1000000000000000000000} \cdot \frac{y}{{z}^{2}}\right)\right)} \]
   3. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \left(x + \left(\frac{313060547623}{100000000000} \cdot y + \left(\frac{55833770631}{5000000000} \cdot \frac{y}{z} + \frac{t \cdot y}{{z}^{2}}\right)\right)\right) - \color{blue}{\left(\frac{15234687407}{1000000000} \cdot \frac{\frac{55833770631}{5000000000} \cdot y - \frac{4769379582500641883561}{100000000000000000000} \cdot y}{{z}^{2}} + \left(\frac{4769379582500641883561}{100000000000000000000} \cdot \frac{y}{z} + \frac{98517059967927196814627}{1000000000000000000000} \cdot \frac{y}{{z}^{2}}\right)\right)} \]

   4. Applied rewrites 96.7%

      \[\leadsto \color{blue}{\left(\mathsf{fma}\left(3.13060547623, y, x\right) + \mathsf{fma}\left(\frac{y}{z}, 11.1667541262, t \cdot \frac{y}{z \cdot z}\right)\right) - \mathsf{fma}\left(\frac{y \cdot -36.52704169880642}{z \cdot z}, 15.234687407, \mathsf{fma}\left(\frac{y}{z \cdot z}, 98.5170599679272, 47.69379582500642 \cdot \frac{y}{z}\right)\right)} \]

   if -2.39999999999999981e28 < z < 2.49999999999999987e48

   1. Initial program 97.9%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 96.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{+29}:\\ \;\;\;\;\mathsf{fma}\left(y, \left(-\frac{\left(-\frac{\left(-\frac{\left(-a\right) + 5864.8025282699045}{z}\right) + 457.9610022158428}{z}\right) + 36.52704169880642}{z}\right) + 3.13060547623, x\right)\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+48}:\\ \;\;\;\;x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -6.4e+29)
   (fma
    y
    (+
     (-
      (/
       (+
        (- (/ (+ (- (/ (+ (- a) 5864.8025282699045) z)) 457.9610022158428) z))
        36.52704169880642)
       z))
     3.13060547623)
    x)
   (if (<= z 4e+48)
     (+
      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)))
     (fma 3.13060547623 y x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -6.4e+29) {
		tmp = fma(y, (-((-((-((-a + 5864.8025282699045) / z) + 457.9610022158428) / z) + 36.52704169880642) / z) + 3.13060547623), x);
	} else if (z <= 4e+48) {
		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));
	} else {
		tmp = fma(3.13060547623, y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -6.4e+29)
		tmp = fma(y, Float64(Float64(-Float64(Float64(Float64(-Float64(Float64(Float64(-Float64(Float64(Float64(-a) + 5864.8025282699045) / z)) + 457.9610022158428) / z)) + 36.52704169880642) / z)) + 3.13060547623), x);
	elseif (z <= 4e+48)
		tmp = 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)));
	else
		tmp = fma(3.13060547623, y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -6.4e+29], N[(y * N[((-N[(N[((-N[(N[((-N[(N[((-a) + 5864.8025282699045), $MachinePrecision] / z), $MachinePrecision]) + 457.9610022158428), $MachinePrecision] / z), $MachinePrecision]) + 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]) + 3.13060547623), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[z, 4e+48], 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], N[(3.13060547623 * y + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.39999999999999973e29

   1. Initial program 10.7%

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

   2. Taylor expanded in t around 0

      \[\leadsto \color{blue}{x + \frac{y \cdot \left(b + z \cdot \left(a + {z}^{2} \cdot \left(\frac{55833770631}{5000000000} + \frac{313060547623}{100000000000} \cdot z\right)\right)\right)}{\frac{607771387771}{1000000000000} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)}} \]

   4. Applied rewrites 14.0%

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

   5. Taylor expanded in z around -inf

      \[\leadsto \mathsf{fma}\left(y, \frac{313060547623}{100000000000} + \color{blue}{-1 \cdot \frac{\frac{3652704169880641883561}{100000000000000000000} + -1 \cdot \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + -1 \cdot \frac{\frac{586480252826990429730394679450703430294089}{100000000000000000000000000000000000000} + -1 \cdot a}{z}}{z}}{z}}, x\right) \]
   6. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(y, -1 \cdot \frac{\frac{3652704169880641883561}{100000000000000000000} + -1 \cdot \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + -1 \cdot \frac{\frac{586480252826990429730394679450703430294089}{100000000000000000000000000000000000000} + -1 \cdot a}{z}}{z}}{z} + \frac{313060547623}{100000000000}, x\right) \]

      2. lower-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, -1 \cdot \frac{\frac{3652704169880641883561}{100000000000000000000} + -1 \cdot \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + -1 \cdot \frac{\frac{586480252826990429730394679450703430294089}{100000000000000000000000000000000000000} + -1 \cdot a}{z}}{z}}{z} + \frac{313060547623}{100000000000}, x\right) \]

   7. Applied rewrites 93.1%

      \[\leadsto \mathsf{fma}\left(y, \left(-\frac{\left(-\frac{\left(-\frac{\left(-a\right) + 5864.8025282699045}{z}\right) + 457.9610022158428}{z}\right) + 36.52704169880642}{z}\right) + \color{blue}{3.13060547623}, x\right) \]

   if -6.39999999999999973e29 < z < 4.00000000000000018e48

   1. Initial program 98.0%

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

   if 4.00000000000000018e48 < z

   1. Initial program 4.8%

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

   2. Taylor expanded in z around inf

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

      1. +-commutative N/A

         \[\leadsto \frac{313060547623}{100000000000} \cdot y + \color{blue}{x} \]

      2. lower-fma.f64 94.8

         \[\leadsto \mathsf{fma}\left(3.13060547623, \color{blue}{y}, x\right) \]

   4. Applied rewrites 94.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(3.13060547623, y, x\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 3: 94.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y, \left(-\frac{\left(-\frac{\left(-\frac{\left(-a\right) + 5864.8025282699045}{z}\right) + 457.9610022158428}{z}\right) + 36.52704169880642}{z}\right) + 3.13060547623, x\right)\\ \mathbf{if}\;z \leq -210000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.18 \cdot 10^{+20}:\\ \;\;\;\;x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\mathsf{fma}\left(\mathsf{fma}\left(31.4690115749, z, 11.9400905721\right), z, 0.607771387771\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (fma
          y
          (+
           (-
            (/
             (+
              (-
               (/
                (+ (- (/ (+ (- a) 5864.8025282699045) z)) 457.9610022158428)
                z))
              36.52704169880642)
             z))
           3.13060547623)
          x)))
   (if (<= z -210000.0)
     t_1
     (if (<= z 1.18e+20)
       (+
        x
        (/
         (*
          y
          (+
           (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z)
           b))
         (fma (fma 31.4690115749 z 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 = fma(y, (-((-((-((-a + 5864.8025282699045) / z) + 457.9610022158428) / z) + 36.52704169880642) / z) + 3.13060547623), x);
	double tmp;
	if (z <= -210000.0) {
		tmp = t_1;
	} else if (z <= 1.18e+20) {
		tmp = x + ((y * ((((((((z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b)) / fma(fma(31.4690115749, z, 11.9400905721), z, 0.607771387771));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(y, Float64(Float64(-Float64(Float64(Float64(-Float64(Float64(Float64(-Float64(Float64(Float64(-a) + 5864.8025282699045) / z)) + 457.9610022158428) / z)) + 36.52704169880642) / z)) + 3.13060547623), x)
	tmp = 0.0
	if (z <= -210000.0)
		tmp = t_1;
	elseif (z <= 1.18e+20)
		tmp = Float64(x + Float64(Float64(y * Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b)) / fma(fma(31.4690115749, z, 11.9400905721), z, 0.607771387771)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[((-N[(N[((-N[(N[((-N[(N[((-a) + 5864.8025282699045), $MachinePrecision] / z), $MachinePrecision]) + 457.9610022158428), $MachinePrecision] / z), $MachinePrecision]) + 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]) + 3.13060547623), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[z, -210000.0], t$95$1, If[LessEqual[z, 1.18e+20], 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[(31.4690115749 * z + 11.9400905721), $MachinePrecision] * z + 0.607771387771), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.1e5 or 1.18e20 < z

   1. Initial program 14.0%

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

   2. Taylor expanded in t around 0

      \[\leadsto \color{blue}{x + \frac{y \cdot \left(b + z \cdot \left(a + {z}^{2} \cdot \left(\frac{55833770631}{5000000000} + \frac{313060547623}{100000000000} \cdot z\right)\right)\right)}{\frac{607771387771}{1000000000000} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)}} \]

   4. Applied rewrites 16.6%

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

   5. Taylor expanded in z around -inf

      \[\leadsto \mathsf{fma}\left(y, \frac{313060547623}{100000000000} + \color{blue}{-1 \cdot \frac{\frac{3652704169880641883561}{100000000000000000000} + -1 \cdot \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + -1 \cdot \frac{\frac{586480252826990429730394679450703430294089}{100000000000000000000000000000000000000} + -1 \cdot a}{z}}{z}}{z}}, x\right) \]
   6. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(y, -1 \cdot \frac{\frac{3652704169880641883561}{100000000000000000000} + -1 \cdot \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + -1 \cdot \frac{\frac{586480252826990429730394679450703430294089}{100000000000000000000000000000000000000} + -1 \cdot a}{z}}{z}}{z} + \frac{313060547623}{100000000000}, x\right) \]

      2. lower-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, -1 \cdot \frac{\frac{3652704169880641883561}{100000000000000000000} + -1 \cdot \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + -1 \cdot \frac{\frac{586480252826990429730394679450703430294089}{100000000000000000000000000000000000000} + -1 \cdot a}{z}}{z}}{z} + \frac{313060547623}{100000000000}, x\right) \]

   7. Applied rewrites 91.7%

      \[\leadsto \mathsf{fma}\left(y, \left(-\frac{\left(-\frac{\left(-\frac{\left(-a\right) + 5864.8025282699045}{z}\right) + 457.9610022158428}{z}\right) + 36.52704169880642}{z}\right) + \color{blue}{3.13060547623}, x\right) \]

   if -2.1e5 < z < 1.18e20

   1. Initial program 99.4%

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

   2. Taylor expanded in z around 0

      \[\leadsto x + \frac{y \cdot \left(\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\color{blue}{\frac{607771387771}{1000000000000} + z \cdot \left(\frac{119400905721}{10000000000} + \frac{314690115749}{10000000000} \cdot z\right)}} \]
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto x + \frac{y \cdot \left(\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{z \cdot \left(\frac{119400905721}{10000000000} + \frac{314690115749}{10000000000} \cdot z\right) + \color{blue}{\frac{607771387771}{1000000000000}}} \]

      2. *-commutative N/A

         \[\leadsto x + \frac{y \cdot \left(\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\frac{119400905721}{10000000000} + \frac{314690115749}{10000000000} \cdot z\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      3. lower-fma.f64 N/A

         \[\leadsto x + \frac{y \cdot \left(\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\mathsf{fma}\left(\frac{119400905721}{10000000000} + \frac{314690115749}{10000000000} \cdot z, \color{blue}{z}, \frac{607771387771}{1000000000000}\right)} \]

      4. +-commutative N/A

         \[\leadsto x + \frac{y \cdot \left(\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\mathsf{fma}\left(\frac{314690115749}{10000000000} \cdot z + \frac{119400905721}{10000000000}, z, \frac{607771387771}{1000000000000}\right)} \]

      5. lower-fma.f64 97.3

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

   4. Applied rewrites 97.3%

      \[\leadsto x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(31.4690115749, z, 11.9400905721\right), z, 0.607771387771\right)}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 94.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y, \left(-\frac{\left(-\frac{\left(-\frac{\left(-a\right) + 5864.8025282699045}{z}\right) + 457.9610022158428}{z}\right) + 36.52704169880642}{z}\right) + 3.13060547623, x\right)\\ \mathbf{if}\;z \leq -13:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.18 \cdot 10^{+20}:\\ \;\;\;\;x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\mathsf{fma}\left(11.9400905721, z, 0.607771387771\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (fma
          y
          (+
           (-
            (/
             (+
              (-
               (/
                (+ (- (/ (+ (- a) 5864.8025282699045) z)) 457.9610022158428)
                z))
              36.52704169880642)
             z))
           3.13060547623)
          x)))
   (if (<= z -13.0)
     t_1
     (if (<= z 1.18e+20)
       (+
        x
        (/
         (*
          y
          (+
           (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z)
           b))
         (fma 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 = fma(y, (-((-((-((-a + 5864.8025282699045) / z) + 457.9610022158428) / z) + 36.52704169880642) / z) + 3.13060547623), x);
	double tmp;
	if (z <= -13.0) {
		tmp = t_1;
	} else if (z <= 1.18e+20) {
		tmp = x + ((y * ((((((((z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b)) / fma(11.9400905721, z, 0.607771387771));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(y, Float64(Float64(-Float64(Float64(Float64(-Float64(Float64(Float64(-Float64(Float64(Float64(-a) + 5864.8025282699045) / z)) + 457.9610022158428) / z)) + 36.52704169880642) / z)) + 3.13060547623), x)
	tmp = 0.0
	if (z <= -13.0)
		tmp = t_1;
	elseif (z <= 1.18e+20)
		tmp = Float64(x + Float64(Float64(y * Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b)) / fma(11.9400905721, z, 0.607771387771)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[((-N[(N[((-N[(N[((-N[(N[((-a) + 5864.8025282699045), $MachinePrecision] / z), $MachinePrecision]) + 457.9610022158428), $MachinePrecision] / z), $MachinePrecision]) + 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]) + 3.13060547623), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[z, -13.0], t$95$1, If[LessEqual[z, 1.18e+20], 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[(11.9400905721 * z + 0.607771387771), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -13 or 1.18e20 < z

   1. Initial program 14.7%

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

   2. Taylor expanded in t around 0

      \[\leadsto \color{blue}{x + \frac{y \cdot \left(b + z \cdot \left(a + {z}^{2} \cdot \left(\frac{55833770631}{5000000000} + \frac{313060547623}{100000000000} \cdot z\right)\right)\right)}{\frac{607771387771}{1000000000000} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)}} \]

   4. Applied rewrites 17.2%

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

   5. Taylor expanded in z around -inf

      \[\leadsto \mathsf{fma}\left(y, \frac{313060547623}{100000000000} + \color{blue}{-1 \cdot \frac{\frac{3652704169880641883561}{100000000000000000000} + -1 \cdot \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + -1 \cdot \frac{\frac{586480252826990429730394679450703430294089}{100000000000000000000000000000000000000} + -1 \cdot a}{z}}{z}}{z}}, x\right) \]
   6. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(y, -1 \cdot \frac{\frac{3652704169880641883561}{100000000000000000000} + -1 \cdot \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + -1 \cdot \frac{\frac{586480252826990429730394679450703430294089}{100000000000000000000000000000000000000} + -1 \cdot a}{z}}{z}}{z} + \frac{313060547623}{100000000000}, x\right) \]

      2. lower-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, -1 \cdot \frac{\frac{3652704169880641883561}{100000000000000000000} + -1 \cdot \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + -1 \cdot \frac{\frac{586480252826990429730394679450703430294089}{100000000000000000000000000000000000000} + -1 \cdot a}{z}}{z}}{z} + \frac{313060547623}{100000000000}, x\right) \]

   7. Applied rewrites 91.4%

      \[\leadsto \mathsf{fma}\left(y, \left(-\frac{\left(-\frac{\left(-\frac{\left(-a\right) + 5864.8025282699045}{z}\right) + 457.9610022158428}{z}\right) + 36.52704169880642}{z}\right) + \color{blue}{3.13060547623}, x\right) \]

   if -13 < z < 1.18e20

   1. Initial program 99.5%

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

   2. Taylor expanded in z around 0

      \[\leadsto x + \frac{y \cdot \left(\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\color{blue}{\frac{607771387771}{1000000000000} + \frac{119400905721}{10000000000} \cdot z}} \]
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto x + \frac{y \cdot \left(\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\frac{119400905721}{10000000000} \cdot z + \color{blue}{\frac{607771387771}{1000000000000}}} \]

      2. lower-fma.f64 97.2

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

   4. Applied rewrites 97.2%

      \[\leadsto x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\color{blue}{\mathsf{fma}\left(11.9400905721, z, 0.607771387771\right)}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 94.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y, \left(-\frac{\left(-\frac{\left(-\frac{\left(-a\right) + 5864.8025282699045}{z}\right) + 457.9610022158428}{z}\right) + 36.52704169880642}{z}\right) + 3.13060547623, x\right)\\ \mathbf{if}\;z \leq -210000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.18 \cdot 10^{+20}:\\ \;\;\;\;x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{0.607771387771}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (fma
          y
          (+
           (-
            (/
             (+
              (-
               (/
                (+ (- (/ (+ (- a) 5864.8025282699045) z)) 457.9610022158428)
                z))
              36.52704169880642)
             z))
           3.13060547623)
          x)))
   (if (<= z -210000.0)
     t_1
     (if (<= z 1.18e+20)
       (+
        x
        (/
         (*
          y
          (+
           (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) 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 = fma(y, (-((-((-((-a + 5864.8025282699045) / z) + 457.9610022158428) / z) + 36.52704169880642) / z) + 3.13060547623), x);
	double tmp;
	if (z <= -210000.0) {
		tmp = t_1;
	} else if (z <= 1.18e+20) {
		tmp = x + ((y * ((((((((z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b)) / 0.607771387771);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(y, Float64(Float64(-Float64(Float64(Float64(-Float64(Float64(Float64(-Float64(Float64(Float64(-a) + 5864.8025282699045) / z)) + 457.9610022158428) / z)) + 36.52704169880642) / z)) + 3.13060547623), x)
	tmp = 0.0
	if (z <= -210000.0)
		tmp = t_1;
	elseif (z <= 1.18e+20)
		tmp = Float64(x + Float64(Float64(y * Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b)) / 0.607771387771));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[((-N[(N[((-N[(N[((-N[(N[((-a) + 5864.8025282699045), $MachinePrecision] / z), $MachinePrecision]) + 457.9610022158428), $MachinePrecision] / z), $MachinePrecision]) + 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]) + 3.13060547623), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[z, -210000.0], t$95$1, If[LessEqual[z, 1.18e+20], 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] / 0.607771387771), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.1e5 or 1.18e20 < z

   1. Initial program 14.0%

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

   2. Taylor expanded in t around 0

      \[\leadsto \color{blue}{x + \frac{y \cdot \left(b + z \cdot \left(a + {z}^{2} \cdot \left(\frac{55833770631}{5000000000} + \frac{313060547623}{100000000000} \cdot z\right)\right)\right)}{\frac{607771387771}{1000000000000} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)}} \]

   4. Applied rewrites 16.6%

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

   5. Taylor expanded in z around -inf

      \[\leadsto \mathsf{fma}\left(y, \frac{313060547623}{100000000000} + \color{blue}{-1 \cdot \frac{\frac{3652704169880641883561}{100000000000000000000} + -1 \cdot \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + -1 \cdot \frac{\frac{586480252826990429730394679450703430294089}{100000000000000000000000000000000000000} + -1 \cdot a}{z}}{z}}{z}}, x\right) \]
   6. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(y, -1 \cdot \frac{\frac{3652704169880641883561}{100000000000000000000} + -1 \cdot \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + -1 \cdot \frac{\frac{586480252826990429730394679450703430294089}{100000000000000000000000000000000000000} + -1 \cdot a}{z}}{z}}{z} + \frac{313060547623}{100000000000}, x\right) \]

      2. lower-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, -1 \cdot \frac{\frac{3652704169880641883561}{100000000000000000000} + -1 \cdot \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + -1 \cdot \frac{\frac{586480252826990429730394679450703430294089}{100000000000000000000000000000000000000} + -1 \cdot a}{z}}{z}}{z} + \frac{313060547623}{100000000000}, x\right) \]

   7. Applied rewrites 91.7%

      \[\leadsto \mathsf{fma}\left(y, \left(-\frac{\left(-\frac{\left(-\frac{\left(-a\right) + 5864.8025282699045}{z}\right) + 457.9610022158428}{z}\right) + 36.52704169880642}{z}\right) + \color{blue}{3.13060547623}, x\right) \]

   if -2.1e5 < z < 1.18e20

   1. Initial program 99.4%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 96.4%

      \[\leadsto x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\color{blue}{0.607771387771}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 91.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y, \left(-\frac{\left(-\frac{\left(-\frac{\left(-a\right) + 5864.8025282699045}{z}\right) + 457.9610022158428}{z}\right) + 36.52704169880642}{z}\right) + 3.13060547623, x\right)\\ \mathbf{if}\;z \leq -13:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+18}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{\mathsf{fma}\left(\mathsf{fma}\left(z \cdot z, \mathsf{fma}\left(3.13060547623, z, 11.1667541262\right), a\right), z, b\right)}{\mathsf{fma}\left(11.9400905721, z, 0.607771387771\right)}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (fma
          y
          (+
           (-
            (/
             (+
              (-
               (/
                (+ (- (/ (+ (- a) 5864.8025282699045) z)) 457.9610022158428)
                z))
              36.52704169880642)
             z))
           3.13060547623)
          x)))
   (if (<= z -13.0)
     t_1
     (if (<= z 3.2e+18)
       (fma
        y
        (/
         (fma (fma (* z z) (fma 3.13060547623 z 11.1667541262) a) z b)
         (fma 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 = fma(y, (-((-((-((-a + 5864.8025282699045) / z) + 457.9610022158428) / z) + 36.52704169880642) / z) + 3.13060547623), x);
	double tmp;
	if (z <= -13.0) {
		tmp = t_1;
	} else if (z <= 3.2e+18) {
		tmp = fma(y, (fma(fma((z * z), fma(3.13060547623, z, 11.1667541262), a), z, b) / fma(11.9400905721, z, 0.607771387771)), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(y, Float64(Float64(-Float64(Float64(Float64(-Float64(Float64(Float64(-Float64(Float64(Float64(-a) + 5864.8025282699045) / z)) + 457.9610022158428) / z)) + 36.52704169880642) / z)) + 3.13060547623), x)
	tmp = 0.0
	if (z <= -13.0)
		tmp = t_1;
	elseif (z <= 3.2e+18)
		tmp = fma(y, Float64(fma(fma(Float64(z * z), fma(3.13060547623, z, 11.1667541262), a), z, b) / fma(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[(y * N[((-N[(N[((-N[(N[((-N[(N[((-a) + 5864.8025282699045), $MachinePrecision] / z), $MachinePrecision]) + 457.9610022158428), $MachinePrecision] / z), $MachinePrecision]) + 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]) + 3.13060547623), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[z, -13.0], t$95$1, If[LessEqual[z, 3.2e+18], N[(y * N[(N[(N[(N[(z * z), $MachinePrecision] * N[(3.13060547623 * z + 11.1667541262), $MachinePrecision] + a), $MachinePrecision] * z + b), $MachinePrecision] / N[(11.9400905721 * z + 0.607771387771), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -13 or 3.2e18 < z

   1. Initial program 15.1%

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

   2. Taylor expanded in t around 0

      \[\leadsto \color{blue}{x + \frac{y \cdot \left(b + z \cdot \left(a + {z}^{2} \cdot \left(\frac{55833770631}{5000000000} + \frac{313060547623}{100000000000} \cdot z\right)\right)\right)}{\frac{607771387771}{1000000000000} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)}} \]

   4. Applied rewrites 17.5%

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

   5. Taylor expanded in z around -inf

      \[\leadsto \mathsf{fma}\left(y, \frac{313060547623}{100000000000} + \color{blue}{-1 \cdot \frac{\frac{3652704169880641883561}{100000000000000000000} + -1 \cdot \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + -1 \cdot \frac{\frac{586480252826990429730394679450703430294089}{100000000000000000000000000000000000000} + -1 \cdot a}{z}}{z}}{z}}, x\right) \]
   6. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(y, -1 \cdot \frac{\frac{3652704169880641883561}{100000000000000000000} + -1 \cdot \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + -1 \cdot \frac{\frac{586480252826990429730394679450703430294089}{100000000000000000000000000000000000000} + -1 \cdot a}{z}}{z}}{z} + \frac{313060547623}{100000000000}, x\right) \]

      2. lower-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, -1 \cdot \frac{\frac{3652704169880641883561}{100000000000000000000} + -1 \cdot \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + -1 \cdot \frac{\frac{586480252826990429730394679450703430294089}{100000000000000000000000000000000000000} + -1 \cdot a}{z}}{z}}{z} + \frac{313060547623}{100000000000}, x\right) \]

   7. Applied rewrites 91.3%

      \[\leadsto \mathsf{fma}\left(y, \left(-\frac{\left(-\frac{\left(-\frac{\left(-a\right) + 5864.8025282699045}{z}\right) + 457.9610022158428}{z}\right) + 36.52704169880642}{z}\right) + \color{blue}{3.13060547623}, x\right) \]

   if -13 < z < 3.2e18

   1. Initial program 99.5%

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

   2. Taylor expanded in t around 0

      \[\leadsto \color{blue}{x + \frac{y \cdot \left(b + z \cdot \left(a + {z}^{2} \cdot \left(\frac{55833770631}{5000000000} + \frac{313060547623}{100000000000} \cdot z\right)\right)\right)}{\frac{607771387771}{1000000000000} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)}} \]

   4. Applied rewrites 94.1%

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

   5. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(y, \frac{\mathsf{fma}\left(\mathsf{fma}\left(z \cdot z, \mathsf{fma}\left(\frac{313060547623}{100000000000}, z, \frac{55833770631}{5000000000}\right), a\right), z, b\right)}{\mathsf{fma}\left(\frac{119400905721}{10000000000}, z, \frac{607771387771}{1000000000000}\right)}, x\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 92.5%

      \[\leadsto \mathsf{fma}\left(y, \frac{\mathsf{fma}\left(\mathsf{fma}\left(z \cdot z, \mathsf{fma}\left(3.13060547623, z, 11.1667541262\right), a\right), z, b\right)}{\mathsf{fma}\left(11.9400905721, z, 0.607771387771\right)}, x\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 90.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+34}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+18}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{\mathsf{fma}\left(\mathsf{fma}\left(z \cdot z, 11.1667541262, a\right), z, b\right)}{0.607771387771}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \left(-\frac{\left(-\frac{\left(-\frac{\left(-a\right) + 5864.8025282699045}{z}\right) + 457.9610022158428}{z}\right) + 36.52704169880642}{z}\right) + 3.13060547623, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -3.6e+34)
   (fma 3.13060547623 y x)
   (if (<= z 3.2e+18)
     (fma y (/ (fma (fma (* z z) 11.1667541262 a) z b) 0.607771387771) x)
     (fma
      y
      (+
       (-
        (/
         (+
          (-
           (/ (+ (- (/ (+ (- a) 5864.8025282699045) z)) 457.9610022158428) z))
          36.52704169880642)
         z))
       3.13060547623)
      x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -3.6e+34) {
		tmp = fma(3.13060547623, y, x);
	} else if (z <= 3.2e+18) {
		tmp = fma(y, (fma(fma((z * z), 11.1667541262, a), z, b) / 0.607771387771), x);
	} else {
		tmp = fma(y, (-((-((-((-a + 5864.8025282699045) / z) + 457.9610022158428) / z) + 36.52704169880642) / z) + 3.13060547623), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -3.6e+34)
		tmp = fma(3.13060547623, y, x);
	elseif (z <= 3.2e+18)
		tmp = fma(y, Float64(fma(fma(Float64(z * z), 11.1667541262, a), z, b) / 0.607771387771), x);
	else
		tmp = fma(y, Float64(Float64(-Float64(Float64(Float64(-Float64(Float64(Float64(-Float64(Float64(Float64(-a) + 5864.8025282699045) / z)) + 457.9610022158428) / z)) + 36.52704169880642) / z)) + 3.13060547623), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -3.6e+34], N[(3.13060547623 * y + x), $MachinePrecision], If[LessEqual[z, 3.2e+18], N[(y * N[(N[(N[(N[(z * z), $MachinePrecision] * 11.1667541262 + a), $MachinePrecision] * z + b), $MachinePrecision] / 0.607771387771), $MachinePrecision] + x), $MachinePrecision], N[(y * N[((-N[(N[((-N[(N[((-N[(N[((-a) + 5864.8025282699045), $MachinePrecision] / z), $MachinePrecision]) + 457.9610022158428), $MachinePrecision] / z), $MachinePrecision]) + 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]) + 3.13060547623), $MachinePrecision] + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.6e34

   1. Initial program 9.6%

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

   2. Taylor expanded in z around inf

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

      1. +-commutative N/A

         \[\leadsto \frac{313060547623}{100000000000} \cdot y + \color{blue}{x} \]

      2. lower-fma.f64 91.3

         \[\leadsto \mathsf{fma}\left(3.13060547623, \color{blue}{y}, x\right) \]

   4. Applied rewrites 91.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(3.13060547623, y, x\right)} \]

   if -3.6e34 < z < 3.2e18

   1. Initial program 98.8%

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

   2. Taylor expanded in t around 0

      \[\leadsto \color{blue}{x + \frac{y \cdot \left(b + z \cdot \left(a + {z}^{2} \cdot \left(\frac{55833770631}{5000000000} + \frac{313060547623}{100000000000} \cdot z\right)\right)\right)}{\frac{607771387771}{1000000000000} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)}} \]

   4. Applied rewrites 93.4%

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

   5. Taylor expanded in z around 0

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

   7. Applied rewrites 89.6%

      \[\leadsto \mathsf{fma}\left(y, \frac{\mathsf{fma}\left(\mathsf{fma}\left(z \cdot z, \mathsf{fma}\left(3.13060547623, z, 11.1667541262\right), a\right), z, b\right)}{0.607771387771}, x\right) \]

   8. Taylor expanded in z around 0

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

   10. Applied rewrites 89.6%

       \[\leadsto \mathsf{fma}\left(y, \frac{\mathsf{fma}\left(\mathsf{fma}\left(z \cdot z, 11.1667541262, a\right), z, b\right)}{0.607771387771}, x\right) \]

   if 3.2e18 < z

   1. Initial program 11.7%

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

   2. Taylor expanded in t around 0

      \[\leadsto \color{blue}{x + \frac{y \cdot \left(b + z \cdot \left(a + {z}^{2} \cdot \left(\frac{55833770631}{5000000000} + \frac{313060547623}{100000000000} \cdot z\right)\right)\right)}{\frac{607771387771}{1000000000000} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)}} \]

   4. Applied rewrites 14.5%

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

   5. Taylor expanded in z around -inf

      \[\leadsto \mathsf{fma}\left(y, \frac{313060547623}{100000000000} + \color{blue}{-1 \cdot \frac{\frac{3652704169880641883561}{100000000000000000000} + -1 \cdot \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + -1 \cdot \frac{\frac{586480252826990429730394679450703430294089}{100000000000000000000000000000000000000} + -1 \cdot a}{z}}{z}}{z}}, x\right) \]
   6. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(y, -1 \cdot \frac{\frac{3652704169880641883561}{100000000000000000000} + -1 \cdot \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + -1 \cdot \frac{\frac{586480252826990429730394679450703430294089}{100000000000000000000000000000000000000} + -1 \cdot a}{z}}{z}}{z} + \frac{313060547623}{100000000000}, x\right) \]

      2. lower-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, -1 \cdot \frac{\frac{3652704169880641883561}{100000000000000000000} + -1 \cdot \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + -1 \cdot \frac{\frac{586480252826990429730394679450703430294089}{100000000000000000000000000000000000000} + -1 \cdot a}{z}}{z}}{z} + \frac{313060547623}{100000000000}, x\right) \]

   7. Applied rewrites 93.4%

      \[\leadsto \mathsf{fma}\left(y, \left(-\frac{\left(-\frac{\left(-\frac{\left(-a\right) + 5864.8025282699045}{z}\right) + 457.9610022158428}{z}\right) + 36.52704169880642}{z}\right) + \color{blue}{3.13060547623}, x\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 8: 90.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+34}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+34}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{\mathsf{fma}\left(\mathsf{fma}\left(z \cdot z, 11.1667541262, a\right), z, b\right)}{0.607771387771}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -3.6e+34)
   (fma 3.13060547623 y x)
   (if (<= z 6.5e+34)
     (fma y (/ (fma (fma (* z z) 11.1667541262 a) z b) 0.607771387771) x)
     (fma 3.13060547623 y x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -3.6e+34) {
		tmp = fma(3.13060547623, y, x);
	} else if (z <= 6.5e+34) {
		tmp = fma(y, (fma(fma((z * z), 11.1667541262, a), z, b) / 0.607771387771), x);
	} else {
		tmp = fma(3.13060547623, y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -3.6e+34)
		tmp = fma(3.13060547623, y, x);
	elseif (z <= 6.5e+34)
		tmp = fma(y, Float64(fma(fma(Float64(z * z), 11.1667541262, a), z, b) / 0.607771387771), x);
	else
		tmp = fma(3.13060547623, y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -3.6e+34], N[(3.13060547623 * y + x), $MachinePrecision], If[LessEqual[z, 6.5e+34], N[(y * N[(N[(N[(N[(z * z), $MachinePrecision] * 11.1667541262 + a), $MachinePrecision] * z + b), $MachinePrecision] / 0.607771387771), $MachinePrecision] + x), $MachinePrecision], N[(3.13060547623 * y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.6e34 or 6.50000000000000017e34 < z

   1. Initial program 8.8%

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

   2. Taylor expanded in z around inf

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

      1. +-commutative N/A

         \[\leadsto \frac{313060547623}{100000000000} \cdot y + \color{blue}{x} \]

      2. lower-fma.f64 92.2

         \[\leadsto \mathsf{fma}\left(3.13060547623, \color{blue}{y}, x\right) \]

   4. Applied rewrites 92.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(3.13060547623, y, x\right)} \]

   if -3.6e34 < z < 6.50000000000000017e34

   1. Initial program 98.3%

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

   2. Taylor expanded in t around 0

      \[\leadsto \color{blue}{x + \frac{y \cdot \left(b + z \cdot \left(a + {z}^{2} \cdot \left(\frac{55833770631}{5000000000} + \frac{313060547623}{100000000000} \cdot z\right)\right)\right)}{\frac{607771387771}{1000000000000} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)}} \]

   4. Applied rewrites 93.1%

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

   5. Taylor expanded in z around 0

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

   7. Applied rewrites 88.5%

      \[\leadsto \mathsf{fma}\left(y, \frac{\mathsf{fma}\left(\mathsf{fma}\left(z \cdot z, \mathsf{fma}\left(3.13060547623, z, 11.1667541262\right), a\right), z, b\right)}{0.607771387771}, x\right) \]

   8. Taylor expanded in z around 0

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

   10. Applied rewrites 88.5%

       \[\leadsto \mathsf{fma}\left(y, \frac{\mathsf{fma}\left(\mathsf{fma}\left(z \cdot z, 11.1667541262, a\right), z, b\right)}{0.607771387771}, x\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 89.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+34}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+34}:\\ \;\;\;\;\mathsf{fma}\left(y, \mathsf{fma}\left(\mathsf{fma}\left(1.6453555072203998, a, -32.324150453290734 \cdot b\right), z, 1.6453555072203998 \cdot b\right), x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -3.6e+34)
   (fma 3.13060547623 y x)
   (if (<= z 6.5e+34)
     (fma
      y
      (fma
       (fma 1.6453555072203998 a (* -32.324150453290734 b))
       z
       (* 1.6453555072203998 b))
      x)
     (fma 3.13060547623 y x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -3.6e+34) {
		tmp = fma(3.13060547623, y, x);
	} else if (z <= 6.5e+34) {
		tmp = fma(y, fma(fma(1.6453555072203998, a, (-32.324150453290734 * b)), z, (1.6453555072203998 * b)), x);
	} else {
		tmp = fma(3.13060547623, y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -3.6e+34)
		tmp = fma(3.13060547623, y, x);
	elseif (z <= 6.5e+34)
		tmp = fma(y, fma(fma(1.6453555072203998, a, Float64(-32.324150453290734 * b)), z, Float64(1.6453555072203998 * b)), x);
	else
		tmp = fma(3.13060547623, y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -3.6e+34], N[(3.13060547623 * y + x), $MachinePrecision], If[LessEqual[z, 6.5e+34], N[(y * N[(N[(1.6453555072203998 * a + N[(-32.324150453290734 * b), $MachinePrecision]), $MachinePrecision] * z + N[(1.6453555072203998 * b), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(3.13060547623 * y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.6e34 or 6.50000000000000017e34 < z

   1. Initial program 8.8%

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

   2. Taylor expanded in z around inf

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

      1. +-commutative N/A

         \[\leadsto \frac{313060547623}{100000000000} \cdot y + \color{blue}{x} \]

      2. lower-fma.f64 92.2

         \[\leadsto \mathsf{fma}\left(3.13060547623, \color{blue}{y}, x\right) \]

   4. Applied rewrites 92.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(3.13060547623, y, x\right)} \]

   if -3.6e34 < z < 6.50000000000000017e34

   1. Initial program 98.3%

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

   2. Taylor expanded in t around 0

      \[\leadsto \color{blue}{x + \frac{y \cdot \left(b + z \cdot \left(a + {z}^{2} \cdot \left(\frac{55833770631}{5000000000} + \frac{313060547623}{100000000000} \cdot z\right)\right)\right)}{\frac{607771387771}{1000000000000} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)}} \]

   4. Applied rewrites 93.1%

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

   5. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(y, \frac{1000000000000}{607771387771} \cdot b + \color{blue}{z \cdot \left(\frac{1000000000000}{607771387771} \cdot a - \frac{11940090572100000000000000}{369386059793087248348441} \cdot b\right)}, x\right) \]
   6. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(y, z \cdot \left(\frac{1000000000000}{607771387771} \cdot a - \frac{11940090572100000000000000}{369386059793087248348441} \cdot b\right) + \frac{1000000000000}{607771387771} \cdot \color{blue}{b}, x\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(y, \left(\frac{1000000000000}{607771387771} \cdot a - \frac{11940090572100000000000000}{369386059793087248348441} \cdot b\right) \cdot z + \frac{1000000000000}{607771387771} \cdot b, x\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(\frac{1000000000000}{607771387771} \cdot a - \frac{11940090572100000000000000}{369386059793087248348441} \cdot b, z, \frac{1000000000000}{607771387771} \cdot b\right), x\right) \]

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

         \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(\frac{1000000000000}{607771387771} \cdot a + \left(\mathsf{neg}\left(\frac{11940090572100000000000000}{369386059793087248348441}\right)\right) \cdot b, z, \frac{1000000000000}{607771387771} \cdot b\right), x\right) \]

      5. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(\mathsf{fma}\left(\frac{1000000000000}{607771387771}, a, \left(\mathsf{neg}\left(\frac{11940090572100000000000000}{369386059793087248348441}\right)\right) \cdot b\right), z, \frac{1000000000000}{607771387771} \cdot b\right), x\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(\mathsf{fma}\left(\frac{1000000000000}{607771387771}, a, \frac{-11940090572100000000000000}{369386059793087248348441} \cdot b\right), z, \frac{1000000000000}{607771387771} \cdot b\right), x\right) \]

      7. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(\mathsf{fma}\left(\frac{1000000000000}{607771387771}, a, \frac{-11940090572100000000000000}{369386059793087248348441} \cdot b\right), z, \frac{1000000000000}{607771387771} \cdot b\right), x\right) \]

      8. lower-*.f64 87.7

         \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(\mathsf{fma}\left(1.6453555072203998, a, -32.324150453290734 \cdot b\right), z, 1.6453555072203998 \cdot b\right), x\right) \]

   7. Applied rewrites 87.7%

      \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(\mathsf{fma}\left(1.6453555072203998, a, -32.324150453290734 \cdot b\right), \color{blue}{z}, 1.6453555072203998 \cdot b\right), x\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 10: 81.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{b}{\mathsf{fma}\left(\mathsf{fma}\left(31.4690115749, z, 11.9400905721\right), z, 0.607771387771\right)}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623 - \frac{36.52704169880642}{z}, x\right)\\ \end{array} \end{array} \]

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 y (/ b (fma (fma 31.4690115749 z 11.9400905721) z 0.607771387771)) x)
   (fma y (- 3.13060547623 (/ 36.52704169880642 z)) x)))

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(y, (b / fma(fma(31.4690115749, z, 11.9400905721), z, 0.607771387771)), x);
	} else {
		tmp = fma(y, (3.13060547623 - (36.52704169880642 / z)), x);
	}
	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(y, Float64(b / fma(fma(31.4690115749, z, 11.9400905721), z, 0.607771387771)), x);
	else
		tmp = fma(y, Float64(3.13060547623 - Float64(36.52704169880642 / z)), x);
	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[(y * N[(b / N[(N[(31.4690115749 * z + 11.9400905721), $MachinePrecision] * z + 0.607771387771), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(y * N[(3.13060547623 - N[(36.52704169880642 / z), $MachinePrecision]), $MachinePrecision] + x), $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 93.8%

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

   2. Taylor expanded in t around 0

      \[\leadsto \color{blue}{x + \frac{y \cdot \left(b + z \cdot \left(a + {z}^{2} \cdot \left(\frac{55833770631}{5000000000} + \frac{313060547623}{100000000000} \cdot z\right)\right)\right)}{\frac{607771387771}{1000000000000} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)}} \]

   4. Applied rewrites 91.1%

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

   5. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(y, \frac{\mathsf{fma}\left(\mathsf{fma}\left(z \cdot z, \mathsf{fma}\left(\frac{313060547623}{100000000000}, z, \frac{55833770631}{5000000000}\right), a\right), z, b\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\frac{314690115749}{10000000000}, z, \frac{119400905721}{10000000000}\right), z, \frac{607771387771}{1000000000000}\right)}, x\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 83.9%

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

   8. Taylor expanded in z around 0

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

   10. Applied rewrites 73.3%

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

   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 0.0%

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

   2. Taylor expanded in t around 0

      \[\leadsto \color{blue}{x + \frac{y \cdot \left(b + z \cdot \left(a + {z}^{2} \cdot \left(\frac{55833770631}{5000000000} + \frac{313060547623}{100000000000} \cdot z\right)\right)\right)}{\frac{607771387771}{1000000000000} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)}} \]

   4. Applied rewrites 0.0%

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

   5. Taylor expanded in z around inf

      \[\leadsto \mathsf{fma}\left(y, \frac{313060547623}{100000000000} - \color{blue}{\frac{3652704169880641883561}{100000000000000000000} \cdot \frac{1}{z}}, x\right) \]
   6. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \frac{313060547623}{100000000000} - \frac{3652704169880641883561}{100000000000000000000} \cdot \color{blue}{\frac{1}{z}}, x\right) \]

      2. associate-*r/ N/A

         \[\leadsto \mathsf{fma}\left(y, \frac{313060547623}{100000000000} - \frac{\frac{3652704169880641883561}{100000000000000000000} \cdot 1}{z}, x\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(y, \frac{313060547623}{100000000000} - \frac{\frac{3652704169880641883561}{100000000000000000000}}{z}, x\right) \]

      4. lower-/.f64 96.7

         \[\leadsto \mathsf{fma}\left(y, 3.13060547623 - \frac{36.52704169880642}{z}, x\right) \]

   7. Applied rewrites 96.7%

      \[\leadsto \mathsf{fma}\left(y, 3.13060547623 - \color{blue}{\frac{36.52704169880642}{z}}, x\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 11: 81.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{b}{\mathsf{fma}\left(11.9400905721, z, 0.607771387771\right)}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623 - \frac{36.52704169880642}{z}, x\right)\\ \end{array} \end{array} \]

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 y (/ b (fma 11.9400905721 z 0.607771387771)) x)
   (fma y (- 3.13060547623 (/ 36.52704169880642 z)) x)))

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(y, (b / fma(11.9400905721, z, 0.607771387771)), x);
	} else {
		tmp = fma(y, (3.13060547623 - (36.52704169880642 / z)), x);
	}
	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(y, Float64(b / fma(11.9400905721, z, 0.607771387771)), x);
	else
		tmp = fma(y, Float64(3.13060547623 - Float64(36.52704169880642 / z)), x);
	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[(y * N[(b / N[(11.9400905721 * z + 0.607771387771), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(y * N[(3.13060547623 - N[(36.52704169880642 / z), $MachinePrecision]), $MachinePrecision] + x), $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 93.8%

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

   2. Taylor expanded in t around 0

      \[\leadsto \color{blue}{x + \frac{y \cdot \left(b + z \cdot \left(a + {z}^{2} \cdot \left(\frac{55833770631}{5000000000} + \frac{313060547623}{100000000000} \cdot z\right)\right)\right)}{\frac{607771387771}{1000000000000} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)}} \]

   4. Applied rewrites 91.1%

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

   5. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(y, \frac{\mathsf{fma}\left(\mathsf{fma}\left(z \cdot z, \mathsf{fma}\left(\frac{313060547623}{100000000000}, z, \frac{55833770631}{5000000000}\right), a\right), z, b\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\frac{314690115749}{10000000000}, z, \frac{119400905721}{10000000000}\right), z, \frac{607771387771}{1000000000000}\right)}, x\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 83.9%

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

   8. Taylor expanded in z around 0

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

   10. Applied rewrites 73.3%

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

   11. Taylor expanded in z around 0

       \[\leadsto \mathsf{fma}\left(y, \frac{b}{\mathsf{fma}\left(\frac{119400905721}{10000000000}, z, \frac{607771387771}{1000000000000}\right)}, x\right) \]
   12. Step-by-step derivation

   13. Applied rewrites 72.7%

       \[\leadsto \mathsf{fma}\left(y, \frac{b}{\mathsf{fma}\left(11.9400905721, z, 0.607771387771\right)}, x\right) \]

   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 0.0%

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

   2. Taylor expanded in t around 0

      \[\leadsto \color{blue}{x + \frac{y \cdot \left(b + z \cdot \left(a + {z}^{2} \cdot \left(\frac{55833770631}{5000000000} + \frac{313060547623}{100000000000} \cdot z\right)\right)\right)}{\frac{607771387771}{1000000000000} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)}} \]

   4. Applied rewrites 0.0%

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

   5. Taylor expanded in z around inf

      \[\leadsto \mathsf{fma}\left(y, \frac{313060547623}{100000000000} - \color{blue}{\frac{3652704169880641883561}{100000000000000000000} \cdot \frac{1}{z}}, x\right) \]
   6. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \frac{313060547623}{100000000000} - \frac{3652704169880641883561}{100000000000000000000} \cdot \color{blue}{\frac{1}{z}}, x\right) \]

      2. associate-*r/ N/A

         \[\leadsto \mathsf{fma}\left(y, \frac{313060547623}{100000000000} - \frac{\frac{3652704169880641883561}{100000000000000000000} \cdot 1}{z}, x\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(y, \frac{313060547623}{100000000000} - \frac{\frac{3652704169880641883561}{100000000000000000000}}{z}, x\right) \]

      4. lower-/.f64 96.7

         \[\leadsto \mathsf{fma}\left(y, 3.13060547623 - \frac{36.52704169880642}{z}, x\right) \]

   7. Applied rewrites 96.7%

      \[\leadsto \mathsf{fma}\left(y, 3.13060547623 - \color{blue}{\frac{36.52704169880642}{z}}, x\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 12: 81.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \leq \infty:\\ \;\;\;\;x + \left(b \cdot y\right) \cdot 1.6453555072203998\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<=
      (/
       (*
        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)
   (+ x (* (* b y) 1.6453555072203998))
   (fma 3.13060547623 y x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((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 = x + ((b * y) * 1.6453555072203998);
	} else {
		tmp = fma(3.13060547623, y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (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 = Float64(x + Float64(Float64(b * y) * 1.6453555072203998));
	else
		tmp = fma(3.13060547623, y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[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], Infinity], N[(x + N[(N[(b * y), $MachinePrecision] * 1.6453555072203998), $MachinePrecision]), $MachinePrecision], N[(3.13060547623 * y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.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 93.8%

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

   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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 72.8

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

   4. Applied rewrites 72.8%

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

   if +inf.0 < (/.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 0.0%

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

   2. Taylor expanded in z around inf

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

      1. +-commutative N/A

         \[\leadsto \frac{313060547623}{100000000000} \cdot y + \color{blue}{x} \]

      2. lower-fma.f64 96.7

         \[\leadsto \mathsf{fma}\left(3.13060547623, \color{blue}{y}, x\right) \]

   4. Applied rewrites 96.7%

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

Alternative 13: 81.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \leq \infty:\\ \;\;\;\;x + \left(b \cdot y\right) \cdot 1.6453555072203998\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623 - \frac{36.52704169880642}{z}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<=
      (/
       (*
        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)
   (+ x (* (* b y) 1.6453555072203998))
   (fma y (- 3.13060547623 (/ 36.52704169880642 z)) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((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 = x + ((b * y) * 1.6453555072203998);
	} else {
		tmp = fma(y, (3.13060547623 - (36.52704169880642 / z)), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (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 = Float64(x + Float64(Float64(b * y) * 1.6453555072203998));
	else
		tmp = fma(y, Float64(3.13060547623 - Float64(36.52704169880642 / z)), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[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], Infinity], N[(x + N[(N[(b * y), $MachinePrecision] * 1.6453555072203998), $MachinePrecision]), $MachinePrecision], N[(y * N[(3.13060547623 - N[(36.52704169880642 / z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.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 93.8%

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

   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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 72.8

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

   4. Applied rewrites 72.8%

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

   if +inf.0 < (/.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 0.0%

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

   2. Taylor expanded in t around 0

      \[\leadsto \color{blue}{x + \frac{y \cdot \left(b + z \cdot \left(a + {z}^{2} \cdot \left(\frac{55833770631}{5000000000} + \frac{313060547623}{100000000000} \cdot z\right)\right)\right)}{\frac{607771387771}{1000000000000} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)}} \]

   4. Applied rewrites 0.0%

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

   5. Taylor expanded in z around inf

      \[\leadsto \mathsf{fma}\left(y, \frac{313060547623}{100000000000} - \color{blue}{\frac{3652704169880641883561}{100000000000000000000} \cdot \frac{1}{z}}, x\right) \]
   6. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \frac{313060547623}{100000000000} - \frac{3652704169880641883561}{100000000000000000000} \cdot \color{blue}{\frac{1}{z}}, x\right) \]

      2. associate-*r/ N/A

         \[\leadsto \mathsf{fma}\left(y, \frac{313060547623}{100000000000} - \frac{\frac{3652704169880641883561}{100000000000000000000} \cdot 1}{z}, x\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{fma}\left(y, \frac{313060547623}{100000000000} - \frac{\frac{3652704169880641883561}{100000000000000000000}}{z}, x\right) \]

      4. lower-/.f64 96.7

         \[\leadsto \mathsf{fma}\left(y, 3.13060547623 - \frac{36.52704169880642}{z}, x\right) \]

   7. Applied rewrites 96.7%

      \[\leadsto \mathsf{fma}\left(y, 3.13060547623 - \color{blue}{\frac{36.52704169880642}{z}}, x\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 14: 81.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \leq \infty:\\ \;\;\;\;x + b \cdot \left(y \cdot 1.6453555072203998\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<=
      (/
       (*
        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)
   (+ x (* b (* y 1.6453555072203998)))
   (fma 3.13060547623 y x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((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 = x + (b * (y * 1.6453555072203998));
	} else {
		tmp = fma(3.13060547623, y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (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 = Float64(x + Float64(b * Float64(y * 1.6453555072203998)));
	else
		tmp = fma(3.13060547623, y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[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], Infinity], N[(x + N[(b * N[(y * 1.6453555072203998), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(3.13060547623 * y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.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 93.8%

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

   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. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-*.f64 72.8

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

   4. Applied rewrites 72.8%

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

      1. lift-*.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-*l* N/A

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

      4. lower-*.f64 N/A

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

      5. lower-*.f64 72.8

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

   6. Applied rewrites 72.8%

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

   if +inf.0 < (/.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 0.0%

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

   2. Taylor expanded in z around inf

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

      1. +-commutative N/A

         \[\leadsto \frac{313060547623}{100000000000} \cdot y + \color{blue}{x} \]

      2. lower-fma.f64 96.7

         \[\leadsto \mathsf{fma}\left(3.13060547623, \color{blue}{y}, x\right) \]

   4. Applied rewrites 96.7%

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

Alternative 15: 81.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(b \cdot y, 1.6453555072203998, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<=
      (/
       (*
        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 (* b y) 1.6453555072203998 x)
   (fma 3.13060547623 y x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((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((b * y), 1.6453555072203998, x);
	} else {
		tmp = fma(3.13060547623, y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (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(b * y), 1.6453555072203998, x);
	else
		tmp = fma(3.13060547623, y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[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], Infinity], N[(N[(b * y), $MachinePrecision] * 1.6453555072203998 + x), $MachinePrecision], N[(3.13060547623 * y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.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 93.8%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 72.8

         \[\leadsto \mathsf{fma}\left(b \cdot y, 1.6453555072203998, x\right) \]

   4. Applied rewrites 72.8%

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

   if +inf.0 < (/.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 0.0%

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

   2. Taylor expanded in z around inf

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

      1. +-commutative N/A

         \[\leadsto \frac{313060547623}{100000000000} \cdot y + \color{blue}{x} \]

      2. lower-fma.f64 96.7

         \[\leadsto \mathsf{fma}\left(3.13060547623, \color{blue}{y}, x\right) \]

   4. Applied rewrites 96.7%

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

Alternative 16: 81.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(y, 1.6453555072203998 \cdot b, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<=
      (/
       (*
        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 (* 1.6453555072203998 b) x)
   (fma 3.13060547623 y x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((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, (1.6453555072203998 * b), x);
	} else {
		tmp = fma(3.13060547623, y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (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(1.6453555072203998 * b), x);
	else
		tmp = fma(3.13060547623, y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[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], Infinity], N[(y * N[(1.6453555072203998 * b), $MachinePrecision] + x), $MachinePrecision], N[(3.13060547623 * y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.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 93.8%

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

   2. Taylor expanded in t around 0

      \[\leadsto \color{blue}{x + \frac{y \cdot \left(b + z \cdot \left(a + {z}^{2} \cdot \left(\frac{55833770631}{5000000000} + \frac{313060547623}{100000000000} \cdot z\right)\right)\right)}{\frac{607771387771}{1000000000000} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)}} \]

   4. Applied rewrites 91.1%

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

   5. Taylor expanded in z around 0

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

      1. lower-*.f64 72.8

         \[\leadsto \mathsf{fma}\left(y, 1.6453555072203998 \cdot b, x\right) \]

   7. Applied rewrites 72.8%

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

   if +inf.0 < (/.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 0.0%

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

   2. Taylor expanded in z around inf

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

      1. +-commutative N/A

         \[\leadsto \frac{313060547623}{100000000000} \cdot y + \color{blue}{x} \]

      2. lower-fma.f64 96.7

         \[\leadsto \mathsf{fma}\left(3.13060547623, \color{blue}{y}, x\right) \]

   4. Applied rewrites 96.7%

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

Alternative 17: 72.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+143}:\\ \;\;\;\;1.6453555072203998 \cdot \left(b \cdot y\right)\\ \mathbf{elif}\;t\_1 \leq 10^{+52}:\\ \;\;\;\;x\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;b \cdot \left(1.6453555072203998 \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (/
          (*
           y
           (+
            (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z)
            b))
          (+
           (*
            (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721)
            z)
           0.607771387771))))
   (if (<= t_1 -2e+143)
     (* 1.6453555072203998 (* b y))
     (if (<= t_1 1e+52)
       x
       (if (<= t_1 INFINITY)
         (* b (* 1.6453555072203998 y))
         (fma 3.13060547623 y x))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (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 tmp;
	if (t_1 <= -2e+143) {
		tmp = 1.6453555072203998 * (b * y);
	} else if (t_1 <= 1e+52) {
		tmp = x;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = b * (1.6453555072203998 * y);
	} else {
		tmp = fma(3.13060547623, y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = 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))
	tmp = 0.0
	if (t_1 <= -2e+143)
		tmp = Float64(1.6453555072203998 * Float64(b * y));
	elseif (t_1 <= 1e+52)
		tmp = x;
	elseif (t_1 <= Inf)
		tmp = Float64(b * Float64(1.6453555072203998 * y));
	else
		tmp = fma(3.13060547623, y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = 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]}, If[LessEqual[t$95$1, -2e+143], N[(1.6453555072203998 * N[(b * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+52], x, If[LessEqual[t$95$1, Infinity], N[(b * N[(1.6453555072203998 * y), $MachinePrecision]), $MachinePrecision], N[(3.13060547623 * y + x), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.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))) < -2e143

   1. Initial program 85.0%

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

   2. Taylor expanded in b around inf

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

      1. associate-/l* N/A

         \[\leadsto b \cdot \color{blue}{\frac{y}{\frac{607771387771}{1000000000000} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)}} \]

      2. lower-*.f64 N/A

         \[\leadsto b \cdot \color{blue}{\frac{y}{\frac{607771387771}{1000000000000} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)}} \]

      3. lower-/.f64 N/A

         \[\leadsto b \cdot \frac{y}{\color{blue}{\frac{607771387771}{1000000000000} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)}} \]

      4. +-commutative N/A

         \[\leadsto b \cdot \frac{y}{z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right) + \color{blue}{\frac{607771387771}{1000000000000}}} \]

      5. *-commutative N/A

         \[\leadsto b \cdot \frac{y}{\left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      6. +-commutative N/A

         \[\leadsto b \cdot \frac{y}{\left(z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right) + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      7. *-commutative N/A

         \[\leadsto b \cdot \frac{y}{\left(\left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      8. +-commutative N/A

         \[\leadsto b \cdot \frac{y}{\left(\left(z \cdot \left(\frac{15234687407}{1000000000} + z\right) + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      9. +-commutative N/A

         \[\leadsto b \cdot \frac{y}{\left(\left(z \cdot \left(z + \frac{15234687407}{1000000000}\right) + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      10. *-commutative N/A

          \[\leadsto b \cdot \frac{y}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

   4. Applied rewrites 51.5%

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

   5. Taylor expanded in z around 0

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 50.5

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

   7. Applied rewrites 50.5%

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

   if -2e143 < (/.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))) < 9.9999999999999999e51

   1. Initial program 99.7%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 66.1%

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

   if 9.9999999999999999e51 < (/.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 88.6%

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

   2. Taylor expanded in b around inf

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

      1. associate-/l* N/A

         \[\leadsto b \cdot \color{blue}{\frac{y}{\frac{607771387771}{1000000000000} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)}} \]

      2. lower-*.f64 N/A

         \[\leadsto b \cdot \color{blue}{\frac{y}{\frac{607771387771}{1000000000000} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)}} \]

      3. lower-/.f64 N/A

         \[\leadsto b \cdot \frac{y}{\color{blue}{\frac{607771387771}{1000000000000} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)}} \]

      4. +-commutative N/A

         \[\leadsto b \cdot \frac{y}{z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right) + \color{blue}{\frac{607771387771}{1000000000000}}} \]

      5. *-commutative N/A

         \[\leadsto b \cdot \frac{y}{\left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      6. +-commutative N/A

         \[\leadsto b \cdot \frac{y}{\left(z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right) + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      7. *-commutative N/A

         \[\leadsto b \cdot \frac{y}{\left(\left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      8. +-commutative N/A

         \[\leadsto b \cdot \frac{y}{\left(\left(z \cdot \left(\frac{15234687407}{1000000000} + z\right) + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      9. +-commutative N/A

         \[\leadsto b \cdot \frac{y}{\left(\left(z \cdot \left(z + \frac{15234687407}{1000000000}\right) + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      10. *-commutative N/A

          \[\leadsto b \cdot \frac{y}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

   4. Applied rewrites 50.0%

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

   5. Taylor expanded in z around 0

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

      1. lower-*.f64 48.6

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

   7. Applied rewrites 48.6%

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

   if +inf.0 < (/.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 0.0%

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

   2. Taylor expanded in z around inf

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

      1. +-commutative N/A

         \[\leadsto \frac{313060547623}{100000000000} \cdot y + \color{blue}{x} \]

      2. lower-fma.f64 96.7

         \[\leadsto \mathsf{fma}\left(3.13060547623, \color{blue}{y}, x\right) \]

   4. Applied rewrites 96.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(3.13060547623, y, x\right)} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 18: 72.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 1.6453555072203998 \cdot \left(b \cdot y\right)\\ t_2 := \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+143}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{+52}:\\ \;\;\;\;x\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* 1.6453555072203998 (* b y)))
        (t_2
         (/
          (*
           y
           (+
            (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z)
            b))
          (+
           (*
            (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721)
            z)
           0.607771387771))))
   (if (<= t_2 -2e+143)
     t_1
     (if (<= t_2 1e+52)
       x
       (if (<= t_2 INFINITY) t_1 (fma 3.13060547623 y x))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 1.6453555072203998 * (b * y);
	double t_2 = (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 tmp;
	if (t_2 <= -2e+143) {
		tmp = t_1;
	} else if (t_2 <= 1e+52) {
		tmp = x;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = fma(3.13060547623, y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(1.6453555072203998 * Float64(b * y))
	t_2 = 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))
	tmp = 0.0
	if (t_2 <= -2e+143)
		tmp = t_1;
	elseif (t_2 <= 1e+52)
		tmp = x;
	elseif (t_2 <= Inf)
		tmp = t_1;
	else
		tmp = fma(3.13060547623, y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(1.6453555072203998 * N[(b * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = 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]}, If[LessEqual[t$95$2, -2e+143], t$95$1, If[LessEqual[t$95$2, 1e+52], x, If[LessEqual[t$95$2, Infinity], t$95$1, N[(3.13060547623 * y + x), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.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))) < -2e143 or 9.9999999999999999e51 < (/.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 87.0%

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

   2. Taylor expanded in b around inf

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

      1. associate-/l* N/A

         \[\leadsto b \cdot \color{blue}{\frac{y}{\frac{607771387771}{1000000000000} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)}} \]

      2. lower-*.f64 N/A

         \[\leadsto b \cdot \color{blue}{\frac{y}{\frac{607771387771}{1000000000000} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)}} \]

      3. lower-/.f64 N/A

         \[\leadsto b \cdot \frac{y}{\color{blue}{\frac{607771387771}{1000000000000} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)}} \]

      4. +-commutative N/A

         \[\leadsto b \cdot \frac{y}{z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right) + \color{blue}{\frac{607771387771}{1000000000000}}} \]

      5. *-commutative N/A

         \[\leadsto b \cdot \frac{y}{\left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      6. +-commutative N/A

         \[\leadsto b \cdot \frac{y}{\left(z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right) + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      7. *-commutative N/A

         \[\leadsto b \cdot \frac{y}{\left(\left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      8. +-commutative N/A

         \[\leadsto b \cdot \frac{y}{\left(\left(z \cdot \left(\frac{15234687407}{1000000000} + z\right) + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      9. +-commutative N/A

         \[\leadsto b \cdot \frac{y}{\left(\left(z \cdot \left(z + \frac{15234687407}{1000000000}\right) + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      10. *-commutative N/A

          \[\leadsto b \cdot \frac{y}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

   4. Applied rewrites 50.7%

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

   5. Taylor expanded in z around 0

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

      1. lower-*.f64 N/A

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

      2. lower-*.f64 49.5

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

   7. Applied rewrites 49.5%

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

   if -2e143 < (/.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))) < 9.9999999999999999e51

   1. Initial program 99.7%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 66.1%

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

   if +inf.0 < (/.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 87.0%

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

   2. Taylor expanded in z around inf

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

      1. +-commutative N/A

         \[\leadsto \frac{313060547623}{100000000000} \cdot y + \color{blue}{x} \]

      2. lower-fma.f64 19.2

         \[\leadsto \mathsf{fma}\left(3.13060547623, \color{blue}{y}, x\right) \]

   4. Applied rewrites 19.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(3.13060547623, y, x\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 19: 62.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \leq 5 \cdot 10^{+286}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<=
      (/
       (*
        y
        (+
         (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z)
         b))
       (+
        (*
         (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721)
         z)
        0.607771387771))
      5e+286)
   x
   (fma 3.13060547623 y x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((y * ((((((((z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b)) / (((((((z + 15.234687407) * z) + 31.4690115749) * z) + 11.9400905721) * z) + 0.607771387771)) <= 5e+286) {
		tmp = x;
	} else {
		tmp = fma(3.13060547623, y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (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)) <= 5e+286)
		tmp = x;
	else
		tmp = fma(3.13060547623, y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[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], 5e+286], x, N[(3.13060547623 * y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.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))) < 5.0000000000000004e286

   1. Initial program 96.3%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 46.6%

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

   if 5.0000000000000004e286 < (/.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 12.8%

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

   2. Taylor expanded in z around inf

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

      1. +-commutative N/A

         \[\leadsto \frac{313060547623}{100000000000} \cdot y + \color{blue}{x} \]

      2. lower-fma.f64 83.3

         \[\leadsto \mathsf{fma}\left(3.13060547623, \color{blue}{y}, x\right) \]

   4. Applied rewrites 83.3%

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

Alternative 20: 44.8% accurate, 52.6× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 59.7%

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

2. Taylor expanded in x around inf

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

4. Applied rewrites 44.8%

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

Reproduce

herbie shell --seed 2025115 
(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))))