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

Percentage Accurate: 58.0% → 98.6%

Time: 6.2s

Alternatives: 14

Speedup: 3.3×

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = x + ((y * ((((((((z * 3.13060547623d0) + 11.1667541262d0) * z) + t) * z) + a) * z) + b)) / (((((((z + 15.234687407d0) * z) + 31.4690115749d0) * z) + 11.9400905721d0) * z) + 0.607771387771d0))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 58.0% 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: 98.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{\left(-a\right) - \mathsf{fma}\left(-15.234687407, 457.9610022158428 + t, 1112.0901850848957\right)}{z}, -1, t\right) + 457.9610022158428}{z}, -1, 36.52704169880642\right)}{z}, -1, 3.13060547623\right), y, x\right)\\ \mathbf{if}\;z \leq -4.8 \cdot 10^{+16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+33}:\\ \;\;\;\;x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (fma
          (fma
           (/
            (fma
             (/
              (+
               (fma
                (/
                 (-
                  (- a)
                  (fma
                   -15.234687407
                   (+ 457.9610022158428 t)
                   1112.0901850848957))
                 z)
                -1.0
                t)
               457.9610022158428)
              z)
             -1.0
             36.52704169880642)
            z)
           -1.0
           3.13060547623)
          y
          x)))
   (if (<= z -4.8e+16)
     t_1
     (if (<= z 8.2e+33)
       (+
        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_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(fma((fma(((fma(((-a - fma(-15.234687407, (457.9610022158428 + t), 1112.0901850848957)) / z), -1.0, t) + 457.9610022158428) / z), -1.0, 36.52704169880642) / z), -1.0, 3.13060547623), y, x);
	double tmp;
	if (z <= -4.8e+16) {
		tmp = t_1;
	} else if (z <= 8.2e+33) {
		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_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(fma(Float64(fma(Float64(Float64(fma(Float64(Float64(Float64(-a) - fma(-15.234687407, Float64(457.9610022158428 + t), 1112.0901850848957)) / z), -1.0, t) + 457.9610022158428) / z), -1.0, 36.52704169880642) / z), -1.0, 3.13060547623), y, x)
	tmp = 0.0
	if (z <= -4.8e+16)
		tmp = t_1;
	elseif (z <= 8.2e+33)
		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_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(N[(N[(N[(N[(N[((-a) - N[(-15.234687407 * N[(457.9610022158428 + t), $MachinePrecision] + 1112.0901850848957), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] * -1.0 + t), $MachinePrecision] + 457.9610022158428), $MachinePrecision] / z), $MachinePrecision] * -1.0 + 36.52704169880642), $MachinePrecision] / z), $MachinePrecision] * -1.0 + 3.13060547623), $MachinePrecision] * y + x), $MachinePrecision]}, If[LessEqual[z, -4.8e+16], t$95$1, If[LessEqual[z, 8.2e+33], 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$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.8e16 or 8.1999999999999999e33 < z

   1. Initial program 10.2%

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

   3. Applied rewrites 14.3%

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

   4. Taylor expanded in z around -inf

      \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{313060547623}{100000000000} + -1 \cdot \frac{\frac{3652704169880641883561}{100000000000000000000} + -1 \cdot \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + \left(t + -1 \cdot \frac{-1 \cdot a - \left(\frac{1112090185084895700201045470302189}{1000000000000000000000000000000} + \frac{-15234687407}{1000000000} \cdot \left(\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t\right)\right)}{z}\right)}{z}}{z}}, y, x\right) \]

   6. Applied rewrites 98.6%

      \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{\left(-a\right) - \mathsf{fma}\left(-15.234687407, 457.9610022158428 + t, 1112.0901850848957\right)}{z}, -1, t\right) + 457.9610022158428}{z}, -1, 36.52704169880642\right)}{z}, -1, 3.13060547623\right)}, y, x\right) \]

   if -4.8e16 < z < 8.1999999999999999e33

   1. Initial program 98.7%

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

Alternative 2: 63.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \leq 5 \cdot 10^{-131}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \end{array} \end{array} \]

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-131)
   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-131) {
		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-131)
		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-131], 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))) < 5.0000000000000004e-131

   1. Initial program 94.3%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 50.1%

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

   if 5.0000000000000004e-131 < (/.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 36.4%

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

   2. Taylor expanded in z around 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 71.2

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

   4. Applied rewrites 71.2%

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

Alternative 3: 99.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{\left(-a\right) - \mathsf{fma}\left(-15.234687407, 457.9610022158428 + t, 1112.0901850848957\right)}{z}, -1, t\right) + 457.9610022158428}{z}, -1, 36.52704169880642\right)}{z}, -1, 3.13060547623\right), y, x\right)\\ \mathbf{if}\;z \leq -4 \cdot 10^{+16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+34}:\\ \;\;\;\;\mathsf{fma}\left(\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(3.13060547623, z, 11.1667541262\right), z, t\right), z, a\right), z, b\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(15.234687407 + z, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (fma
          (fma
           (/
            (fma
             (/
              (+
               (fma
                (/
                 (-
                  (- a)
                  (fma
                   -15.234687407
                   (+ 457.9610022158428 t)
                   1112.0901850848957))
                 z)
                -1.0
                t)
               457.9610022158428)
              z)
             -1.0
             36.52704169880642)
            z)
           -1.0
           3.13060547623)
          y
          x)))
   (if (<= z -4e+16)
     t_1
     (if (<= z 2.1e+34)
       (fma
        (/
         (fma (fma (fma (fma 3.13060547623 z 11.1667541262) z t) z a) z b)
         (fma
          (fma (fma (+ 15.234687407 z) z 31.4690115749) z 11.9400905721)
          z
          0.607771387771))
        y
        x)
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(fma((fma(((fma(((-a - fma(-15.234687407, (457.9610022158428 + t), 1112.0901850848957)) / z), -1.0, t) + 457.9610022158428) / z), -1.0, 36.52704169880642) / z), -1.0, 3.13060547623), y, x);
	double tmp;
	if (z <= -4e+16) {
		tmp = t_1;
	} else if (z <= 2.1e+34) {
		tmp = fma((fma(fma(fma(fma(3.13060547623, z, 11.1667541262), z, t), z, a), z, b) / fma(fma(fma((15.234687407 + z), z, 31.4690115749), z, 11.9400905721), z, 0.607771387771)), y, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(fma(Float64(fma(Float64(Float64(fma(Float64(Float64(Float64(-a) - fma(-15.234687407, Float64(457.9610022158428 + t), 1112.0901850848957)) / z), -1.0, t) + 457.9610022158428) / z), -1.0, 36.52704169880642) / z), -1.0, 3.13060547623), y, x)
	tmp = 0.0
	if (z <= -4e+16)
		tmp = t_1;
	elseif (z <= 2.1e+34)
		tmp = fma(Float64(fma(fma(fma(fma(3.13060547623, z, 11.1667541262), z, t), z, a), z, b) / fma(fma(fma(Float64(15.234687407 + z), z, 31.4690115749), z, 11.9400905721), z, 0.607771387771)), y, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(N[(N[(N[(N[(N[((-a) - N[(-15.234687407 * N[(457.9610022158428 + t), $MachinePrecision] + 1112.0901850848957), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] * -1.0 + t), $MachinePrecision] + 457.9610022158428), $MachinePrecision] / z), $MachinePrecision] * -1.0 + 36.52704169880642), $MachinePrecision] / z), $MachinePrecision] * -1.0 + 3.13060547623), $MachinePrecision] * y + x), $MachinePrecision]}, If[LessEqual[z, -4e+16], t$95$1, If[LessEqual[z, 2.1e+34], N[(N[(N[(N[(N[(N[(3.13060547623 * z + 11.1667541262), $MachinePrecision] * z + t), $MachinePrecision] * z + a), $MachinePrecision] * z + b), $MachinePrecision] / N[(N[(N[(N[(15.234687407 + z), $MachinePrecision] * z + 31.4690115749), $MachinePrecision] * z + 11.9400905721), $MachinePrecision] * z + 0.607771387771), $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -4e16 or 2.10000000000000017e34 < z

   1. Initial program 10.2%

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

   3. Applied rewrites 14.3%

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

   4. Taylor expanded in z around -inf

      \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{313060547623}{100000000000} + -1 \cdot \frac{\frac{3652704169880641883561}{100000000000000000000} + -1 \cdot \frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + \left(t + -1 \cdot \frac{-1 \cdot a - \left(\frac{1112090185084895700201045470302189}{1000000000000000000000000000000} + \frac{-15234687407}{1000000000} \cdot \left(\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t\right)\right)}{z}\right)}{z}}{z}}, y, x\right) \]

   6. Applied rewrites 98.6%

      \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\frac{\left(-a\right) - \mathsf{fma}\left(-15.234687407, 457.9610022158428 + t, 1112.0901850848957\right)}{z}, -1, t\right) + 457.9610022158428}{z}, -1, 36.52704169880642\right)}{z}, -1, 3.13060547623\right)}, y, x\right) \]

   if -4e16 < z < 2.10000000000000017e34

   1. Initial program 98.6%

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

   3. Applied rewrites 99.4%

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

Alternative 4: 98.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\left(\frac{457.9610022158428 + t}{z \cdot z} + 3.13060547623\right) - \frac{36.52704169880642}{z}, y, x\right)\\ \mathbf{if}\;z \leq -2.6 \cdot 10^{+46}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+34}:\\ \;\;\;\;\mathsf{fma}\left(\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(3.13060547623, z, 11.1667541262\right), z, t\right), z, a\right), z, b\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(15.234687407 + z, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (fma
          (-
           (+ (/ (+ 457.9610022158428 t) (* z z)) 3.13060547623)
           (/ 36.52704169880642 z))
          y
          x)))
   (if (<= z -2.6e+46)
     t_1
     (if (<= z 3.2e+34)
       (fma
        (/
         (fma (fma (fma (fma 3.13060547623 z 11.1667541262) z t) z a) z b)
         (fma
          (fma (fma (+ 15.234687407 z) z 31.4690115749) z 11.9400905721)
          z
          0.607771387771))
        y
        x)
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(((((457.9610022158428 + t) / (z * z)) + 3.13060547623) - (36.52704169880642 / z)), y, x);
	double tmp;
	if (z <= -2.6e+46) {
		tmp = t_1;
	} else if (z <= 3.2e+34) {
		tmp = fma((fma(fma(fma(fma(3.13060547623, z, 11.1667541262), z, t), z, a), z, b) / fma(fma(fma((15.234687407 + z), z, 31.4690115749), z, 11.9400905721), z, 0.607771387771)), y, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(Float64(Float64(Float64(457.9610022158428 + t) / Float64(z * z)) + 3.13060547623) - Float64(36.52704169880642 / z)), y, x)
	tmp = 0.0
	if (z <= -2.6e+46)
		tmp = t_1;
	elseif (z <= 3.2e+34)
		tmp = fma(Float64(fma(fma(fma(fma(3.13060547623, z, 11.1667541262), z, t), z, a), z, b) / fma(fma(fma(Float64(15.234687407 + z), z, 31.4690115749), z, 11.9400905721), z, 0.607771387771)), y, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(N[(457.9610022158428 + t), $MachinePrecision] / N[(z * z), $MachinePrecision]), $MachinePrecision] + 3.13060547623), $MachinePrecision] - N[(36.52704169880642 / z), $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision]}, If[LessEqual[z, -2.6e+46], t$95$1, If[LessEqual[z, 3.2e+34], N[(N[(N[(N[(N[(N[(3.13060547623 * z + 11.1667541262), $MachinePrecision] * z + t), $MachinePrecision] * z + a), $MachinePrecision] * z + b), $MachinePrecision] / N[(N[(N[(N[(15.234687407 + z), $MachinePrecision] * z + 31.4690115749), $MachinePrecision] * z + 11.9400905721), $MachinePrecision] * z + 0.607771387771), $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.60000000000000013e46 or 3.1999999999999998e34 < z

   1. Initial program 6.9%

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

   3. Applied rewrites 10.4%

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

   4. Taylor expanded in z around inf

      \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\frac{313060547623}{100000000000} + \left(\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000}}{{z}^{2}} + \frac{t}{{z}^{2}}\right)\right) - \frac{3652704169880641883561}{100000000000000000000} \cdot \frac{1}{z}}, y, x\right) \]
   5. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\left(\frac{313060547623}{100000000000} + \left(\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000}}{{z}^{2}} + \frac{t}{{z}^{2}}\right)\right) - \color{blue}{\frac{3652704169880641883561}{100000000000000000000} \cdot \frac{1}{z}}, y, x\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(\left(\left(\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000}}{{z}^{2}} + \frac{t}{{z}^{2}}\right) + \frac{313060547623}{100000000000}\right) - \color{blue}{\frac{3652704169880641883561}{100000000000000000000}} \cdot \frac{1}{z}, y, x\right) \]

      3. lower-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(\left(\left(\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000}}{{z}^{2}} + \frac{t}{{z}^{2}}\right) + \frac{313060547623}{100000000000}\right) - \color{blue}{\frac{3652704169880641883561}{100000000000000000000}} \cdot \frac{1}{z}, y, x\right) \]

      4. div-add-rev N/A

         \[\leadsto \mathsf{fma}\left(\left(\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{{z}^{2}} + \frac{313060547623}{100000000000}\right) - \frac{3652704169880641883561}{100000000000000000000} \cdot \frac{1}{z}, y, x\right) \]

      5. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\left(\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{{z}^{2}} + \frac{313060547623}{100000000000}\right) - \frac{3652704169880641883561}{100000000000000000000} \cdot \frac{1}{z}, y, x\right) \]

      6. lower-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(\left(\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{{z}^{2}} + \frac{313060547623}{100000000000}\right) - \frac{3652704169880641883561}{100000000000000000000} \cdot \frac{1}{z}, y, x\right) \]

      7. pow2 N/A

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

      8. lift-*.f64 N/A

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. lower-/.f64 97.6

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

   6. Applied rewrites 97.6%

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

   if -2.60000000000000013e46 < z < 3.1999999999999998e34

   1. Initial program 97.7%

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

   3. Applied rewrites 99.0%

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

Alternative 5: 97.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\left(\frac{457.9610022158428 + t}{z \cdot z} + 3.13060547623\right) - \frac{36.52704169880642}{z}, y, x\right)\\ \mathbf{if}\;z \leq -5.8 \cdot 10^{+35}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 0.0265:\\ \;\;\;\;\mathsf{fma}\left(\frac{\mathsf{fma}\left(\mathsf{fma}\left(t, z, a\right), z, b\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(15.234687407 + z, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (fma
          (-
           (+ (/ (+ 457.9610022158428 t) (* z z)) 3.13060547623)
           (/ 36.52704169880642 z))
          y
          x)))
   (if (<= z -5.8e+35)
     t_1
     (if (<= z 0.0265)
       (fma
        (/
         (fma (fma t z a) z b)
         (fma
          (fma (fma (+ 15.234687407 z) z 31.4690115749) z 11.9400905721)
          z
          0.607771387771))
        y
        x)
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(((((457.9610022158428 + t) / (z * z)) + 3.13060547623) - (36.52704169880642 / z)), y, x);
	double tmp;
	if (z <= -5.8e+35) {
		tmp = t_1;
	} else if (z <= 0.0265) {
		tmp = fma((fma(fma(t, z, a), z, b) / fma(fma(fma((15.234687407 + z), z, 31.4690115749), z, 11.9400905721), z, 0.607771387771)), y, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(Float64(Float64(Float64(457.9610022158428 + t) / Float64(z * z)) + 3.13060547623) - Float64(36.52704169880642 / z)), y, x)
	tmp = 0.0
	if (z <= -5.8e+35)
		tmp = t_1;
	elseif (z <= 0.0265)
		tmp = fma(Float64(fma(fma(t, z, a), z, b) / fma(fma(fma(Float64(15.234687407 + z), z, 31.4690115749), z, 11.9400905721), z, 0.607771387771)), y, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(N[(457.9610022158428 + t), $MachinePrecision] / N[(z * z), $MachinePrecision]), $MachinePrecision] + 3.13060547623), $MachinePrecision] - N[(36.52704169880642 / z), $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision]}, If[LessEqual[z, -5.8e+35], t$95$1, If[LessEqual[z, 0.0265], N[(N[(N[(N[(t * z + a), $MachinePrecision] * z + b), $MachinePrecision] / N[(N[(N[(N[(15.234687407 + z), $MachinePrecision] * z + 31.4690115749), $MachinePrecision] * z + 11.9400905721), $MachinePrecision] * z + 0.607771387771), $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.79999999999999989e35 or 0.0264999999999999993 < z

   1. Initial program 12.1%

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

   3. Applied rewrites 16.3%

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

   4. Taylor expanded in z around inf

      \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\frac{313060547623}{100000000000} + \left(\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000}}{{z}^{2}} + \frac{t}{{z}^{2}}\right)\right) - \frac{3652704169880641883561}{100000000000000000000} \cdot \frac{1}{z}}, y, x\right) \]
   5. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\left(\frac{313060547623}{100000000000} + \left(\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000}}{{z}^{2}} + \frac{t}{{z}^{2}}\right)\right) - \color{blue}{\frac{3652704169880641883561}{100000000000000000000} \cdot \frac{1}{z}}, y, x\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(\left(\left(\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000}}{{z}^{2}} + \frac{t}{{z}^{2}}\right) + \frac{313060547623}{100000000000}\right) - \color{blue}{\frac{3652704169880641883561}{100000000000000000000}} \cdot \frac{1}{z}, y, x\right) \]

      3. lower-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(\left(\left(\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000}}{{z}^{2}} + \frac{t}{{z}^{2}}\right) + \frac{313060547623}{100000000000}\right) - \color{blue}{\frac{3652704169880641883561}{100000000000000000000}} \cdot \frac{1}{z}, y, x\right) \]

      4. div-add-rev N/A

         \[\leadsto \mathsf{fma}\left(\left(\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{{z}^{2}} + \frac{313060547623}{100000000000}\right) - \frac{3652704169880641883561}{100000000000000000000} \cdot \frac{1}{z}, y, x\right) \]

      5. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\left(\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{{z}^{2}} + \frac{313060547623}{100000000000}\right) - \frac{3652704169880641883561}{100000000000000000000} \cdot \frac{1}{z}, y, x\right) \]

      6. lower-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(\left(\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{{z}^{2}} + \frac{313060547623}{100000000000}\right) - \frac{3652704169880641883561}{100000000000000000000} \cdot \frac{1}{z}, y, x\right) \]

      7. pow2 N/A

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

      8. lift-*.f64 N/A

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. lower-/.f64 95.3

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

   6. Applied rewrites 95.3%

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

   if -5.79999999999999989e35 < z < 0.0264999999999999993

   1. Initial program 98.9%

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

   3. Applied rewrites 99.4%

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

   4. Taylor expanded in z around 0

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

   6. Applied rewrites 98.5%

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

Alternative 6: 96.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\left(\frac{457.9610022158428 + t}{z \cdot z} + 3.13060547623\right) - \frac{36.52704169880642}{z}, y, x\right)\\ \mathbf{if}\;z \leq -5.8 \cdot 10^{+35}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 0.0265:\\ \;\;\;\;\mathsf{fma}\left(\frac{\mathsf{fma}\left(\mathsf{fma}\left(t, z, a\right), z, b\right)}{\mathsf{fma}\left(\mathsf{fma}\left(z \cdot z, z, 11.9400905721\right), z, 0.607771387771\right)}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (fma
          (-
           (+ (/ (+ 457.9610022158428 t) (* z z)) 3.13060547623)
           (/ 36.52704169880642 z))
          y
          x)))
   (if (<= z -5.8e+35)
     t_1
     (if (<= z 0.0265)
       (fma
        (/
         (fma (fma t z a) z b)
         (fma (fma (* z z) z 11.9400905721) z 0.607771387771))
        y
        x)
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(((((457.9610022158428 + t) / (z * z)) + 3.13060547623) - (36.52704169880642 / z)), y, x);
	double tmp;
	if (z <= -5.8e+35) {
		tmp = t_1;
	} else if (z <= 0.0265) {
		tmp = fma((fma(fma(t, z, a), z, b) / fma(fma((z * z), z, 11.9400905721), z, 0.607771387771)), y, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(Float64(Float64(Float64(457.9610022158428 + t) / Float64(z * z)) + 3.13060547623) - Float64(36.52704169880642 / z)), y, x)
	tmp = 0.0
	if (z <= -5.8e+35)
		tmp = t_1;
	elseif (z <= 0.0265)
		tmp = fma(Float64(fma(fma(t, z, a), z, b) / fma(fma(Float64(z * z), z, 11.9400905721), z, 0.607771387771)), y, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(N[(457.9610022158428 + t), $MachinePrecision] / N[(z * z), $MachinePrecision]), $MachinePrecision] + 3.13060547623), $MachinePrecision] - N[(36.52704169880642 / z), $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision]}, If[LessEqual[z, -5.8e+35], t$95$1, If[LessEqual[z, 0.0265], N[(N[(N[(N[(t * z + a), $MachinePrecision] * z + b), $MachinePrecision] / N[(N[(N[(z * z), $MachinePrecision] * z + 11.9400905721), $MachinePrecision] * z + 0.607771387771), $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.79999999999999989e35 or 0.0264999999999999993 < z

   1. Initial program 12.1%

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

   3. Applied rewrites 16.3%

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

   4. Taylor expanded in z around inf

      \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\frac{313060547623}{100000000000} + \left(\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000}}{{z}^{2}} + \frac{t}{{z}^{2}}\right)\right) - \frac{3652704169880641883561}{100000000000000000000} \cdot \frac{1}{z}}, y, x\right) \]
   5. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\left(\frac{313060547623}{100000000000} + \left(\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000}}{{z}^{2}} + \frac{t}{{z}^{2}}\right)\right) - \color{blue}{\frac{3652704169880641883561}{100000000000000000000} \cdot \frac{1}{z}}, y, x\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(\left(\left(\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000}}{{z}^{2}} + \frac{t}{{z}^{2}}\right) + \frac{313060547623}{100000000000}\right) - \color{blue}{\frac{3652704169880641883561}{100000000000000000000}} \cdot \frac{1}{z}, y, x\right) \]

      3. lower-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(\left(\left(\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000}}{{z}^{2}} + \frac{t}{{z}^{2}}\right) + \frac{313060547623}{100000000000}\right) - \color{blue}{\frac{3652704169880641883561}{100000000000000000000}} \cdot \frac{1}{z}, y, x\right) \]

      4. div-add-rev N/A

         \[\leadsto \mathsf{fma}\left(\left(\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{{z}^{2}} + \frac{313060547623}{100000000000}\right) - \frac{3652704169880641883561}{100000000000000000000} \cdot \frac{1}{z}, y, x\right) \]

      5. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\left(\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{{z}^{2}} + \frac{313060547623}{100000000000}\right) - \frac{3652704169880641883561}{100000000000000000000} \cdot \frac{1}{z}, y, x\right) \]

      6. lower-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(\left(\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{{z}^{2}} + \frac{313060547623}{100000000000}\right) - \frac{3652704169880641883561}{100000000000000000000} \cdot \frac{1}{z}, y, x\right) \]

      7. pow2 N/A

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

      8. lift-*.f64 N/A

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. lower-/.f64 95.3

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

   6. Applied rewrites 95.3%

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

   if -5.79999999999999989e35 < z < 0.0264999999999999993

   1. Initial program 98.9%

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

   3. Applied rewrites 99.4%

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

   4. Taylor expanded in z around 0

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

   6. Applied rewrites 98.5%

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

   7. Taylor expanded in z around inf

      \[\leadsto \mathsf{fma}\left(\frac{\mathsf{fma}\left(\mathsf{fma}\left(t, z, a\right), z, b\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\color{blue}{{z}^{2}}, z, \frac{119400905721}{10000000000}\right), z, \frac{607771387771}{1000000000000}\right)}, y, x\right) \]
   8. Step-by-step derivation

      1. pow2 N/A

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

      2. lift-*.f64 97.7

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

   9. Applied rewrites 97.7%

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

Alternative 7: 95.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\left(\frac{457.9610022158428 + t}{z \cdot z} + 3.13060547623\right) - \frac{36.52704169880642}{z}, y, x\right)\\ \mathbf{if}\;z \leq -7.5 \cdot 10^{+14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 0.0265:\\ \;\;\;\;\mathsf{fma}\left(\frac{\mathsf{fma}\left(\mathsf{fma}\left(t, z, a\right), z, b\right)}{\mathsf{fma}\left(11.9400905721, z, 0.607771387771\right)}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (fma
          (-
           (+ (/ (+ 457.9610022158428 t) (* z z)) 3.13060547623)
           (/ 36.52704169880642 z))
          y
          x)))
   (if (<= z -7.5e+14)
     t_1
     (if (<= z 0.0265)
       (fma (/ (fma (fma t z a) z b) (fma 11.9400905721 z 0.607771387771)) y x)
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(((((457.9610022158428 + t) / (z * z)) + 3.13060547623) - (36.52704169880642 / z)), y, x);
	double tmp;
	if (z <= -7.5e+14) {
		tmp = t_1;
	} else if (z <= 0.0265) {
		tmp = fma((fma(fma(t, z, a), z, b) / fma(11.9400905721, z, 0.607771387771)), y, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(Float64(Float64(Float64(457.9610022158428 + t) / Float64(z * z)) + 3.13060547623) - Float64(36.52704169880642 / z)), y, x)
	tmp = 0.0
	if (z <= -7.5e+14)
		tmp = t_1;
	elseif (z <= 0.0265)
		tmp = fma(Float64(fma(fma(t, z, a), z, b) / fma(11.9400905721, z, 0.607771387771)), y, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(N[(457.9610022158428 + t), $MachinePrecision] / N[(z * z), $MachinePrecision]), $MachinePrecision] + 3.13060547623), $MachinePrecision] - N[(36.52704169880642 / z), $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision]}, If[LessEqual[z, -7.5e+14], t$95$1, If[LessEqual[z, 0.0265], N[(N[(N[(N[(t * z + a), $MachinePrecision] * z + b), $MachinePrecision] / N[(11.9400905721 * z + 0.607771387771), $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -7.5e14 or 0.0264999999999999993 < z

   1. Initial program 14.3%

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

   3. Applied rewrites 18.9%

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

   4. Taylor expanded in z around inf

      \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\frac{313060547623}{100000000000} + \left(\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000}}{{z}^{2}} + \frac{t}{{z}^{2}}\right)\right) - \frac{3652704169880641883561}{100000000000000000000} \cdot \frac{1}{z}}, y, x\right) \]
   5. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\left(\frac{313060547623}{100000000000} + \left(\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000}}{{z}^{2}} + \frac{t}{{z}^{2}}\right)\right) - \color{blue}{\frac{3652704169880641883561}{100000000000000000000} \cdot \frac{1}{z}}, y, x\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{fma}\left(\left(\left(\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000}}{{z}^{2}} + \frac{t}{{z}^{2}}\right) + \frac{313060547623}{100000000000}\right) - \color{blue}{\frac{3652704169880641883561}{100000000000000000000}} \cdot \frac{1}{z}, y, x\right) \]

      3. lower-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(\left(\left(\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000}}{{z}^{2}} + \frac{t}{{z}^{2}}\right) + \frac{313060547623}{100000000000}\right) - \color{blue}{\frac{3652704169880641883561}{100000000000000000000}} \cdot \frac{1}{z}, y, x\right) \]

      4. div-add-rev N/A

         \[\leadsto \mathsf{fma}\left(\left(\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{{z}^{2}} + \frac{313060547623}{100000000000}\right) - \frac{3652704169880641883561}{100000000000000000000} \cdot \frac{1}{z}, y, x\right) \]

      5. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\left(\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{{z}^{2}} + \frac{313060547623}{100000000000}\right) - \frac{3652704169880641883561}{100000000000000000000} \cdot \frac{1}{z}, y, x\right) \]

      6. lower-+.f64 N/A

         \[\leadsto \mathsf{fma}\left(\left(\frac{\frac{45796100221584283915100827016327}{100000000000000000000000000000} + t}{{z}^{2}} + \frac{313060547623}{100000000000}\right) - \frac{3652704169880641883561}{100000000000000000000} \cdot \frac{1}{z}, y, x\right) \]

      7. pow2 N/A

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

      8. lift-*.f64 N/A

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. lower-/.f64 94.5

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

   6. Applied rewrites 94.5%

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

   if -7.5e14 < z < 0.0264999999999999993

   1. Initial program 99.6%

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

   3. Applied rewrites 99.7%

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

   4. Taylor expanded in z around 0

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

   6. Applied rewrites 99.0%

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

   7. Taylor expanded in z around 0

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

   9. Applied rewrites 97.2%

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

Alternative 8: 92.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+88}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{+14}:\\ \;\;\;\;x + \frac{\frac{y}{z}}{z} \cdot t\\ \mathbf{elif}\;z \leq 2.95 \cdot 10^{+40}:\\ \;\;\;\;\mathsf{fma}\left(\frac{\mathsf{fma}\left(\mathsf{fma}\left(t, z, a\right), z, b\right)}{\mathsf{fma}\left(11.9400905721, z, 0.607771387771\right)}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -3.4e+88)
   (fma 3.13060547623 y x)
   (if (<= z -7.5e+14)
     (+ x (* (/ (/ y z) z) t))
     (if (<= z 2.95e+40)
       (fma (/ (fma (fma t z a) z b) (fma 11.9400905721 z 0.607771387771)) y 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 <= -3.4e+88) {
		tmp = fma(3.13060547623, y, x);
	} else if (z <= -7.5e+14) {
		tmp = x + (((y / z) / z) * t);
	} else if (z <= 2.95e+40) {
		tmp = fma((fma(fma(t, z, a), z, b) / fma(11.9400905721, z, 0.607771387771)), y, x);
	} else {
		tmp = fma(3.13060547623, y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -3.4e+88)
		tmp = fma(3.13060547623, y, x);
	elseif (z <= -7.5e+14)
		tmp = Float64(x + Float64(Float64(Float64(y / z) / z) * t));
	elseif (z <= 2.95e+40)
		tmp = fma(Float64(fma(fma(t, z, a), z, b) / fma(11.9400905721, z, 0.607771387771)), y, x);
	else
		tmp = fma(3.13060547623, y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -3.4e+88], N[(3.13060547623 * y + x), $MachinePrecision], If[LessEqual[z, -7.5e+14], N[(x + N[(N[(N[(y / z), $MachinePrecision] / z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.95e+40], N[(N[(N[(N[(t * z + a), $MachinePrecision] * z + b), $MachinePrecision] / N[(11.9400905721 * z + 0.607771387771), $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision], N[(3.13060547623 * y + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.40000000000000004e88 or 2.94999999999999995e40 < z

   1. Initial program 3.9%

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

   2. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-fma.f64 95.7

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

   4. Applied rewrites 95.7%

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

   if -3.40000000000000004e88 < z < -7.5e14

   1. Initial program 51.9%

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

   2. Taylor expanded in z around inf

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

      1. lower--.f64 N/A

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

   4. Applied rewrites 79.3%

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

   5. Taylor expanded in t around inf

      \[\leadsto x + \frac{t \cdot y}{\color{blue}{{z}^{2}}} \]
   6. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto x + t \cdot \frac{y}{\color{blue}{{z}^{2}}} \]

      2. pow2 N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lift-*.f64 N/A

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

      7. lift-/.f64 N/A

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

      8. pow2 N/A

         \[\leadsto x + \frac{y}{{z}^{2}} \cdot t \]

      9. lower-*.f64 N/A

         \[\leadsto x + \frac{y}{{z}^{2}} \cdot t \]

      10. pow2 N/A

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

      11. associate-/r* N/A

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

      12. lower-/.f64 N/A

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

      13. lift-/.f64 57.9

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

   7. Applied rewrites 57.9%

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

   if -7.5e14 < z < 2.94999999999999995e40

   1. Initial program 98.5%

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

   3. Applied rewrites 99.4%

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

   4. Taylor expanded in z around 0

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

   6. Applied rewrites 98.1%

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

   7. Taylor expanded in z around 0

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

   9. Applied rewrites 94.5%

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

Alternative 9: 93.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+46}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \mathbf{elif}\;z \leq 2.95 \cdot 10^{+40}:\\ \;\;\;\;\mathsf{fma}\left(\frac{\mathsf{fma}\left(\mathsf{fma}\left(t, z, a\right), z, b\right)}{\mathsf{fma}\left(\mathsf{fma}\left(31.4690115749, z, 11.9400905721\right), z, 0.607771387771\right)}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -3.7e+46)
   (fma 3.13060547623 y x)
   (if (<= z 2.95e+40)
     (fma
      (/
       (fma (fma t z a) z b)
       (fma (fma 31.4690115749 z 11.9400905721) z 0.607771387771))
      y
      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 <= -3.7e+46) {
		tmp = fma(3.13060547623, y, x);
	} else if (z <= 2.95e+40) {
		tmp = fma((fma(fma(t, z, a), z, b) / fma(fma(31.4690115749, z, 11.9400905721), z, 0.607771387771)), y, x);
	} else {
		tmp = fma(3.13060547623, y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -3.7e+46)
		tmp = fma(3.13060547623, y, x);
	elseif (z <= 2.95e+40)
		tmp = fma(Float64(fma(fma(t, z, a), z, b) / fma(fma(31.4690115749, z, 11.9400905721), z, 0.607771387771)), y, x);
	else
		tmp = fma(3.13060547623, y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -3.7e+46], N[(3.13060547623 * y + x), $MachinePrecision], If[LessEqual[z, 2.95e+40], N[(N[(N[(N[(t * z + a), $MachinePrecision] * z + b), $MachinePrecision] / N[(N[(31.4690115749 * z + 11.9400905721), $MachinePrecision] * z + 0.607771387771), $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision], N[(3.13060547623 * y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.6999999999999999e46 or 2.94999999999999995e40 < z

   1. Initial program 6.2%

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

   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 93.7

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

   4. Applied rewrites 93.7%

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

   if -3.6999999999999999e46 < z < 2.94999999999999995e40

   1. Initial program 97.5%

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

   3. Applied rewrites 99.0%

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

   4. Taylor expanded in z around 0

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

   6. Applied rewrites 97.2%

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

   7. Taylor expanded in z around 0

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

   9. Applied rewrites 93.3%

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

Alternative 10: 93.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+46}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \mathbf{elif}\;z \leq 2.95 \cdot 10^{+40}:\\ \;\;\;\;\mathsf{fma}\left(\frac{\mathsf{fma}\left(\mathsf{fma}\left(t, z, a\right), z, b\right)}{0.607771387771}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -3.6e+46)
   (fma 3.13060547623 y x)
   (if (<= z 2.95e+40)
     (fma (/ (fma (fma t z a) z b) 0.607771387771) y 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+46) {
		tmp = fma(3.13060547623, y, x);
	} else if (z <= 2.95e+40) {
		tmp = fma((fma(fma(t, z, a), z, b) / 0.607771387771), y, 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+46)
		tmp = fma(3.13060547623, y, x);
	elseif (z <= 2.95e+40)
		tmp = fma(Float64(fma(fma(t, z, a), z, b) / 0.607771387771), y, 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+46], N[(3.13060547623 * y + x), $MachinePrecision], If[LessEqual[z, 2.95e+40], N[(N[(N[(N[(t * z + a), $MachinePrecision] * z + b), $MachinePrecision] / 0.607771387771), $MachinePrecision] * y + x), $MachinePrecision], N[(3.13060547623 * y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.5999999999999999e46 or 2.94999999999999995e40 < z

   1. Initial program 6.2%

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

   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 93.7

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

   4. Applied rewrites 93.7%

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

   if -3.5999999999999999e46 < z < 2.94999999999999995e40

   1. Initial program 97.5%

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

   3. Applied rewrites 99.0%

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

   4. Taylor expanded in z around 0

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

   6. Applied rewrites 97.2%

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

   7. Taylor expanded in z around 0

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

   9. Applied rewrites 92.4%

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

Alternative 11: 90.2% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+46}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+38}:\\ \;\;\;\;\mathsf{fma}\left(\frac{\mathsf{fma}\left(a, z, b\right)}{0.607771387771}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -3.6e+46)
   (fma 3.13060547623 y x)
   (if (<= z 1.55e+38)
     (fma (/ (fma a z b) 0.607771387771) y 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+46) {
		tmp = fma(3.13060547623, y, x);
	} else if (z <= 1.55e+38) {
		tmp = fma((fma(a, z, b) / 0.607771387771), y, 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+46)
		tmp = fma(3.13060547623, y, x);
	elseif (z <= 1.55e+38)
		tmp = fma(Float64(fma(a, z, b) / 0.607771387771), y, 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+46], N[(3.13060547623 * y + x), $MachinePrecision], If[LessEqual[z, 1.55e+38], N[(N[(N[(a * z + b), $MachinePrecision] / 0.607771387771), $MachinePrecision] * y + x), $MachinePrecision], N[(3.13060547623 * y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.5999999999999999e46 or 1.55000000000000009e38 < z

   1. Initial program 6.5%

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

   2. Taylor expanded in z around 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 93.6

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

   4. Applied rewrites 93.6%

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

   if -3.5999999999999999e46 < z < 1.55000000000000009e38

   1. Initial program 97.6%

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

   3. Applied rewrites 99.0%

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

   4. Taylor expanded in z around 0

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

   6. Applied rewrites 97.3%

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

   7. Taylor expanded in z around 0

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

   9. Applied rewrites 92.6%

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

   10. Taylor expanded in z around 0

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

   12. Applied rewrites 87.6%

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

Alternative 12: 83.4% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.55 \cdot 10^{+46}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-5}:\\ \;\;\;\;\mathsf{fma}\left(1.6453555072203998 \cdot b, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -3.55e+46)
   (fma 3.13060547623 y x)
   (if (<= z 7e-5)
     (fma (* 1.6453555072203998 b) y 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 <= -3.55e+46) {
		tmp = fma(3.13060547623, y, x);
	} else if (z <= 7e-5) {
		tmp = fma((1.6453555072203998 * b), y, x);
	} else {
		tmp = fma(3.13060547623, y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -3.55e+46)
		tmp = fma(3.13060547623, y, x);
	elseif (z <= 7e-5)
		tmp = fma(Float64(1.6453555072203998 * b), y, x);
	else
		tmp = fma(3.13060547623, y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -3.55e+46], N[(3.13060547623 * y + x), $MachinePrecision], If[LessEqual[z, 7e-5], N[(N[(1.6453555072203998 * b), $MachinePrecision] * y + x), $MachinePrecision], N[(3.13060547623 * y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.55e46 or 6.9999999999999994e-5 < z

   1. Initial program 11.4%

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

   2. Taylor expanded in z around 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 90.2

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

   4. Applied rewrites 90.2%

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

   if -3.55e46 < z < 6.9999999999999994e-5

   1. Initial program 98.5%

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

   3. Applied rewrites 99.2%

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

   4. Taylor expanded in z around 0

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

      1. lower-*.f64 77.5

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

   6. Applied rewrites 77.5%

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

Alternative 13: 83.4% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.55 \cdot 10^{+46}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-5}:\\ \;\;\;\;\mathsf{fma}\left(b \cdot y, 1.6453555072203998, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -3.55e+46)
   (fma 3.13060547623 y x)
   (if (<= z 7e-5)
     (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 (z <= -3.55e+46) {
		tmp = fma(3.13060547623, y, x);
	} else if (z <= 7e-5) {
		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 (z <= -3.55e+46)
		tmp = fma(3.13060547623, y, x);
	elseif (z <= 7e-5)
		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[z, -3.55e+46], N[(3.13060547623 * y + x), $MachinePrecision], If[LessEqual[z, 7e-5], N[(N[(b * y), $MachinePrecision] * 1.6453555072203998 + x), $MachinePrecision], N[(3.13060547623 * y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.55e46 or 6.9999999999999994e-5 < z

   1. Initial program 11.4%

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

   2. Taylor expanded in z around 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 90.2

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

   4. Applied rewrites 90.2%

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

   if -3.55e46 < z < 6.9999999999999994e-5

   1. Initial program 98.5%

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

   2. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + \frac{1000000000000}{607771387771} \cdot \left(b \cdot y\right)} \]
   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 77.6

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

   4. Applied rewrites 77.6%

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

Alternative 14: 45.3% accurate, 79.0× 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 58.0%

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

2. Taylor expanded in x around inf

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

4. Applied rewrites 45.3%

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

Developer Target 1: 98.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\left(3.13060547623 - \frac{36.527041698806414}{z}\right) + \frac{t}{z \cdot z}\right) \cdot \frac{y}{1}\\ \mathbf{if}\;z < -6.499344996252632 \cdot 10^{+53}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z < 7.066965436914287 \cdot 10^{+59}:\\ \;\;\;\;x + \frac{y}{\frac{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}{\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+
          x
          (*
           (+ (- 3.13060547623 (/ 36.527041698806414 z)) (/ t (* z z)))
           (/ y 1.0)))))
   (if (< z -6.499344996252632e+53)
     t_1
     (if (< z 7.066965436914287e+59)
       (+
        x
        (/
         y
         (/
          (+
           (*
            (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721)
            z)
           0.607771387771)
          (+
           (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z)
           b))))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (((3.13060547623 - (36.527041698806414 / z)) + (t / (z * z))) * (y / 1.0));
	double tmp;
	if (z < -6.499344996252632e+53) {
		tmp = t_1;
	} else if (z < 7.066965436914287e+59) {
		tmp = x + (y / ((((((((z + 15.234687407) * z) + 31.4690115749) * z) + 11.9400905721) * z) + 0.607771387771) / ((((((((z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (((3.13060547623d0 - (36.527041698806414d0 / z)) + (t / (z * z))) * (y / 1.0d0))
    if (z < (-6.499344996252632d+53)) then
        tmp = t_1
    else if (z < 7.066965436914287d+59) then
        tmp = x + (y / ((((((((z + 15.234687407d0) * z) + 31.4690115749d0) * z) + 11.9400905721d0) * z) + 0.607771387771d0) / ((((((((z * 3.13060547623d0) + 11.1667541262d0) * z) + t) * z) + a) * z) + b)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (((3.13060547623 - (36.527041698806414 / z)) + (t / (z * z))) * (y / 1.0));
	double tmp;
	if (z < -6.499344996252632e+53) {
		tmp = t_1;
	} else if (z < 7.066965436914287e+59) {
		tmp = x + (y / ((((((((z + 15.234687407) * z) + 31.4690115749) * z) + 11.9400905721) * z) + 0.607771387771) / ((((((((z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (((3.13060547623 - (36.527041698806414 / z)) + (t / (z * z))) * (y / 1.0))
	tmp = 0
	if z < -6.499344996252632e+53:
		tmp = t_1
	elif z < 7.066965436914287e+59:
		tmp = x + (y / ((((((((z + 15.234687407) * z) + 31.4690115749) * z) + 11.9400905721) * z) + 0.607771387771) / ((((((((z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(Float64(3.13060547623 - Float64(36.527041698806414 / z)) + Float64(t / Float64(z * z))) * Float64(y / 1.0)))
	tmp = 0.0
	if (z < -6.499344996252632e+53)
		tmp = t_1;
	elseif (z < 7.066965436914287e+59)
		tmp = Float64(x + Float64(y / Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(z + 15.234687407) * z) + 31.4690115749) * z) + 11.9400905721) * z) + 0.607771387771) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (((3.13060547623 - (36.527041698806414 / z)) + (t / (z * z))) * (y / 1.0));
	tmp = 0.0;
	if (z < -6.499344996252632e+53)
		tmp = t_1;
	elseif (z < 7.066965436914287e+59)
		tmp = x + (y / ((((((((z + 15.234687407) * z) + 31.4690115749) * z) + 11.9400905721) * z) + 0.607771387771) / ((((((((z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(N[(3.13060547623 - N[(36.527041698806414 / z), $MachinePrecision]), $MachinePrecision] + N[(t / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(y / 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[z, -6.499344996252632e+53], t$95$1, If[Less[z, 7.066965436914287e+59], N[(x + N[(y / N[(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] / 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]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2025105 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, D"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< z -649934499625263200000000000000000000000000000000000000) (+ x (* (+ (- 313060547623/100000000000 (/ 18263520849403207/500000000000000 z)) (/ t (* z z))) (/ y 1))) (if (< z 706696543691428700000000000000000000000000000000000000000000) (+ x (/ y (/ (+ (* (+ (* (+ (* (+ z 15234687407/1000000000) z) 314690115749/10000000000) z) 119400905721/10000000000) z) 607771387771/1000000000000) (+ (* (+ (* (+ (* (+ (* z 313060547623/100000000000) 55833770631/5000000000) z) t) z) a) z) b)))) (+ x (* (+ (- 313060547623/100000000000 (/ 18263520849403207/500000000000000 z)) (/ t (* z z))) (/ y 1))))))

  (+ 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))))