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

Percentage Accurate: 58.3% → 97.0%

Time: 9.8s

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: 58.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z \cdot z}\\ \mathbf{if}\;z \leq -1.15 \cdot 10^{+46} \lor \neg \left(z \leq 4.9 \cdot 10^{+31}\right):\\ \;\;\;\;x + \left(\mathsf{fma}\left(3.13060547623, y, \mathsf{fma}\left(\frac{y}{z}, 11.1667541262, t \cdot t\_1\right)\right) - \mathsf{fma}\left(\frac{y \cdot -36.52704169880642}{z \cdot z}, 15.234687407, \mathsf{fma}\left(t\_1, 98.5170599679272, 47.69379582500642 \cdot \frac{y}{z}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ y (* z z))))
   (if (or (<= z -1.15e+46) (not (<= z 4.9e+31)))
     (+
      x
      (-
       (fma 3.13060547623 y (fma (/ y z) 11.1667541262 (* t t_1)))
       (fma
        (/ (* y -36.52704169880642) (* z z))
        15.234687407
        (fma t_1 98.5170599679272 (* 47.69379582500642 (/ y z))))))
     (+
      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) {
	double t_1 = y / (z * z);
	double tmp;
	if ((z <= -1.15e+46) || !(z <= 4.9e+31)) {
		tmp = x + (fma(3.13060547623, y, fma((y / z), 11.1667541262, (t * t_1))) - fma(((y * -36.52704169880642) / (z * z)), 15.234687407, fma(t_1, 98.5170599679272, (47.69379582500642 * (y / z)))));
	} else {
		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));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y / Float64(z * z))
	tmp = 0.0
	if ((z <= -1.15e+46) || !(z <= 4.9e+31))
		tmp = Float64(x + Float64(fma(3.13060547623, y, fma(Float64(y / z), 11.1667541262, Float64(t * t_1))) - fma(Float64(Float64(y * -36.52704169880642) / Float64(z * z)), 15.234687407, fma(t_1, 98.5170599679272, Float64(47.69379582500642 * Float64(y / z))))));
	else
		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)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y / N[(z * z), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[z, -1.15e+46], N[Not[LessEqual[z, 4.9e+31]], $MachinePrecision]], N[(x + N[(N[(3.13060547623 * y + N[(N[(y / z), $MachinePrecision] * 11.1667541262 + N[(t * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(y * -36.52704169880642), $MachinePrecision] / N[(z * z), $MachinePrecision]), $MachinePrecision] * 15.234687407 + N[(t$95$1 * 98.5170599679272 + N[(47.69379582500642 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 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]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.15e46 or 4.89999999999999996e31 < z

   1. Initial program 8.1%

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

   3. Taylor expanded in z around inf

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

      1. lower--.f64 N/A

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

   5. Applied rewrites 97.2%

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

   if -1.15e46 < z < 4.89999999999999996e31

   1. Initial program 99.6%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+46} \lor \neg \left(z \leq 4.9 \cdot 10^{+31}\right):\\ \;\;\;\;x + \left(\mathsf{fma}\left(3.13060547623, y, \mathsf{fma}\left(\frac{y}{z}, 11.1667541262, t \cdot \frac{y}{z \cdot z}\right)\right) - \mathsf{fma}\left(\frac{y \cdot -36.52704169880642}{z \cdot z}, 15.234687407, \mathsf{fma}\left(\frac{y}{z \cdot z}, 98.5170599679272, 47.69379582500642 \cdot \frac{y}{z}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 72.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 1.6453555072203998 \cdot \left(b \cdot y\right)\\ t_2 := \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+163}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+60}:\\ \;\;\;\;x\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* 1.6453555072203998 (* b y)))
        (t_2
         (/
          (*
           y
           (+
            (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z)
            b))
          (+
           (*
            (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721)
            z)
           0.607771387771))))
   (if (<= t_2 -5e+163)
     t_1
     (if (<= t_2 2e+60)
       x
       (if (<= t_2 INFINITY) t_1 (fma 3.13060547623 y x))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 1.6453555072203998 * (b * y);
	double t_2 = (y * ((((((((z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b)) / (((((((z + 15.234687407) * z) + 31.4690115749) * z) + 11.9400905721) * z) + 0.607771387771);
	double tmp;
	if (t_2 <= -5e+163) {
		tmp = t_1;
	} else if (t_2 <= 2e+60) {
		tmp = x;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = fma(3.13060547623, y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(1.6453555072203998 * Float64(b * y))
	t_2 = Float64(Float64(y * Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b)) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(z + 15.234687407) * z) + 31.4690115749) * z) + 11.9400905721) * z) + 0.607771387771))
	tmp = 0.0
	if (t_2 <= -5e+163)
		tmp = t_1;
	elseif (t_2 <= 2e+60)
		tmp = x;
	elseif (t_2 <= Inf)
		tmp = t_1;
	else
		tmp = fma(3.13060547623, y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(1.6453555072203998 * N[(b * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * N[(N[(N[(N[(N[(N[(N[(N[(z * 3.13060547623), $MachinePrecision] + 11.1667541262), $MachinePrecision] * z), $MachinePrecision] + t), $MachinePrecision] * z), $MachinePrecision] + a), $MachinePrecision] * z), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(z + 15.234687407), $MachinePrecision] * z), $MachinePrecision] + 31.4690115749), $MachinePrecision] * z), $MachinePrecision] + 11.9400905721), $MachinePrecision] * z), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+163], t$95$1, If[LessEqual[t$95$2, 2e+60], x, If[LessEqual[t$95$2, Infinity], t$95$1, N[(3.13060547623 * y + x), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z #s(literal 313060547623/100000000000 binary64)) #s(literal 55833770631/5000000000 binary64)) z) t) z) a) z) b)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z #s(literal 15234687407/1000000000 binary64)) z) #s(literal 314690115749/10000000000 binary64)) z) #s(literal 119400905721/10000000000 binary64)) z) #s(literal 607771387771/1000000000000 binary64))) < -5e163 or 1.9999999999999999e60 < (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z #s(literal 313060547623/100000000000 binary64)) #s(literal 55833770631/5000000000 binary64)) z) t) z) a) z) b)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z #s(literal 15234687407/1000000000 binary64)) z) #s(literal 314690115749/10000000000 binary64)) z) #s(literal 119400905721/10000000000 binary64)) z) #s(literal 607771387771/1000000000000 binary64))) < +inf.0

   1. Initial program 82.7%

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

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + \frac{1000000000000}{607771387771} \cdot \left(b \cdot y\right)} \]
   4. 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 60.9

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

   5. Applied rewrites 60.9%

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

   6. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

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

      2. lift-*.f64 52.2

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

   8. Applied rewrites 52.2%

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

   if -5e163 < (/.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))) < 1.9999999999999999e60

   1. Initial program 99.6%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 59.2%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-fma.f64 97.2

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

   5. Applied rewrites 97.2%

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

Alternative 3: 95.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}\\ \mathbf{if}\;t\_1 \leq 10^{+241}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{\mathsf{fma}\left(\mathsf{fma}\left(z \cdot z, \mathsf{fma}\left(3.13060547623, z, 11.1667541262\right), a\right), z, b\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(15.234687407 + z, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+
          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)))))
   (if (<= t_1 1e+241)
     t_1
     (if (<= t_1 INFINITY)
       (fma
        y
        (/
         (fma (fma (* z z) (fma 3.13060547623 z 11.1667541262) a) z b)
         (fma
          (fma (fma (+ 15.234687407 z) z 31.4690115749) z 11.9400905721)
          z
          0.607771387771))
        x)
       (fma 3.13060547623 y x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_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));
	double tmp;
	if (t_1 <= 1e+241) {
		tmp = t_1;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = fma(y, (fma(fma((z * z), fma(3.13060547623, z, 11.1667541262), a), z, b) / fma(fma(fma((15.234687407 + z), z, 31.4690115749), z, 11.9400905721), z, 0.607771387771)), x);
	} else {
		tmp = fma(3.13060547623, y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = 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)))
	tmp = 0.0
	if (t_1 <= 1e+241)
		tmp = t_1;
	elseif (t_1 <= Inf)
		tmp = fma(y, Float64(fma(fma(Float64(z * z), fma(3.13060547623, z, 11.1667541262), a), z, b) / fma(fma(fma(Float64(15.234687407 + z), z, 31.4690115749), z, 11.9400905721), z, 0.607771387771)), x);
	else
		tmp = fma(3.13060547623, y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = 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]}, If[LessEqual[t$95$1, 1e+241], t$95$1, If[LessEqual[t$95$1, Infinity], N[(y * N[(N[(N[(N[(z * z), $MachinePrecision] * N[(3.13060547623 * z + 11.1667541262), $MachinePrecision] + 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] + x), $MachinePrecision], N[(3.13060547623 * y + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z #s(literal 313060547623/100000000000 binary64)) #s(literal 55833770631/5000000000 binary64)) z) t) z) a) z) b)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z #s(literal 15234687407/1000000000 binary64)) z) #s(literal 314690115749/10000000000 binary64)) z) #s(literal 119400905721/10000000000 binary64)) z) #s(literal 607771387771/1000000000000 binary64)))) < 1.0000000000000001e241

   1. Initial program 97.3%

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

   if 1.0000000000000001e241 < (+.f64 x (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z #s(literal 313060547623/100000000000 binary64)) #s(literal 55833770631/5000000000 binary64)) z) t) z) a) z) b)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z #s(literal 15234687407/1000000000 binary64)) z) #s(literal 314690115749/10000000000 binary64)) z) #s(literal 119400905721/10000000000 binary64)) z) #s(literal 607771387771/1000000000000 binary64)))) < +inf.0

   1. Initial program 75.1%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-fma.f64 31.6

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

   5. Applied rewrites 31.6%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 93.4%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-fma.f64 97.2

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

   5. Applied rewrites 97.2%

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

Alternative 4: 63.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \leq 10^{+277}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \end{array} \end{array} \]

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))
      1e+277)
   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)) <= 1e+277) {
		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)) <= 1e+277)
		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], 1e+277], 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))) < 1e277

   1. Initial program 97.5%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 47.7%

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

   if 1e277 < (/.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 11.8%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-fma.f64 84.2

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

   5. Applied rewrites 84.2%

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

Alternative 5: 94.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+43} \lor \neg \left(z \leq 2.3 \cdot 10^{+31}\right):\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \mathsf{fma}\left(\mathsf{fma}\left(t, z, a\right), z, b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.15e+43) (not (<= z 2.3e+31)))
   (fma 3.13060547623 y x)
   (+
    x
    (/
     (* y (fma (fma 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) {
	double tmp;
	if ((z <= -1.15e+43) || !(z <= 2.3e+31)) {
		tmp = fma(3.13060547623, y, x);
	} else {
		tmp = x + ((y * fma(fma(t, z, a), z, b)) / (((((((z + 15.234687407) * z) + 31.4690115749) * z) + 11.9400905721) * z) + 0.607771387771));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.15e+43) || !(z <= 2.3e+31))
		tmp = fma(3.13060547623, y, x);
	else
		tmp = Float64(x + Float64(Float64(y * fma(fma(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
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.15e+43], N[Not[LessEqual[z, 2.3e+31]], $MachinePrecision]], N[(3.13060547623 * y + x), $MachinePrecision], N[(x + N[(N[(y * N[(N[(t * z + a), $MachinePrecision] * z + 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]]

Derivation

1. Split input into 2 regimes

2. if z < -1.1500000000000001e43 or 2.3e31 < z

   1. Initial program 8.8%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-fma.f64 93.4

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

   5. Applied rewrites 93.4%

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

   if -1.1500000000000001e43 < z < 2.3e31

   1. Initial program 99.6%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

         \[\leadsto x + \frac{y \cdot \mathsf{fma}\left(t \cdot z + a, z, b\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      5. lower-fma.f64 98.8

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

   5. Applied rewrites 98.8%

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

4. Final simplification 96.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+43} \lor \neg \left(z \leq 2.3 \cdot 10^{+31}\right):\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \mathsf{fma}\left(\mathsf{fma}\left(t, z, a\right), z, b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 93.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+43} \lor \neg \left(z \leq 2.3 \cdot 10^{+31}\right):\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + t \cdot z\right)\right)}{\left(\left(z \cdot z\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.15e+43) (not (<= z 2.3e+31)))
   (fma 3.13060547623 y x)
   (+
    x
    (/
     (* y (+ b (* z (+ a (* t z)))))
     (+ (* (+ (* (* z z) z) 11.9400905721) z) 0.607771387771)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.15e+43) || !(z <= 2.3e+31)) {
		tmp = fma(3.13060547623, y, x);
	} else {
		tmp = x + ((y * (b + (z * (a + (t * z))))) / (((((z * z) * z) + 11.9400905721) * z) + 0.607771387771));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.15e+43) || !(z <= 2.3e+31))
		tmp = fma(3.13060547623, y, x);
	else
		tmp = Float64(x + Float64(Float64(y * Float64(b + Float64(z * Float64(a + Float64(t * z))))) / Float64(Float64(Float64(Float64(Float64(z * z) * z) + 11.9400905721) * z) + 0.607771387771)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.15e+43], N[Not[LessEqual[z, 2.3e+31]], $MachinePrecision]], N[(3.13060547623 * y + x), $MachinePrecision], N[(x + N[(N[(y * N[(b + N[(z * N[(a + N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(N[(N[(z * z), $MachinePrecision] * z), $MachinePrecision] + 11.9400905721), $MachinePrecision] * z), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.1500000000000001e43 or 2.3e31 < z

   1. Initial program 8.8%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-fma.f64 93.4

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

   5. Applied rewrites 93.4%

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

   if -1.1500000000000001e43 < z < 2.3e31

   1. Initial program 99.6%

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

   3. Taylor expanded in t around inf

      \[\leadsto x + \frac{y \cdot \color{blue}{\left(t \cdot {z}^{2}\right)}}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto x + \frac{y \cdot \left({z}^{2} \cdot \color{blue}{t}\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      2. lower-*.f64 N/A

         \[\leadsto x + \frac{y \cdot \left({z}^{2} \cdot \color{blue}{t}\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      3. unpow2 N/A

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

      4. lower-*.f64 47.9

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

   5. Applied rewrites 47.9%

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

   6. Taylor expanded in z around inf

      \[\leadsto x + \frac{y \cdot \left(\left(z \cdot z\right) \cdot t\right)}{\left(\color{blue}{{z}^{2}} \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]
   7. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto x + \frac{y \cdot \left(\left(z \cdot z\right) \cdot t\right)}{\left({z}^{2} \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      2. pow2 N/A

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

      3. lift-*.f64 47.9

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

   8. Applied rewrites 47.9%

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

   9. Taylor expanded in z around 0

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

       1. lower-+.f64 N/A

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

       2. lower-*.f64 N/A

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

       3. lower-+.f64 N/A

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

       4. lower-*.f64 97.4

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

   11. Applied rewrites 97.4%

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

4. Final simplification 95.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+43} \lor \neg \left(z \leq 2.3 \cdot 10^{+31}\right):\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + t \cdot z\right)\right)}{\left(\left(z \cdot z\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 92.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+33} \lor \neg \left(z \leq 1.18 \cdot 10^{+30}\right):\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{0.607771387771}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.45e+33) (not (<= z 1.18e+30)))
   (fma 3.13060547623 y x)
   (+
    x
    (/
     (*
      y
      (+
       (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z)
       b))
     0.607771387771))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.45e+33) || !(z <= 1.18e+30)) {
		tmp = fma(3.13060547623, y, x);
	} else {
		tmp = x + ((y * ((((((((z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b)) / 0.607771387771);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.45e+33) || !(z <= 1.18e+30))
		tmp = fma(3.13060547623, y, x);
	else
		tmp = Float64(x + Float64(Float64(y * Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b)) / 0.607771387771));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.45e+33], N[Not[LessEqual[z, 1.18e+30]], $MachinePrecision]], N[(3.13060547623 * y + x), $MachinePrecision], N[(x + N[(N[(y * N[(N[(N[(N[(N[(N[(N[(N[(z * 3.13060547623), $MachinePrecision] + 11.1667541262), $MachinePrecision] * z), $MachinePrecision] + t), $MachinePrecision] * z), $MachinePrecision] + a), $MachinePrecision] * z), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / 0.607771387771), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.45000000000000012e33 or 1.18e30 < z

   1. Initial program 10.3%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-fma.f64 92.7

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

   5. Applied rewrites 92.7%

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

   if -1.45000000000000012e33 < z < 1.18e30

   1. Initial program 99.6%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 95.9%

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

4. Final simplification 94.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+33} \lor \neg \left(z \leq 1.18 \cdot 10^{+30}\right):\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{0.607771387771}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 92.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -13:\\ \;\;\;\;x + \mathsf{fma}\left(-36.52704169880642, \frac{y}{z}, 3.13060547623 \cdot y\right)\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+30}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + t \cdot z\right)\right)}{\mathsf{fma}\left(11.9400905721, z, 0.607771387771\right)}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -13.0)
   (+ x (fma -36.52704169880642 (/ y z) (* 3.13060547623 y)))
   (if (<= z 1.15e+30)
     (+
      x
      (/ (* y (+ b (* z (+ a (* t z))))) (fma 11.9400905721 z 0.607771387771)))
     (fma 3.13060547623 y x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -13.0) {
		tmp = x + fma(-36.52704169880642, (y / z), (3.13060547623 * y));
	} else if (z <= 1.15e+30) {
		tmp = x + ((y * (b + (z * (a + (t * z))))) / fma(11.9400905721, z, 0.607771387771));
	} else {
		tmp = fma(3.13060547623, y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -13.0)
		tmp = Float64(x + fma(-36.52704169880642, Float64(y / z), Float64(3.13060547623 * y)));
	elseif (z <= 1.15e+30)
		tmp = Float64(x + Float64(Float64(y * Float64(b + Float64(z * Float64(a + Float64(t * z))))) / fma(11.9400905721, z, 0.607771387771)));
	else
		tmp = fma(3.13060547623, y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -13.0], N[(x + N[(-36.52704169880642 * N[(y / z), $MachinePrecision] + N[(3.13060547623 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.15e+30], N[(x + N[(N[(y * N[(b + N[(z * N[(a + N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(11.9400905721 * z + 0.607771387771), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(3.13060547623 * y + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -13

   1. Initial program 20.1%

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

   3. Taylor expanded in z around inf

      \[\leadsto x + \color{blue}{\left(\left(\frac{313060547623}{100000000000} \cdot y + \frac{55833770631}{5000000000} \cdot \frac{y}{z}\right) - \frac{4769379582500641883561}{100000000000000000000} \cdot \frac{y}{z}\right)} \]
   4. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto x + \left(\left(\frac{313060547623}{100000000000} \cdot y + \frac{55833770631}{5000000000} \cdot \frac{y}{z}\right) - \color{blue}{\frac{4769379582500641883561}{100000000000000000000} \cdot \frac{y}{z}}\right) \]

      2. +-commutative N/A

         \[\leadsto x + \left(\left(\frac{55833770631}{5000000000} \cdot \frac{y}{z} + \frac{313060547623}{100000000000} \cdot y\right) - \color{blue}{\frac{4769379582500641883561}{100000000000000000000}} \cdot \frac{y}{z}\right) \]

      3. *-commutative N/A

         \[\leadsto x + \left(\left(\frac{y}{z} \cdot \frac{55833770631}{5000000000} + \frac{313060547623}{100000000000} \cdot y\right) - \frac{4769379582500641883561}{100000000000000000000} \cdot \frac{y}{z}\right) \]

      4. lower-fma.f64 N/A

         \[\leadsto x + \left(\mathsf{fma}\left(\frac{y}{z}, \frac{55833770631}{5000000000}, \frac{313060547623}{100000000000} \cdot y\right) - \color{blue}{\frac{4769379582500641883561}{100000000000000000000}} \cdot \frac{y}{z}\right) \]

      5. lower-/.f64 N/A

         \[\leadsto x + \left(\mathsf{fma}\left(\frac{y}{z}, \frac{55833770631}{5000000000}, \frac{313060547623}{100000000000} \cdot y\right) - \frac{4769379582500641883561}{100000000000000000000} \cdot \frac{y}{z}\right) \]

      6. lower-*.f64 N/A

         \[\leadsto x + \left(\mathsf{fma}\left(\frac{y}{z}, \frac{55833770631}{5000000000}, \frac{313060547623}{100000000000} \cdot y\right) - \frac{4769379582500641883561}{100000000000000000000} \cdot \frac{y}{z}\right) \]

      7. lower-*.f64 N/A

         \[\leadsto x + \left(\mathsf{fma}\left(\frac{y}{z}, \frac{55833770631}{5000000000}, \frac{313060547623}{100000000000} \cdot y\right) - \frac{4769379582500641883561}{100000000000000000000} \cdot \color{blue}{\frac{y}{z}}\right) \]

      8. lower-/.f64 88.4

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

   5. Applied rewrites 88.4%

      \[\leadsto x + \color{blue}{\left(\mathsf{fma}\left(\frac{y}{z}, 11.1667541262, 3.13060547623 \cdot y\right) - 47.69379582500642 \cdot \frac{y}{z}\right)} \]
   6. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto x + \left(\mathsf{fma}\left(\frac{y}{z}, \frac{55833770631}{5000000000}, \frac{313060547623}{100000000000} \cdot y\right) - \color{blue}{\frac{4769379582500641883561}{100000000000000000000} \cdot \frac{y}{z}}\right) \]

      2. lift-/.f64 N/A

         \[\leadsto x + \left(\mathsf{fma}\left(\frac{y}{z}, \frac{55833770631}{5000000000}, \frac{313060547623}{100000000000} \cdot y\right) - \frac{4769379582500641883561}{100000000000000000000} \cdot \frac{y}{z}\right) \]

      3. lift-*.f64 N/A

         \[\leadsto x + \left(\mathsf{fma}\left(\frac{y}{z}, \frac{55833770631}{5000000000}, \frac{313060547623}{100000000000} \cdot y\right) - \frac{4769379582500641883561}{100000000000000000000} \cdot \frac{y}{z}\right) \]

      4. lift-fma.f64 N/A

         \[\leadsto x + \left(\left(\frac{y}{z} \cdot \frac{55833770631}{5000000000} + \frac{313060547623}{100000000000} \cdot y\right) - \color{blue}{\frac{4769379582500641883561}{100000000000000000000}} \cdot \frac{y}{z}\right) \]

      5. lift-*.f64 N/A

         \[\leadsto x + \left(\left(\frac{y}{z} \cdot \frac{55833770631}{5000000000} + \frac{313060547623}{100000000000} \cdot y\right) - \frac{4769379582500641883561}{100000000000000000000} \cdot \color{blue}{\frac{y}{z}}\right) \]

      6. lift-/.f64 N/A

         \[\leadsto x + \left(\left(\frac{y}{z} \cdot \frac{55833770631}{5000000000} + \frac{313060547623}{100000000000} \cdot y\right) - \frac{4769379582500641883561}{100000000000000000000} \cdot \frac{y}{\color{blue}{z}}\right) \]

      7. +-commutative N/A

         \[\leadsto x + \left(\left(\frac{313060547623}{100000000000} \cdot y + \frac{y}{z} \cdot \frac{55833770631}{5000000000}\right) - \color{blue}{\frac{4769379582500641883561}{100000000000000000000}} \cdot \frac{y}{z}\right) \]

      8. *-commutative N/A

         \[\leadsto x + \left(\left(\frac{313060547623}{100000000000} \cdot y + \frac{55833770631}{5000000000} \cdot \frac{y}{z}\right) - \frac{4769379582500641883561}{100000000000000000000} \cdot \frac{y}{z}\right) \]

      9. associate--l+ N/A

         \[\leadsto x + \left(\frac{313060547623}{100000000000} \cdot y + \color{blue}{\left(\frac{55833770631}{5000000000} \cdot \frac{y}{z} - \frac{4769379582500641883561}{100000000000000000000} \cdot \frac{y}{z}\right)}\right) \]

      10. lower-+.f64 N/A

          \[\leadsto x + \left(\frac{313060547623}{100000000000} \cdot y + \color{blue}{\left(\frac{55833770631}{5000000000} \cdot \frac{y}{z} - \frac{4769379582500641883561}{100000000000000000000} \cdot \frac{y}{z}\right)}\right) \]

      11. lift-*.f64 N/A

          \[\leadsto x + \left(\frac{313060547623}{100000000000} \cdot y + \left(\color{blue}{\frac{55833770631}{5000000000} \cdot \frac{y}{z}} - \frac{4769379582500641883561}{100000000000000000000} \cdot \frac{y}{z}\right)\right) \]

      12. associate-*r/ N/A

          \[\leadsto x + \left(\frac{313060547623}{100000000000} \cdot y + \left(\frac{\frac{55833770631}{5000000000} \cdot y}{z} - \color{blue}{\frac{4769379582500641883561}{100000000000000000000}} \cdot \frac{y}{z}\right)\right) \]

      13. associate-*r/ N/A

          \[\leadsto x + \left(\frac{313060547623}{100000000000} \cdot y + \left(\frac{\frac{55833770631}{5000000000} \cdot y}{z} - \frac{\frac{4769379582500641883561}{100000000000000000000} \cdot y}{\color{blue}{z}}\right)\right) \]

      14. div-sub N/A

          \[\leadsto x + \left(\frac{313060547623}{100000000000} \cdot y + \frac{\frac{55833770631}{5000000000} \cdot y - \frac{4769379582500641883561}{100000000000000000000} \cdot y}{\color{blue}{z}}\right) \]

      15. lower-/.f64 N/A

          \[\leadsto x + \left(\frac{313060547623}{100000000000} \cdot y + \frac{\frac{55833770631}{5000000000} \cdot y - \frac{4769379582500641883561}{100000000000000000000} \cdot y}{\color{blue}{z}}\right) \]

      16. distribute-rgt-out-- N/A

          \[\leadsto x + \left(\frac{313060547623}{100000000000} \cdot y + \frac{y \cdot \left(\frac{55833770631}{5000000000} - \frac{4769379582500641883561}{100000000000000000000}\right)}{z}\right) \]

      17. lower-*.f64 N/A

          \[\leadsto x + \left(\frac{313060547623}{100000000000} \cdot y + \frac{y \cdot \left(\frac{55833770631}{5000000000} - \frac{4769379582500641883561}{100000000000000000000}\right)}{z}\right) \]

      18. metadata-eval 88.4

          \[\leadsto x + \left(3.13060547623 \cdot y + \frac{y \cdot -36.52704169880642}{z}\right) \]

   7. Applied rewrites 88.4%

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

   8. Taylor expanded in z around inf

      \[\leadsto x + \left(\frac{-3652704169880641883561}{100000000000000000000} \cdot \frac{y}{z} + \color{blue}{\frac{313060547623}{100000000000} \cdot y}\right) \]
   9. Step-by-step derivation

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lift-*.f64 88.4

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

   10. Applied rewrites 88.4%

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

   if -13 < z < 1.15e30

   1. Initial program 99.6%

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

   3. Taylor expanded in t around inf

      \[\leadsto x + \frac{y \cdot \color{blue}{\left(t \cdot {z}^{2}\right)}}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto x + \frac{y \cdot \left({z}^{2} \cdot \color{blue}{t}\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      2. lower-*.f64 N/A

         \[\leadsto x + \frac{y \cdot \left({z}^{2} \cdot \color{blue}{t}\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      3. unpow2 N/A

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

      4. lower-*.f64 45.7

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

   5. Applied rewrites 45.7%

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

   6. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lift-fma.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-fma.f64 N/A

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

      6. lift-+.f64 N/A

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

      7. lift-fma.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-fma.f64 45.3

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

   8. Applied rewrites 45.3%

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

   9. Taylor expanded in z around 0

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

       1. lower-+.f64 N/A

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

       2. lower-*.f64 N/A

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

       3. lower-+.f64 N/A

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

       4. lower-*.f64 96.8

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

   11. Applied rewrites 96.8%

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

   if 1.15e30 < z

   1. Initial program 9.0%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-fma.f64 93.1

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

   5. Applied rewrites 93.1%

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

4. Final simplification 93.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -13:\\ \;\;\;\;x + \mathsf{fma}\left(-36.52704169880642, \frac{y}{z}, 3.13060547623 \cdot y\right)\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+30}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + t \cdot z\right)\right)}{\mathsf{fma}\left(11.9400905721, z, 0.607771387771\right)}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 83.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+16} \lor \neg \left(z \leq 1.15 \cdot 10^{+30}\right):\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \mathsf{fma}\left(\mathsf{fma}\left(1.6453555072203998 \cdot a, y, -32.324150453290734 \cdot \left(b \cdot y\right)\right), z, \left(b \cdot y\right) \cdot 1.6453555072203998\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.7e+16) (not (<= z 1.15e+30)))
   (fma 3.13060547623 y x)
   (+
    x
    (fma
     (fma (* 1.6453555072203998 a) y (* -32.324150453290734 (* b y)))
     z
     (* (* b y) 1.6453555072203998)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.7e+16) || !(z <= 1.15e+30)) {
		tmp = fma(3.13060547623, y, x);
	} else {
		tmp = x + fma(fma((1.6453555072203998 * a), y, (-32.324150453290734 * (b * y))), z, ((b * y) * 1.6453555072203998));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.7e+16) || !(z <= 1.15e+30))
		tmp = fma(3.13060547623, y, x);
	else
		tmp = Float64(x + fma(fma(Float64(1.6453555072203998 * a), y, Float64(-32.324150453290734 * Float64(b * y))), z, Float64(Float64(b * y) * 1.6453555072203998)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.7e+16], N[Not[LessEqual[z, 1.15e+30]], $MachinePrecision]], N[(3.13060547623 * y + x), $MachinePrecision], N[(x + N[(N[(N[(1.6453555072203998 * a), $MachinePrecision] * y + N[(-32.324150453290734 * N[(b * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * z + N[(N[(b * y), $MachinePrecision] * 1.6453555072203998), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.7e16 or 1.15e30 < z

   1. Initial program 12.4%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-fma.f64 92.2

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

   5. Applied rewrites 92.2%

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

   if -1.7e16 < z < 1.15e30

   1. Initial program 99.6%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

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

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

      5. associate-*r* N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. metadata-eval N/A

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

      10. lower-*.f64 N/A

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

      13. lower-*.f64 79.2

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

   5. Applied rewrites 79.2%

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

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+16} \lor \neg \left(z \leq 1.15 \cdot 10^{+30}\right):\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \mathsf{fma}\left(\mathsf{fma}\left(1.6453555072203998 \cdot a, y, -32.324150453290734 \cdot \left(b \cdot y\right)\right), z, \left(b \cdot y\right) \cdot 1.6453555072203998\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 83.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+29}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-60}:\\ \;\;\;\;\mathsf{fma}\left(b, y \cdot 1.6453555072203998, x\right)\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+30}:\\ \;\;\;\;x + \frac{y \cdot \left(a \cdot z\right)}{\mathsf{fma}\left(11.9400905721, z, 0.607771387771\right)}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.15e+29)
   (fma 3.13060547623 y x)
   (if (<= z 7.5e-60)
     (fma b (* y 1.6453555072203998) x)
     (if (<= z 1.15e+30)
       (+ x (/ (* y (* a z)) (fma 11.9400905721 z 0.607771387771)))
       (fma 3.13060547623 y x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.15e+29) {
		tmp = fma(3.13060547623, y, x);
	} else if (z <= 7.5e-60) {
		tmp = fma(b, (y * 1.6453555072203998), x);
	} else if (z <= 1.15e+30) {
		tmp = x + ((y * (a * z)) / fma(11.9400905721, z, 0.607771387771));
	} else {
		tmp = fma(3.13060547623, y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.15e+29)
		tmp = fma(3.13060547623, y, x);
	elseif (z <= 7.5e-60)
		tmp = fma(b, Float64(y * 1.6453555072203998), x);
	elseif (z <= 1.15e+30)
		tmp = Float64(x + Float64(Float64(y * Float64(a * z)) / fma(11.9400905721, z, 0.607771387771)));
	else
		tmp = fma(3.13060547623, y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.15e+29], N[(3.13060547623 * y + x), $MachinePrecision], If[LessEqual[z, 7.5e-60], N[(b * N[(y * 1.6453555072203998), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[z, 1.15e+30], N[(x + N[(N[(y * N[(a * z), $MachinePrecision]), $MachinePrecision] / N[(11.9400905721 * z + 0.607771387771), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(3.13060547623 * y + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.1500000000000001e29 or 1.15e30 < z

   1. Initial program 11.0%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-fma.f64 92.1

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

   5. Applied rewrites 92.1%

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

   if -1.1500000000000001e29 < z < 7.5000000000000002e-60

   1. Initial program 99.6%

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

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + \frac{1000000000000}{607771387771} \cdot \left(b \cdot y\right)} \]
   4. 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 84.5

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

   5. Applied rewrites 84.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b \cdot y, 1.6453555072203998, x\right)} \]
   6. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. lift-fma.f64 N/A

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

      3. associate-*l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-*.f64 84.6

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

   7. Applied rewrites 84.6%

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

   if 7.5000000000000002e-60 < z < 1.15e30

   1. Initial program 99.5%

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

   3. Taylor expanded in t around inf

      \[\leadsto x + \frac{y \cdot \color{blue}{\left(t \cdot {z}^{2}\right)}}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto x + \frac{y \cdot \left({z}^{2} \cdot \color{blue}{t}\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      2. lower-*.f64 N/A

         \[\leadsto x + \frac{y \cdot \left({z}^{2} \cdot \color{blue}{t}\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      3. unpow2 N/A

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

      4. lower-*.f64 33.0

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

   5. Applied rewrites 33.0%

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

   6. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lift-fma.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-fma.f64 N/A

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

      6. lift-+.f64 N/A

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

      7. lift-fma.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-fma.f64 29.9

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

   8. Applied rewrites 29.9%

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

   9. Taylor expanded in a around inf

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

       1. lower-*.f64 62.8

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

   11. Applied rewrites 62.8%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+29}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-60}:\\ \;\;\;\;\mathsf{fma}\left(b, y \cdot 1.6453555072203998, x\right)\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+30}:\\ \;\;\;\;x + \frac{y \cdot \left(a \cdot z\right)}{\mathsf{fma}\left(11.9400905721, z, 0.607771387771\right)}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 83.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+29}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-55}:\\ \;\;\;\;\mathsf{fma}\left(b, y \cdot 1.6453555072203998, x\right)\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+31}:\\ \;\;\;\;x + \frac{\left(a \cdot y\right) \cdot z}{\mathsf{fma}\left(11.9400905721, z, 0.607771387771\right)}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.15e+29)
   (fma 3.13060547623 y x)
   (if (<= z 2.4e-55)
     (fma b (* y 1.6453555072203998) x)
     (if (<= z 1.2e+31)
       (+ x (/ (* (* a y) z) (fma 11.9400905721 z 0.607771387771)))
       (fma 3.13060547623 y x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.15e+29) {
		tmp = fma(3.13060547623, y, x);
	} else if (z <= 2.4e-55) {
		tmp = fma(b, (y * 1.6453555072203998), x);
	} else if (z <= 1.2e+31) {
		tmp = x + (((a * y) * z) / fma(11.9400905721, z, 0.607771387771));
	} else {
		tmp = fma(3.13060547623, y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.15e+29)
		tmp = fma(3.13060547623, y, x);
	elseif (z <= 2.4e-55)
		tmp = fma(b, Float64(y * 1.6453555072203998), x);
	elseif (z <= 1.2e+31)
		tmp = Float64(x + Float64(Float64(Float64(a * y) * z) / fma(11.9400905721, z, 0.607771387771)));
	else
		tmp = fma(3.13060547623, y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.15e+29], N[(3.13060547623 * y + x), $MachinePrecision], If[LessEqual[z, 2.4e-55], N[(b * N[(y * 1.6453555072203998), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[z, 1.2e+31], N[(x + N[(N[(N[(a * y), $MachinePrecision] * z), $MachinePrecision] / N[(11.9400905721 * z + 0.607771387771), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(3.13060547623 * y + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.1500000000000001e29 or 1.19999999999999991e31 < z

   1. Initial program 11.0%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-fma.f64 92.1

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

   5. Applied rewrites 92.1%

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

   if -1.1500000000000001e29 < z < 2.39999999999999991e-55

   1. Initial program 99.6%

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

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + \frac{1000000000000}{607771387771} \cdot \left(b \cdot y\right)} \]
   4. 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 83.9

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

   5. Applied rewrites 83.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b \cdot y, 1.6453555072203998, x\right)} \]
   6. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. lift-fma.f64 N/A

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

      3. associate-*l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-*.f64 84.0

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

   7. Applied rewrites 84.0%

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

   if 2.39999999999999991e-55 < z < 1.19999999999999991e31

   1. Initial program 99.4%

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

   3. Taylor expanded in t around inf

      \[\leadsto x + \frac{y \cdot \color{blue}{\left(t \cdot {z}^{2}\right)}}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto x + \frac{y \cdot \left({z}^{2} \cdot \color{blue}{t}\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      2. lower-*.f64 N/A

         \[\leadsto x + \frac{y \cdot \left({z}^{2} \cdot \color{blue}{t}\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      3. unpow2 N/A

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

      4. lower-*.f64 37.6

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

   5. Applied rewrites 37.6%

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

   6. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lift-fma.f64 N/A

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

      4. lift-+.f64 N/A

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

      5. lift-fma.f64 N/A

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

      6. lift-+.f64 N/A

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

      7. lift-fma.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-fma.f64 34.0

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

   8. Applied rewrites 34.0%

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

   9. Taylor expanded in a around inf

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

       1. associate-*r* N/A

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

       2. lower-*.f64 N/A

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

       3. lower-*.f64 64.5

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

   11. Applied rewrites 64.5%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+29}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-55}:\\ \;\;\;\;\mathsf{fma}\left(b, y \cdot 1.6453555072203998, x\right)\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+31}:\\ \;\;\;\;x + \frac{\left(a \cdot y\right) \cdot z}{\mathsf{fma}\left(11.9400905721, z, 0.607771387771\right)}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 83.1% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+29} \lor \neg \left(z \leq 48000000000\right):\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b, y \cdot 1.6453555072203998, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.15e+29) (not (<= z 48000000000.0)))
   (fma 3.13060547623 y x)
   (fma b (* y 1.6453555072203998) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.15e+29) || !(z <= 48000000000.0)) {
		tmp = fma(3.13060547623, y, x);
	} else {
		tmp = fma(b, (y * 1.6453555072203998), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.15e+29) || !(z <= 48000000000.0))
		tmp = fma(3.13060547623, y, x);
	else
		tmp = fma(b, Float64(y * 1.6453555072203998), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.15e+29], N[Not[LessEqual[z, 48000000000.0]], $MachinePrecision]], N[(3.13060547623 * y + x), $MachinePrecision], N[(b * N[(y * 1.6453555072203998), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.1500000000000001e29 or 4.8e10 < z

   1. Initial program 13.7%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-fma.f64 90.0

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

   5. Applied rewrites 90.0%

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

   if -1.1500000000000001e29 < z < 4.8e10

   1. Initial program 99.6%

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

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + \frac{1000000000000}{607771387771} \cdot \left(b \cdot y\right)} \]
   4. 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 80.6

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

   5. Applied rewrites 80.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b \cdot y, 1.6453555072203998, x\right)} \]
   6. Step-by-step derivation

      1. lift-*.f64 N/A

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

      2. lift-fma.f64 N/A

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

      3. associate-*l* N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-*.f64 80.7

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

   7. Applied rewrites 80.7%

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

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+29} \lor \neg \left(z \leq 48000000000\right):\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b, y \cdot 1.6453555072203998, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 51.1% accurate, 4.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+158} \lor \neg \left(y \leq 1.02 \cdot 10^{+135}\right):\\ \;\;\;\;3.13060547623 \cdot y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -7.5e+158) (not (<= y 1.02e+135))) (* 3.13060547623 y) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -7.5e+158) || !(y <= 1.02e+135)) {
		tmp = 3.13060547623 * y;
	} else {
		tmp = x;
	}
	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) :: tmp
    if ((y <= (-7.5d+158)) .or. (.not. (y <= 1.02d+135))) then
        tmp = 3.13060547623d0 * y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -7.5e+158) || !(y <= 1.02e+135)) {
		tmp = 3.13060547623 * y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -7.5e+158) or not (y <= 1.02e+135):
		tmp = 3.13060547623 * y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -7.5e+158) || !(y <= 1.02e+135))
		tmp = Float64(3.13060547623 * y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -7.5e+158) || ~((y <= 1.02e+135)))
		tmp = 3.13060547623 * y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -7.5e+158], N[Not[LessEqual[y, 1.02e+135]], $MachinePrecision]], N[(3.13060547623 * y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -7.5000000000000004e158 or 1.01999999999999993e135 < y

   1. Initial program 48.7%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-fma.f64 50.5

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

   5. Applied rewrites 50.5%

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

   6. Taylor expanded in x around 0

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

      1. lift-*.f64 41.8

         \[\leadsto 3.13060547623 \cdot y \]

   8. Applied rewrites 41.8%

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

   if -7.5000000000000004e158 < y < 1.01999999999999993e135

   1. Initial program 59.5%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 59.7%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 54.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+158} \lor \neg \left(y \leq 1.02 \cdot 10^{+135}\right):\\ \;\;\;\;3.13060547623 \cdot y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 44.8% 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 56.3%

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

3. Taylor expanded in x around inf

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

5. Applied rewrites 46.1%

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

Developer Target 1: 98.4% 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 2025064 
(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))))