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

Percentage Accurate: 59.1% → 97.9%

Time: 6.2s

Alternatives: 14

Speedup: 11.3×

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: 59.1% 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: 97.9% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 93.9%

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

   3. Applied rewrites 97.2%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in z around inf

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

      1. lower--.f64 N/A

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

   4. Applied rewrites 99.2%

      \[\leadsto x + \color{blue}{\left(\mathsf{fma}\left(3.13060547623, y, \mathsf{fma}\left(\frac{y}{z}, 11.1667541262, t \cdot \frac{y}{z \cdot z}\right)\right) - \mathsf{fma}\left(\frac{y \cdot -36.52704169880642}{z \cdot z}, 15.234687407, \mathsf{fma}\left(\frac{y}{z \cdot z}, 98.5170599679272, 47.69379582500642 \cdot \frac{y}{z}\right)\right)\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 71.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b \cdot y\right) \cdot 1.6453555072203998\\ t_2 := \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{-52}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+151}:\\ \;\;\;\;x\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + 3.13060547623 \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* b y) 1.6453555072203998))
        (t_2
         (/
          (*
           y
           (+
            (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z)
            b))
          (+
           (*
            (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721)
            z)
           0.607771387771))))
   (if (<= t_2 -2e-52)
     t_1
     (if (<= t_2 5e+151)
       x
       (if (<= t_2 INFINITY) t_1 (+ x (* 3.13060547623 y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b * y) * 1.6453555072203998;
	double t_2 = (y * ((((((((z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b)) / (((((((z + 15.234687407) * z) + 31.4690115749) * z) + 11.9400905721) * z) + 0.607771387771);
	double tmp;
	if (t_2 <= -2e-52) {
		tmp = t_1;
	} else if (t_2 <= 5e+151) {
		tmp = x;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = x + (3.13060547623 * y);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b * y) * 1.6453555072203998;
	double t_2 = (y * ((((((((z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b)) / (((((((z + 15.234687407) * z) + 31.4690115749) * z) + 11.9400905721) * z) + 0.607771387771);
	double tmp;
	if (t_2 <= -2e-52) {
		tmp = t_1;
	} else if (t_2 <= 5e+151) {
		tmp = x;
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = x + (3.13060547623 * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (b * y) * 1.6453555072203998
	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)
	tmp = 0
	if t_2 <= -2e-52:
		tmp = t_1
	elif t_2 <= 5e+151:
		tmp = x
	elif t_2 <= math.inf:
		tmp = t_1
	else:
		tmp = x + (3.13060547623 * y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b * y) * 1.6453555072203998)
	t_2 = Float64(Float64(y * Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b)) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(z + 15.234687407) * z) + 31.4690115749) * z) + 11.9400905721) * z) + 0.607771387771))
	tmp = 0.0
	if (t_2 <= -2e-52)
		tmp = t_1;
	elseif (t_2 <= 5e+151)
		tmp = x;
	elseif (t_2 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(3.13060547623 * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (b * y) * 1.6453555072203998;
	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);
	tmp = 0.0;
	if (t_2 <= -2e-52)
		tmp = t_1;
	elseif (t_2 <= 5e+151)
		tmp = x;
	elseif (t_2 <= Inf)
		tmp = t_1;
	else
		tmp = x + (3.13060547623 * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b * y), $MachinePrecision] * 1.6453555072203998), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * N[(N[(N[(N[(N[(N[(N[(N[(z * 3.13060547623), $MachinePrecision] + 11.1667541262), $MachinePrecision] * z), $MachinePrecision] + t), $MachinePrecision] * z), $MachinePrecision] + a), $MachinePrecision] * z), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(z + 15.234687407), $MachinePrecision] * z), $MachinePrecision] + 31.4690115749), $MachinePrecision] * z), $MachinePrecision] + 11.9400905721), $MachinePrecision] * z), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e-52], t$95$1, If[LessEqual[t$95$2, 5e+151], x, If[LessEqual[t$95$2, Infinity], t$95$1, N[(x + N[(3.13060547623 * y), $MachinePrecision]), $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))) < -2e-52 or 5.0000000000000002e151 < (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z #s(literal 313060547623/100000000000 binary64)) #s(literal 55833770631/5000000000 binary64)) z) t) z) a) z) b)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z #s(literal 15234687407/1000000000 binary64)) z) #s(literal 314690115749/10000000000 binary64)) z) #s(literal 119400905721/10000000000 binary64)) z) #s(literal 607771387771/1000000000000 binary64))) < +inf.0

   1. Initial program 88.9%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 63.0

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

   4. Applied rewrites 63.0%

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

   5. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-*.f64 45.7

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

   7. Applied rewrites 45.7%

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

   if -2e-52 < (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z #s(literal 313060547623/100000000000 binary64)) #s(literal 55833770631/5000000000 binary64)) z) t) z) a) z) b)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z #s(literal 15234687407/1000000000 binary64)) z) #s(literal 314690115749/10000000000 binary64)) z) #s(literal 119400905721/10000000000 binary64)) z) #s(literal 607771387771/1000000000000 binary64))) < 5.0000000000000002e151

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 68.0%

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

   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. Taylor expanded in z around inf

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

      1. lower-*.f64 97.8

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

   4. Applied rewrites 97.8%

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

Alternative 3: 98.1% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<=
      (+
       x
       (/
        (*
         y
         (+
          (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z)
          b))
        (+
         (*
          (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721)
          z)
         0.607771387771)))
      INFINITY)
   (fma
    (/
     (fma (fma (fma (fma 3.13060547623 z 11.1667541262) z t) z a) z b)
     (fma
      (fma (fma (+ 15.234687407 z) z 31.4690115749) z 11.9400905721)
      z
      0.607771387771))
    y
    x)
   (fma
    y
    (-
     (+ (/ (+ 457.9610022158428 t) (* z z)) 3.13060547623)
     (/ 36.52704169880642 z))
    x)))

C

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

Julia

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(x + N[(N[(y * N[(N[(N[(N[(N[(N[(N[(N[(z * 3.13060547623), $MachinePrecision] + 11.1667541262), $MachinePrecision] * z), $MachinePrecision] + t), $MachinePrecision] * z), $MachinePrecision] + a), $MachinePrecision] * z), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(z + 15.234687407), $MachinePrecision] * z), $MachinePrecision] + 31.4690115749), $MachinePrecision] * z), $MachinePrecision] + 11.9400905721), $MachinePrecision] * z), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(N[(N[(N[(N[(3.13060547623 * z + 11.1667541262), $MachinePrecision] * z + t), $MachinePrecision] * z + a), $MachinePrecision] * z + b), $MachinePrecision] / N[(N[(N[(N[(15.234687407 + z), $MachinePrecision] * z + 31.4690115749), $MachinePrecision] * z + 11.9400905721), $MachinePrecision] * z + 0.607771387771), $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision], N[(y * N[(N[(N[(N[(457.9610022158428 + t), $MachinePrecision] / N[(z * z), $MachinePrecision]), $MachinePrecision] + 3.13060547623), $MachinePrecision] - N[(36.52704169880642 / z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 93.9%

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

   3. Applied rewrites 97.2%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in a around 0

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

   4. Applied rewrites 0.0%

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

   5. Taylor expanded in z around inf

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 N/A

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

      4. div-add-rev N/A

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

      5. lower-/.f64 N/A

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

      6. lower-+.f64 N/A

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

      7. pow2 N/A

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

      8. lift-*.f64 N/A

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. lower-/.f64 99.6

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

   7. Applied rewrites 99.6%

      \[\leadsto \mathsf{fma}\left(y, \left(\frac{457.9610022158428 + t}{z \cdot z} + 3.13060547623\right) - \color{blue}{\frac{36.52704169880642}{z}}, x\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 95.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y, \left(\frac{457.9610022158428 + t}{z \cdot z} + 3.13060547623\right) - \frac{36.52704169880642}{z}, x\right)\\ \mathbf{if}\;z \leq -1.2 \cdot 10^{+34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2400000000:\\ \;\;\;\;x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{0.607771387771}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (fma
          y
          (-
           (+ (/ (+ 457.9610022158428 t) (* z z)) 3.13060547623)
           (/ 36.52704169880642 z))
          x)))
   (if (<= z -1.2e+34)
     t_1
     (if (<= z 2400000000.0)
       (+
        x
        (/
         (*
          y
          (+
           (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z)
           b))
         0.607771387771))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(y, ((((457.9610022158428 + t) / (z * z)) + 3.13060547623) - (36.52704169880642 / z)), x);
	double tmp;
	if (z <= -1.2e+34) {
		tmp = t_1;
	} else if (z <= 2400000000.0) {
		tmp = x + ((y * ((((((((z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b)) / 0.607771387771);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(y, Float64(Float64(Float64(Float64(457.9610022158428 + t) / Float64(z * z)) + 3.13060547623) - Float64(36.52704169880642 / z)), x)
	tmp = 0.0
	if (z <= -1.2e+34)
		tmp = t_1;
	elseif (z <= 2400000000.0)
		tmp = Float64(x + Float64(Float64(y * Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b)) / 0.607771387771));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(N[(N[(N[(457.9610022158428 + t), $MachinePrecision] / N[(z * z), $MachinePrecision]), $MachinePrecision] + 3.13060547623), $MachinePrecision] - N[(36.52704169880642 / z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[z, -1.2e+34], t$95$1, If[LessEqual[z, 2400000000.0], N[(x + N[(N[(y * N[(N[(N[(N[(N[(N[(N[(N[(z * 3.13060547623), $MachinePrecision] + 11.1667541262), $MachinePrecision] * z), $MachinePrecision] + t), $MachinePrecision] * z), $MachinePrecision] + a), $MachinePrecision] * z), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / 0.607771387771), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.19999999999999993e34 or 2.4e9 < z

   1. Initial program 12.3%

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

   2. Taylor expanded in a around 0

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

   4. Applied rewrites 15.1%

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

   5. Taylor expanded in z around inf

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 N/A

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

      4. div-add-rev N/A

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

      5. lower-/.f64 N/A

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

      6. lower-+.f64 N/A

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

      7. pow2 N/A

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

      8. lift-*.f64 N/A

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. lower-/.f64 95.5

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

   7. Applied rewrites 95.5%

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

   if -1.19999999999999993e34 < z < 2.4e9

   1. Initial program 99.0%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 95.5%

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

Alternative 5: 91.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y, \left(\frac{457.9610022158428 + t}{z \cdot z} + 3.13060547623\right) - \frac{36.52704169880642}{z}, x\right)\\ \mathbf{if}\;z \leq -115000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 15500000:\\ \;\;\;\;x + \frac{\mathsf{fma}\left(\mathsf{fma}\left(z \cdot y, t, a \cdot y\right), z, b \cdot y\right)}{11.9400905721 \cdot z + 0.607771387771}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (fma
          y
          (-
           (+ (/ (+ 457.9610022158428 t) (* z z)) 3.13060547623)
           (/ 36.52704169880642 z))
          x)))
   (if (<= z -115000.0)
     t_1
     (if (<= z 15500000.0)
       (+
        x
        (/
         (fma (fma (* z y) t (* a y)) z (* b y))
         (+ (* 11.9400905721 z) 0.607771387771)))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(y, ((((457.9610022158428 + t) / (z * z)) + 3.13060547623) - (36.52704169880642 / z)), x);
	double tmp;
	if (z <= -115000.0) {
		tmp = t_1;
	} else if (z <= 15500000.0) {
		tmp = x + (fma(fma((z * y), t, (a * y)), z, (b * y)) / ((11.9400905721 * z) + 0.607771387771));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(y, Float64(Float64(Float64(Float64(457.9610022158428 + t) / Float64(z * z)) + 3.13060547623) - Float64(36.52704169880642 / z)), x)
	tmp = 0.0
	if (z <= -115000.0)
		tmp = t_1;
	elseif (z <= 15500000.0)
		tmp = Float64(x + Float64(fma(fma(Float64(z * y), t, Float64(a * y)), z, Float64(b * y)) / Float64(Float64(11.9400905721 * z) + 0.607771387771)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(N[(N[(N[(457.9610022158428 + t), $MachinePrecision] / N[(z * z), $MachinePrecision]), $MachinePrecision] + 3.13060547623), $MachinePrecision] - N[(36.52704169880642 / z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[z, -115000.0], t$95$1, If[LessEqual[z, 15500000.0], N[(x + N[(N[(N[(N[(z * y), $MachinePrecision] * t + N[(a * y), $MachinePrecision]), $MachinePrecision] * z + N[(b * y), $MachinePrecision]), $MachinePrecision] / N[(N[(11.9400905721 * z), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -115000 or 1.55e7 < z

   1. Initial program 16.1%

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

   2. Taylor expanded in a around 0

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

   4. Applied rewrites 18.6%

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

   5. Taylor expanded in z around inf

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 N/A

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

      4. div-add-rev N/A

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

      5. lower-/.f64 N/A

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

      6. lower-+.f64 N/A

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

      7. pow2 N/A

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

      8. lift-*.f64 N/A

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. lower-/.f64 94.0

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

   7. Applied rewrites 94.0%

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

   if -115000 < z < 1.55e7

   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. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. lower-*.f64 N/A

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

      10. lower-*.f64 90.3

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

   4. Applied rewrites 90.3%

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

   5. Taylor expanded in z around 0

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

   7. Applied rewrites 89.2%

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

Alternative 6: 92.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y, \left(\frac{457.9610022158428 + t}{z \cdot z} + 3.13060547623\right) - \frac{36.52704169880642}{z}, x\right)\\ \mathbf{if}\;z \leq -6.2 \cdot 10^{+33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 14000000:\\ \;\;\;\;x + y \cdot \mathsf{fma}\left(1.6453555072203998, b, z \cdot \mathsf{fma}\left(-32.324150453290734, b, 1.6453555072203998 \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (fma
          y
          (-
           (+ (/ (+ 457.9610022158428 t) (* z z)) 3.13060547623)
           (/ 36.52704169880642 z))
          x)))
   (if (<= z -6.2e+33)
     t_1
     (if (<= z 14000000.0)
       (+
        x
        (*
         y
         (fma
          1.6453555072203998
          b
          (* z (fma -32.324150453290734 b (* 1.6453555072203998 a))))))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(y, ((((457.9610022158428 + t) / (z * z)) + 3.13060547623) - (36.52704169880642 / z)), x);
	double tmp;
	if (z <= -6.2e+33) {
		tmp = t_1;
	} else if (z <= 14000000.0) {
		tmp = x + (y * fma(1.6453555072203998, b, (z * fma(-32.324150453290734, b, (1.6453555072203998 * a)))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(y, Float64(Float64(Float64(Float64(457.9610022158428 + t) / Float64(z * z)) + 3.13060547623) - Float64(36.52704169880642 / z)), x)
	tmp = 0.0
	if (z <= -6.2e+33)
		tmp = t_1;
	elseif (z <= 14000000.0)
		tmp = Float64(x + Float64(y * fma(1.6453555072203998, b, Float64(z * fma(-32.324150453290734, b, Float64(1.6453555072203998 * a))))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(N[(N[(N[(457.9610022158428 + t), $MachinePrecision] / N[(z * z), $MachinePrecision]), $MachinePrecision] + 3.13060547623), $MachinePrecision] - N[(36.52704169880642 / z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[z, -6.2e+33], t$95$1, If[LessEqual[z, 14000000.0], N[(x + N[(y * N[(1.6453555072203998 * b + N[(z * N[(-32.324150453290734 * b + N[(1.6453555072203998 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -6.2e33 or 1.4e7 < z

   1. Initial program 12.7%

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

   2. Taylor expanded in a around 0

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

   4. Applied rewrites 15.4%

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

   5. Taylor expanded in z around inf

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 N/A

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

      4. div-add-rev N/A

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

      5. lower-/.f64 N/A

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

      6. lower-+.f64 N/A

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

      7. pow2 N/A

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

      8. lift-*.f64 N/A

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. lower-/.f64 95.4

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

   7. Applied rewrites 95.4%

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

   if -6.2e33 < z < 1.4e7

   1. Initial program 99.0%

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

   2. Taylor expanded in z around 0

      \[\leadsto x + \color{blue}{\left(\frac{1000000000000}{607771387771} \cdot \left(b \cdot y\right) + z \cdot \left(\frac{1000000000000}{607771387771} \cdot \left(a \cdot y\right) - \frac{11940090572100000000000000}{369386059793087248348441} \cdot \left(b \cdot y\right)\right)\right)} \]
   3. 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 79.3

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

   4. Applied rewrites 79.3%

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

   5. Taylor expanded in y around 0

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

      1. lower-*.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-fma.f64 N/A

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

      5. lift-*.f64 90.1

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

   7. Applied rewrites 90.1%

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

Alternative 7: 89.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+34}:\\ \;\;\;\;x + 3.13060547623 \cdot y\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+44}:\\ \;\;\;\;x + y \cdot \mathsf{fma}\left(1.6453555072203998, b, z \cdot \mathsf{fma}\left(-32.324150453290734, b, 1.6453555072203998 \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.2e+34)
   (+ x (* 3.13060547623 y))
   (if (<= z 3.3e+44)
     (+
      x
      (*
       y
       (fma
        1.6453555072203998
        b
        (* z (fma -32.324150453290734 b (* 1.6453555072203998 a))))))
     (fma 3.13060547623 y x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.2e+34) {
		tmp = x + (3.13060547623 * y);
	} else if (z <= 3.3e+44) {
		tmp = x + (y * fma(1.6453555072203998, b, (z * fma(-32.324150453290734, b, (1.6453555072203998 * a)))));
	} else {
		tmp = fma(3.13060547623, y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.2e+34)
		tmp = Float64(x + Float64(3.13060547623 * y));
	elseif (z <= 3.3e+44)
		tmp = Float64(x + Float64(y * fma(1.6453555072203998, b, Float64(z * fma(-32.324150453290734, b, Float64(1.6453555072203998 * a))))));
	else
		tmp = fma(3.13060547623, y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.2e+34], N[(x + N[(3.13060547623 * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.3e+44], N[(x + N[(y * N[(1.6453555072203998 * b + N[(z * N[(-32.324150453290734 * b + N[(1.6453555072203998 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(3.13060547623 * y + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.19999999999999993e34

   1. Initial program 9.1%

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

   2. Taylor expanded in z around inf

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

      1. lower-*.f64 92.5

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

   4. Applied rewrites 92.5%

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

   if -1.19999999999999993e34 < z < 3.30000000000000013e44

   1. Initial program 97.8%

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

   2. Taylor expanded in z around 0

      \[\leadsto x + \color{blue}{\left(\frac{1000000000000}{607771387771} \cdot \left(b \cdot y\right) + z \cdot \left(\frac{1000000000000}{607771387771} \cdot \left(a \cdot y\right) - \frac{11940090572100000000000000}{369386059793087248348441} \cdot \left(b \cdot y\right)\right)\right)} \]
   3. 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 76.6

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

   4. Applied rewrites 76.6%

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

   5. Taylor expanded in y around 0

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

      1. lower-*.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-fma.f64 N/A

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

      5. lift-*.f64 86.8

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

   7. Applied rewrites 86.8%

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

   if 3.30000000000000013e44 < z

   1. Initial program 6.8%

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

   2. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-fma.f64 94.2

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

   4. Applied rewrites 94.2%

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

Alternative 8: 86.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.58 \cdot 10^{+38}:\\ \;\;\;\;x + 3.13060547623 \cdot y\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+14}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{\mathsf{fma}\left(z \cdot z, t, b\right)}{0.607771387771}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.58e+38)
   (+ x (* 3.13060547623 y))
   (if (<= z 4.8e+14)
     (fma y (/ (fma (* z z) t b) 0.607771387771) x)
     (fma 3.13060547623 y x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.58e+38) {
		tmp = x + (3.13060547623 * y);
	} else if (z <= 4.8e+14) {
		tmp = fma(y, (fma((z * z), t, b) / 0.607771387771), x);
	} else {
		tmp = fma(3.13060547623, y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.58e+38)
		tmp = Float64(x + Float64(3.13060547623 * y));
	elseif (z <= 4.8e+14)
		tmp = fma(y, Float64(fma(Float64(z * z), t, b) / 0.607771387771), x);
	else
		tmp = fma(3.13060547623, y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.58e+38], N[(x + N[(3.13060547623 * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.8e+14], N[(y * N[(N[(N[(z * z), $MachinePrecision] * t + b), $MachinePrecision] / 0.607771387771), $MachinePrecision] + x), $MachinePrecision], N[(3.13060547623 * y + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.58e38

   1. Initial program 8.4%

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

   2. Taylor expanded in z around inf

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

      1. lower-*.f64 93.2

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

   4. Applied rewrites 93.2%

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

   if -1.58e38 < z < 4.8e14

   1. Initial program 98.8%

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

   2. Taylor expanded in a around 0

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

   4. Applied rewrites 85.2%

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

   5. Taylor expanded in z around 0

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

   7. Applied rewrites 82.1%

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

   8. Taylor expanded in z around 0

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

   10. Applied rewrites 81.8%

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

   if 4.8e14 < z

   1. Initial program 13.9%

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

   2. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-fma.f64 89.3

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

   4. Applied rewrites 89.3%

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

Alternative 9: 83.5% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.55 \cdot 10^{+16}:\\ \;\;\;\;x + 3.13060547623 \cdot y\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+14}:\\ \;\;\;\;\mathsf{fma}\left(1.6453555072203998 \cdot b, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -3.55e+16)
   (+ x (* 3.13060547623 y))
   (if (<= z 1.4e+14)
     (fma (* 1.6453555072203998 b) y x)
     (fma 3.13060547623 y x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -3.55e+16) {
		tmp = x + (3.13060547623 * y);
	} else if (z <= 1.4e+14) {
		tmp = fma((1.6453555072203998 * b), y, x);
	} else {
		tmp = fma(3.13060547623, y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -3.55e+16)
		tmp = Float64(x + Float64(3.13060547623 * y));
	elseif (z <= 1.4e+14)
		tmp = fma(Float64(1.6453555072203998 * b), y, x);
	else
		tmp = fma(3.13060547623, y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -3.55e+16], N[(x + N[(3.13060547623 * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.4e+14], N[(N[(1.6453555072203998 * b), $MachinePrecision] * y + x), $MachinePrecision], N[(3.13060547623 * y + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.55e16

   1. Initial program 12.6%

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

   2. Taylor expanded in z around inf

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

      1. lower-*.f64 90.2

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

   4. Applied rewrites 90.2%

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

   if -3.55e16 < z < 1.4e14

   1. Initial program 99.5%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 78.0

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

   4. Applied rewrites 78.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b \cdot y, 1.6453555072203998, x\right)} \]
   5. 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. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 78.0

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

   6. Applied rewrites 78.0%

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

   if 1.4e14 < z

   1. Initial program 13.9%

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

   2. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-fma.f64 89.2

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

   4. Applied rewrites 89.2%

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

Alternative 10: 83.5% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.55 \cdot 10^{+16}:\\ \;\;\;\;x + 3.13060547623 \cdot y\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+14}:\\ \;\;\;\;\mathsf{fma}\left(b, 1.6453555072203998 \cdot y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -3.55e+16)
   (+ x (* 3.13060547623 y))
   (if (<= z 1.4e+14)
     (fma b (* 1.6453555072203998 y) x)
     (fma 3.13060547623 y x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -3.55e+16) {
		tmp = x + (3.13060547623 * y);
	} else if (z <= 1.4e+14) {
		tmp = fma(b, (1.6453555072203998 * y), x);
	} else {
		tmp = fma(3.13060547623, y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -3.55e+16)
		tmp = Float64(x + Float64(3.13060547623 * y));
	elseif (z <= 1.4e+14)
		tmp = fma(b, Float64(1.6453555072203998 * y), x);
	else
		tmp = fma(3.13060547623, y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -3.55e+16], N[(x + N[(3.13060547623 * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.4e+14], N[(b * N[(1.6453555072203998 * y), $MachinePrecision] + x), $MachinePrecision], N[(3.13060547623 * y + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.55e16

   1. Initial program 12.6%

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

   2. Taylor expanded in z around inf

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

      1. lower-*.f64 90.2

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

   4. Applied rewrites 90.2%

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

   if -3.55e16 < z < 1.4e14

   1. Initial program 99.5%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 78.0

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

   4. Applied rewrites 78.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b \cdot y, 1.6453555072203998, x\right)} \]
   5. 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. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-*.f64 78.0

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

   6. Applied rewrites 78.0%

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

   if 1.4e14 < z

   1. Initial program 13.9%

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

   2. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-fma.f64 89.2

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

   4. Applied rewrites 89.2%

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

Alternative 11: 51.3% accurate, 4.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{-118}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 8.6 \cdot 10^{-75}:\\ \;\;\;\;3.13060547623 \cdot y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -1.1e-118) x (if (<= x 8.6e-75) (* 3.13060547623 y) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.1e-118) {
		tmp = x;
	} else if (x <= 8.6e-75) {
		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 (x <= (-1.1d-118)) then
        tmp = x
    else if (x <= 8.6d-75) 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 (x <= -1.1e-118) {
		tmp = x;
	} else if (x <= 8.6e-75) {
		tmp = 3.13060547623 * y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -1.1e-118:
		tmp = x
	elif x <= 8.6e-75:
		tmp = 3.13060547623 * y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -1.1e-118)
		tmp = x;
	elseif (x <= 8.6e-75)
		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 (x <= -1.1e-118)
		tmp = x;
	elseif (x <= 8.6e-75)
		tmp = 3.13060547623 * y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -1.1e-118], x, If[LessEqual[x, 8.6e-75], N[(3.13060547623 * y), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.09999999999999992e-118 or 8.5999999999999998e-75 < x

   1. Initial program 59.1%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 60.1%

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

   if -1.09999999999999992e-118 < x < 8.5999999999999998e-75

   1. Initial program 59.1%

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

   2. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-fma.f64 45.8

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

   4. Applied rewrites 45.8%

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

   5. Taylor expanded in x around 0

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

      1. lower-*.f64 35.0

         \[\leadsto 3.13060547623 \cdot y \]

   7. Applied rewrites 35.0%

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

Alternative 12: 62.2% accurate, 8.8× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 59.1%

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

2. Taylor expanded in z around inf

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

   1. lower-*.f64 62.2

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

4. Applied rewrites 62.2%

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

Alternative 13: 62.2% accurate, 11.3× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(3.13060547623, y, x\right) \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b) {
	return fma(3.13060547623, y, x);
}

Julia

function code(x, y, z, t, a, b)
	return fma(3.13060547623, y, x)
end

Wolfram

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

Derivation

1. Initial program 59.1%

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

2. Taylor expanded in z around inf

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

   1. +-commutative N/A

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

   2. lower-fma.f64 62.2

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

4. Applied rewrites 62.2%

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

Alternative 14: 44.9% 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 59.1%

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

2. Taylor expanded in x around inf

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

4. Applied rewrites 44.9%

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

Developer Target 1: 98.5% 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 2025093 
(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))))