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

Percentage Accurate: 58.5% → 97.9%

Time: 12.7s

Alternatives: 11

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: 58.5% 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

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

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (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 (/ t z) (/ y z) (* (/ y z) 11.1667541262)))
     (fma
      (/ (* y -36.52704169880642) z)
      (/ 15.234687407 z)
      (fma (/ y (* z z)) 98.5170599679272 (* 47.69379582500642 (/ y z))))))))

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 = x + (fma(3.13060547623, y, fma((t / z), (y / z), ((y / z) * 11.1667541262))) - fma(((y * -36.52704169880642) / z), (15.234687407 / z), fma((y / (z * z)), 98.5170599679272, (47.69379582500642 * (y / z)))));
	}
	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 = Float64(x + Float64(fma(3.13060547623, y, fma(Float64(t / z), Float64(y / z), Float64(Float64(y / z) * 11.1667541262))) - fma(Float64(Float64(y * -36.52704169880642) / z), Float64(15.234687407 / z), fma(Float64(y / Float64(z * z)), 98.5170599679272, Float64(47.69379582500642 * Float64(y / z))))));
	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[(x + N[(N[(3.13060547623 * y + N[(N[(t / z), $MachinePrecision] * N[(y / z), $MachinePrecision] + N[(N[(y / z), $MachinePrecision] * 11.1667541262), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(y * -36.52704169880642), $MachinePrecision] / z), $MachinePrecision] * N[(15.234687407 / z), $MachinePrecision] + N[(N[(y / N[(z * z), $MachinePrecision]), $MachinePrecision] * 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 95.0%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

   4. Applied rewrites 97.3%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in z around inf

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

      1. lower-*.f64 95.5

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

   5. Applied rewrites 95.5%

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

   6. Taylor expanded in z around inf

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

      1. lower--.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. +-commutative N/A

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

      4. unpow2 N/A

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

      5. times-frac N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lower-/.f64 N/A

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

   8. Applied rewrites 98.9%

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

Alternative 2: 97.1% accurate, 0.5× speedup

Math

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

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)
   (+ x (fma (/ y z) -36.52704169880642 (* 3.13060547623 y)))))

C

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

Julia

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(x + N[(N[(y * N[(N[(N[(N[(N[(N[(N[(N[(z * 3.13060547623), $MachinePrecision] + 11.1667541262), $MachinePrecision] * z), $MachinePrecision] + t), $MachinePrecision] * z), $MachinePrecision] + a), $MachinePrecision] * z), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(z + 15.234687407), $MachinePrecision] * z), $MachinePrecision] + 31.4690115749), $MachinePrecision] * z), $MachinePrecision] + 11.9400905721), $MachinePrecision] * z), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(N[(N[(N[(N[(3.13060547623 * z + 11.1667541262), $MachinePrecision] * z + t), $MachinePrecision] * z + a), $MachinePrecision] * z + b), $MachinePrecision] / N[(N[(N[(N[(15.234687407 + z), $MachinePrecision] * z + 31.4690115749), $MachinePrecision] * z + 11.9400905721), $MachinePrecision] * z + 0.607771387771), $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision], N[(x + N[(N[(y / z), $MachinePrecision] * -36.52704169880642 + N[(3.13060547623 * y), $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 95.0%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

   4. Applied rewrites 97.3%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. +-commutative N/A

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

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

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. metadata-eval N/A

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

      7. lower-*.f64 95.5

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

   5. Applied rewrites 95.5%

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

Alternative 3: 92.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.41:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \mathbf{elif}\;z \leq 420000000:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(t, z, a\right), z, b\right), \frac{y}{0.607771387771 + 11.9400905721 \cdot z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \mathsf{fma}\left(\frac{y}{z}, -36.52704169880642, 3.13060547623 \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -0.41)
   (fma 3.13060547623 y x)
   (if (<= z 420000000.0)
     (fma (fma (fma t z a) z b) (/ y (+ 0.607771387771 (* 11.9400905721 z))) x)
     (+ x (fma (/ y z) -36.52704169880642 (* 3.13060547623 y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -0.41) {
		tmp = fma(3.13060547623, y, x);
	} else if (z <= 420000000.0) {
		tmp = fma(fma(fma(t, z, a), z, b), (y / (0.607771387771 + (11.9400905721 * z))), x);
	} else {
		tmp = x + fma((y / z), -36.52704169880642, (3.13060547623 * y));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -0.41)
		tmp = fma(3.13060547623, y, x);
	elseif (z <= 420000000.0)
		tmp = fma(fma(fma(t, z, a), z, b), Float64(y / Float64(0.607771387771 + Float64(11.9400905721 * z))), x);
	else
		tmp = Float64(x + fma(Float64(y / z), -36.52704169880642, Float64(3.13060547623 * y)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -0.41], N[(3.13060547623 * y + x), $MachinePrecision], If[LessEqual[z, 420000000.0], N[(N[(N[(t * z + a), $MachinePrecision] * z + b), $MachinePrecision] * N[(y / N[(0.607771387771 + N[(11.9400905721 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(x + N[(N[(y / z), $MachinePrecision] * -36.52704169880642 + N[(3.13060547623 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.409999999999999976

   1. Initial program 13.7%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-fma.f64 90.3

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

   5. Applied rewrites 90.3%

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

   if -0.409999999999999976 < z < 4.2e8

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0

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

      1. lower-*.f64 99.4

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

   5. Applied rewrites 99.4%

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

   6. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 93.8

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

   8. Applied rewrites 93.8%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

   10. Applied rewrites 93.9%

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

   11. Taylor expanded in z around 0

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

       1. +-commutative N/A

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

       2. *-commutative N/A

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

       3. lower-fma.f64 N/A

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

       4. +-commutative N/A

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

       5. lower-fma.f64 99.4

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

   13. Applied rewrites 99.4%

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

   if 4.2e8 < z

   1. Initial program 18.3%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. +-commutative N/A

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

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

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. metadata-eval N/A

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

      7. lower-*.f64 88.3

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

   5. Applied rewrites 88.3%

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

Alternative 4: 89.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+18}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \mathbf{elif}\;z \leq 0.122:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(a, z, b\right), \mathsf{fma}\left(y \cdot z, -32.324150453290734, 1.6453555072203998 \cdot y\right), x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \mathsf{fma}\left(\frac{y}{z}, -36.52704169880642, 3.13060547623 \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -4.2e+18)
   (fma 3.13060547623 y x)
   (if (<= z 0.122)
     (fma
      (fma a z b)
      (fma (* y z) -32.324150453290734 (* 1.6453555072203998 y))
      x)
     (+ x (fma (/ y z) -36.52704169880642 (* 3.13060547623 y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -4.2e+18) {
		tmp = fma(3.13060547623, y, x);
	} else if (z <= 0.122) {
		tmp = fma(fma(a, z, b), fma((y * z), -32.324150453290734, (1.6453555072203998 * y)), x);
	} else {
		tmp = x + fma((y / z), -36.52704169880642, (3.13060547623 * y));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -4.2e+18)
		tmp = fma(3.13060547623, y, x);
	elseif (z <= 0.122)
		tmp = fma(fma(a, z, b), fma(Float64(y * z), -32.324150453290734, Float64(1.6453555072203998 * y)), x);
	else
		tmp = Float64(x + fma(Float64(y / z), -36.52704169880642, Float64(3.13060547623 * y)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -4.2e+18], N[(3.13060547623 * y + x), $MachinePrecision], If[LessEqual[z, 0.122], N[(N[(a * z + b), $MachinePrecision] * N[(N[(y * z), $MachinePrecision] * -32.324150453290734 + N[(1.6453555072203998 * y), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(x + N[(N[(y / z), $MachinePrecision] * -36.52704169880642 + N[(3.13060547623 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.2e18

   1. Initial program 13.7%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-fma.f64 90.3

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

   5. Applied rewrites 90.3%

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

   if -4.2e18 < z < 0.122

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0

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

      1. lower-*.f64 99.4

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

   5. Applied rewrites 99.4%

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

   6. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 93.8

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

   8. Applied rewrites 93.8%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

   10. Applied rewrites 93.9%

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

   11. Taylor expanded in z around 0

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

       1. *-commutative N/A

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

       2. lower-fma.f64 N/A

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

       3. lower-*.f64 N/A

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

       4. lower-*.f64 93.9

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

   13. Applied rewrites 93.9%

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

   if 0.122 < z

   1. Initial program 18.3%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. +-commutative N/A

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

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

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. metadata-eval N/A

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

      7. lower-*.f64 88.3

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

   5. Applied rewrites 88.3%

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

Alternative 5: 89.9% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+18}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \mathbf{elif}\;z \leq 90000000:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(a, z, b\right), 1.6453555072203998 \cdot y, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \mathsf{fma}\left(\frac{y}{z}, -36.52704169880642, 3.13060547623 \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -4.2e+18)
   (fma 3.13060547623 y x)
   (if (<= z 90000000.0)
     (fma (fma a z b) (* 1.6453555072203998 y) x)
     (+ x (fma (/ y z) -36.52704169880642 (* 3.13060547623 y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -4.2e+18) {
		tmp = fma(3.13060547623, y, x);
	} else if (z <= 90000000.0) {
		tmp = fma(fma(a, z, b), (1.6453555072203998 * y), x);
	} else {
		tmp = x + fma((y / z), -36.52704169880642, (3.13060547623 * y));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -4.2e+18)
		tmp = fma(3.13060547623, y, x);
	elseif (z <= 90000000.0)
		tmp = fma(fma(a, z, b), Float64(1.6453555072203998 * y), x);
	else
		tmp = Float64(x + fma(Float64(y / z), -36.52704169880642, Float64(3.13060547623 * y)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -4.2e+18], N[(3.13060547623 * y + x), $MachinePrecision], If[LessEqual[z, 90000000.0], N[(N[(a * z + b), $MachinePrecision] * N[(1.6453555072203998 * y), $MachinePrecision] + x), $MachinePrecision], N[(x + N[(N[(y / z), $MachinePrecision] * -36.52704169880642 + N[(3.13060547623 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.2e18

   1. Initial program 13.7%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-fma.f64 90.3

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

   5. Applied rewrites 90.3%

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

   if -4.2e18 < z < 9e7

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0

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

      1. lower-*.f64 99.4

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

   5. Applied rewrites 99.4%

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

   6. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 93.8

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

   8. Applied rewrites 93.8%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

   10. Applied rewrites 93.9%

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

   11. Taylor expanded in z around 0

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

       1. lower-*.f64 93.2

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

   13. Applied rewrites 93.2%

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

   if 9e7 < z

   1. Initial program 18.3%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. +-commutative N/A

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

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

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. metadata-eval N/A

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

      7. lower-*.f64 88.3

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

   5. Applied rewrites 88.3%

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

Alternative 6: 89.9% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+18} \lor \neg \left(z \leq 90000000\right):\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(a, z, b\right), 1.6453555072203998 \cdot y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -4.2e+18) (not (<= z 90000000.0)))
   (fma 3.13060547623 y x)
   (fma (fma a z b) (* 1.6453555072203998 y) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -4.2e+18) || !(z <= 90000000.0)) {
		tmp = fma(3.13060547623, y, x);
	} else {
		tmp = fma(fma(a, z, b), (1.6453555072203998 * y), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -4.2e+18) || !(z <= 90000000.0))
		tmp = fma(3.13060547623, y, x);
	else
		tmp = fma(fma(a, z, b), Float64(1.6453555072203998 * y), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -4.2e+18], N[Not[LessEqual[z, 90000000.0]], $MachinePrecision]], N[(3.13060547623 * y + x), $MachinePrecision], N[(N[(a * z + b), $MachinePrecision] * N[(1.6453555072203998 * y), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.2e18 or 9e7 < z

   1. Initial program 16.0%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-fma.f64 89.2

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

   5. Applied rewrites 89.2%

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

   if -4.2e18 < z < 9e7

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0

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

      1. lower-*.f64 99.4

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

   5. Applied rewrites 99.4%

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

   6. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 93.8

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

   8. Applied rewrites 93.8%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

   10. Applied rewrites 93.9%

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

   11. Taylor expanded in z around 0

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

       1. lower-*.f64 93.2

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

   13. Applied rewrites 93.2%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+18} \lor \neg \left(z \leq 90000000\right):\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(a, z, b\right), 1.6453555072203998 \cdot y, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 83.3% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+18} \lor \neg \left(z \leq 90000000\right):\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(-b\right) \cdot \left(-1.6453555072203998 \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -3.4e+18) (not (<= z 90000000.0)))
   (fma 3.13060547623 y x)
   (+ x (* (- b) (* -1.6453555072203998 y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3.4e+18) || !(z <= 90000000.0)) {
		tmp = fma(3.13060547623, y, x);
	} else {
		tmp = x + (-b * (-1.6453555072203998 * y));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -3.4e+18) || !(z <= 90000000.0))
		tmp = fma(3.13060547623, y, x);
	else
		tmp = Float64(x + Float64(Float64(-b) * Float64(-1.6453555072203998 * y)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -3.4e+18], N[Not[LessEqual[z, 90000000.0]], $MachinePrecision]], N[(3.13060547623 * y + x), $MachinePrecision], N[(x + N[((-b) * N[(-1.6453555072203998 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.4e18 or 9e7 < z

   1. Initial program 16.0%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-fma.f64 89.2

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

   5. Applied rewrites 89.2%

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

   if -3.4e18 < z < 9e7

   1. Initial program 99.7%

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

   3. Taylor expanded in b around -inf

      \[\leadsto x + \color{blue}{-1 \cdot \left(b \cdot \left(-1 \cdot \frac{y}{\frac{607771387771}{1000000000000} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)} + -1 \cdot \frac{y \cdot \left(z \cdot \left(a + z \cdot \left(t + z \cdot \left(\frac{55833770631}{5000000000} + \frac{313060547623}{100000000000} \cdot z\right)\right)\right)\right)}{b \cdot \left(\frac{607771387771}{1000000000000} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)\right)}\right)\right)} \]

   5. Applied rewrites 91.3%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 78.7%

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

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+18} \lor \neg \left(z \leq 90000000\right):\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(-b\right) \cdot \left(-1.6453555072203998 \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 83.3% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+18} \lor \neg \left(z \leq 90000000\right):\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b \cdot y, 1.6453555072203998, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -3.4e+18) (not (<= z 90000000.0)))
   (fma 3.13060547623 y x)
   (fma (* b y) 1.6453555072203998 x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3.4e+18) || !(z <= 90000000.0)) {
		tmp = fma(3.13060547623, y, x);
	} else {
		tmp = fma((b * y), 1.6453555072203998, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -3.4e+18) || !(z <= 90000000.0))
		tmp = fma(3.13060547623, y, x);
	else
		tmp = fma(Float64(b * y), 1.6453555072203998, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -3.4e+18], N[Not[LessEqual[z, 90000000.0]], $MachinePrecision]], N[(3.13060547623 * y + x), $MachinePrecision], N[(N[(b * y), $MachinePrecision] * 1.6453555072203998 + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.4e18 or 9e7 < z

   1. Initial program 16.0%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-fma.f64 89.2

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

   5. Applied rewrites 89.2%

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

   if -3.4e18 < z < 9e7

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 78.7

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

   5. Applied rewrites 78.7%

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

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+18} \lor \neg \left(z \leq 90000000\right):\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b \cdot y, 1.6453555072203998, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 49.7% accurate, 4.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+15} \lor \neg \left(y \leq 1.46 \cdot 10^{+152}\right):\\ \;\;\;\;3.13060547623 \cdot y\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -5e+15) (not (<= y 1.46e+152))) (* 3.13060547623 y) (* 1.0 x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -5e+15) || !(y <= 1.46e+152)) {
		tmp = 3.13060547623 * y;
	} else {
		tmp = 1.0 * x;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-5d+15)) .or. (.not. (y <= 1.46d+152))) then
        tmp = 3.13060547623d0 * y
    else
        tmp = 1.0d0 * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -5e+15) || !(y <= 1.46e+152)) {
		tmp = 3.13060547623 * y;
	} else {
		tmp = 1.0 * x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -5e+15) or not (y <= 1.46e+152):
		tmp = 3.13060547623 * y
	else:
		tmp = 1.0 * x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -5e+15) || !(y <= 1.46e+152))
		tmp = Float64(3.13060547623 * y);
	else
		tmp = Float64(1.0 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -5e+15) || ~((y <= 1.46e+152)))
		tmp = 3.13060547623 * y;
	else
		tmp = 1.0 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -5e+15], N[Not[LessEqual[y, 1.46e+152]], $MachinePrecision]], N[(3.13060547623 * y), $MachinePrecision], N[(1.0 * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5e15 or 1.46e152 < y

   1. Initial program 53.3%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-fma.f64 52.0

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

   5. Applied rewrites 52.0%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 43.5%

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

   if -5e15 < y < 1.46e152

   1. Initial program 64.2%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-fma.f64 71.8

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

   5. Applied rewrites 71.8%

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

   6. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(1 + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(\frac{55833770631}{5000000000} + \frac{313060547623}{100000000000} \cdot z\right)\right)\right)\right)}{x \cdot \left(\frac{607771387771}{1000000000000} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)\right)}\right)} \]

   8. Applied rewrites 52.8%

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

   9. Taylor expanded in x around inf

      \[\leadsto 1 \cdot x \]
   10. Step-by-step derivation

   11. Applied rewrites 61.6%

       \[\leadsto 1 \cdot x \]
3. Recombined 2 regimes into one program.

4. Final simplification 54.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+15} \lor \neg \left(y \leq 1.46 \cdot 10^{+152}\right):\\ \;\;\;\;3.13060547623 \cdot y\\ \mathbf{else}:\\ \;\;\;\;1 \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 62.1% 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 60.1%

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

3. Taylor expanded in z around inf

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

   1. +-commutative N/A

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

   2. lower-fma.f64 64.3

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

5. Applied rewrites 64.3%

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

Alternative 11: 23.1% accurate, 13.2× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 60.1%

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

3. Taylor expanded in z around inf

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

   1. +-commutative N/A

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

   2. lower-fma.f64 64.3

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

5. Applied rewrites 64.3%

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

6. Taylor expanded in x around 0

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

8. Applied rewrites 25.9%

   \[\leadsto 3.13060547623 \cdot \color{blue}{y} \]
9. Add Preprocessing

Developer Target 1: 98.4% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(N[(3.13060547623 - N[(36.527041698806414 / z), $MachinePrecision]), $MachinePrecision] + N[(t / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(y / 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[z, -6.499344996252632e+53], t$95$1, If[Less[z, 7.066965436914287e+59], N[(x + N[(y / N[(N[(N[(N[(N[(N[(N[(N[(z + 15.234687407), $MachinePrecision] * z), $MachinePrecision] + 31.4690115749), $MachinePrecision] * z), $MachinePrecision] + 11.9400905721), $MachinePrecision] * z), $MachinePrecision] + 0.607771387771), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(N[(z * 3.13060547623), $MachinePrecision] + 11.1667541262), $MachinePrecision] * z), $MachinePrecision] + t), $MachinePrecision] * z), $MachinePrecision] + a), $MachinePrecision] * z), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2025008 
(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))))