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

Percentage Accurate: 58.2% → 98.4%

Time: 6.1s

Alternatives: 19

Speedup: 8.8×

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 58.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-\frac{\left(-\frac{\left(\left(-\frac{\left(-a\right) - \mathsf{fma}\left(-15.234687407, 457.9610022158428 + t, 1112.0901850848957\right)}{z}\right) + t\right) + 457.9610022158428}{z}\right) + 36.52704169880642}{z}\right) + 3.13060547623\\ \mathbf{if}\;z \leq -4.3 \cdot 10^{+20}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, y, x\right)\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{+18}:\\ \;\;\;\;\mathsf{fma}\left(\frac{\mathsf{fma}\left(\mathsf{fma}\left(t, z, a\right), z, b\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(15.234687407 + z, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+
          (-
           (/
            (+
             (-
              (/
               (+
                (+
                 (-
                  (/
                   (-
                    (- a)
                    (fma
                     -15.234687407
                     (+ 457.9610022158428 t)
                     1112.0901850848957))
                   z))
                 t)
                457.9610022158428)
               z))
             36.52704169880642)
            z))
          3.13060547623)))
   (if (<= z -4.3e+20)
     (fma t_1 y x)
     (if (<= z 7.4e+18)
       (fma
        (/
         (fma (fma t z a) z b)
         (fma
          (fma (fma (+ 15.234687407 z) z 31.4690115749) z 11.9400905721)
          z
          0.607771387771))
        y
        x)
       (+ x (* y t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -((-(((-((-a - fma(-15.234687407, (457.9610022158428 + t), 1112.0901850848957)) / z) + t) + 457.9610022158428) / z) + 36.52704169880642) / z) + 3.13060547623;
	double tmp;
	if (z <= -4.3e+20) {
		tmp = fma(t_1, y, x);
	} else if (z <= 7.4e+18) {
		tmp = fma((fma(fma(t, z, a), z, b) / fma(fma(fma((15.234687407 + z), z, 31.4690115749), z, 11.9400905721), z, 0.607771387771)), y, x);
	} else {
		tmp = x + (y * t_1);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(-Float64(Float64(Float64(-Float64(Float64(Float64(Float64(-Float64(Float64(Float64(-a) - fma(-15.234687407, Float64(457.9610022158428 + t), 1112.0901850848957)) / z)) + t) + 457.9610022158428) / z)) + 36.52704169880642) / z)) + 3.13060547623)
	tmp = 0.0
	if (z <= -4.3e+20)
		tmp = fma(t_1, y, x);
	elseif (z <= 7.4e+18)
		tmp = fma(Float64(fma(fma(t, z, a), z, b) / fma(fma(fma(Float64(15.234687407 + z), z, 31.4690115749), z, 11.9400905721), z, 0.607771387771)), y, x);
	else
		tmp = Float64(x + Float64(y * t_1));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[((-N[(N[((-N[(N[(N[((-N[(N[((-a) - N[(-15.234687407 * N[(457.9610022158428 + t), $MachinePrecision] + 1112.0901850848957), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]) + t), $MachinePrecision] + 457.9610022158428), $MachinePrecision] / z), $MachinePrecision]) + 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]) + 3.13060547623), $MachinePrecision]}, If[LessEqual[z, -4.3e+20], N[(t$95$1 * y + x), $MachinePrecision], If[LessEqual[z, 7.4e+18], N[(N[(N[(N[(t * z + a), $MachinePrecision] * z + b), $MachinePrecision] / N[(N[(N[(N[(15.234687407 + z), $MachinePrecision] * z + 31.4690115749), $MachinePrecision] * z + 11.9400905721), $MachinePrecision] * z + 0.607771387771), $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision], N[(x + N[(y * t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.3e20

   1. Initial program 58.2%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 65.6

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

   4. Applied rewrites 65.6%

      \[\leadsto x + \frac{y \cdot \color{blue}{\mathsf{fma}\left(a, z, b\right)}}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   5. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-+.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-+.f64 N/A

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

      10. associate-/l* N/A

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

   6. Applied rewrites 67.1%

      \[\leadsto x + \color{blue}{y \cdot \frac{\mathsf{fma}\left(a, z, b\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687407, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}} \]
   7. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 67.1

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

      6. lift-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 67.1

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

   8. Applied rewrites 67.1%

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

   9. Taylor expanded in z around -inf

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

   11. Applied rewrites 56.3%

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

   if -4.3e20 < z < 7.4e18

   1. Initial program 58.2%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 65.6

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

   4. Applied rewrites 65.6%

      \[\leadsto x + \frac{y \cdot \color{blue}{\mathsf{fma}\left(a, z, b\right)}}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   5. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-+.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-+.f64 N/A

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

      10. associate-/l* N/A

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

   6. Applied rewrites 67.1%

      \[\leadsto x + \color{blue}{y \cdot \frac{\mathsf{fma}\left(a, z, b\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687407, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}} \]
   7. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 67.1

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

      6. lift-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 67.1

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

   8. Applied rewrites 67.1%

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

   9. Taylor expanded in z around 0

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

       1. +-commutative N/A

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

       2. *-commutative N/A

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

       3. lower-fma.f64 N/A

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

       4. +-commutative N/A

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

       5. lower-fma.f64 63.2

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

   11. Applied rewrites 63.2%

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

   if 7.4e18 < z

   1. Initial program 58.2%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 65.6

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

   4. Applied rewrites 65.6%

      \[\leadsto x + \frac{y \cdot \color{blue}{\mathsf{fma}\left(a, z, b\right)}}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   5. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-+.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-+.f64 N/A

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

      10. associate-/l* N/A

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

   6. Applied rewrites 67.1%

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

   7. Taylor expanded in z around -inf

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

   9. Applied rewrites 56.3%

      \[\leadsto x + y \cdot \color{blue}{\left(\left(-\frac{\left(-\frac{\left(\left(-\frac{\left(-a\right) - \mathsf{fma}\left(-15.234687407, 457.9610022158428 + t, 1112.0901850848957\right)}{z}\right) + t\right) + 457.9610022158428}{z}\right) + 36.52704169880642}{z}\right) + 3.13060547623\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 2: 98.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\left(-\frac{\left(-\frac{\left(\left(-\frac{\left(-a\right) - \mathsf{fma}\left(-15.234687407, 457.9610022158428 + t, 1112.0901850848957\right)}{z}\right) + t\right) + 457.9610022158428}{z}\right) + 36.52704169880642}{z}\right) + 3.13060547623, y, x\right)\\ \mathbf{if}\;z \leq -4.3 \cdot 10^{+20}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{+18}:\\ \;\;\;\;\mathsf{fma}\left(\frac{\mathsf{fma}\left(\mathsf{fma}\left(t, z, a\right), z, b\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(15.234687407 + z, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (fma
          (+
           (-
            (/
             (+
              (-
               (/
                (+
                 (+
                  (-
                   (/
                    (-
                     (- a)
                     (fma
                      -15.234687407
                      (+ 457.9610022158428 t)
                      1112.0901850848957))
                    z))
                  t)
                 457.9610022158428)
                z))
              36.52704169880642)
             z))
           3.13060547623)
          y
          x)))
   (if (<= z -4.3e+20)
     t_1
     (if (<= z 7.4e+18)
       (fma
        (/
         (fma (fma t z a) z b)
         (fma
          (fma (fma (+ 15.234687407 z) z 31.4690115749) z 11.9400905721)
          z
          0.607771387771))
        y
        x)
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma((-((-(((-((-a - fma(-15.234687407, (457.9610022158428 + t), 1112.0901850848957)) / z) + t) + 457.9610022158428) / z) + 36.52704169880642) / z) + 3.13060547623), y, x);
	double tmp;
	if (z <= -4.3e+20) {
		tmp = t_1;
	} else if (z <= 7.4e+18) {
		tmp = fma((fma(fma(t, z, a), z, b) / fma(fma(fma((15.234687407 + z), z, 31.4690115749), z, 11.9400905721), z, 0.607771387771)), y, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(Float64(-Float64(Float64(Float64(-Float64(Float64(Float64(Float64(-Float64(Float64(Float64(-a) - fma(-15.234687407, Float64(457.9610022158428 + t), 1112.0901850848957)) / z)) + t) + 457.9610022158428) / z)) + 36.52704169880642) / z)) + 3.13060547623), y, x)
	tmp = 0.0
	if (z <= -4.3e+20)
		tmp = t_1;
	elseif (z <= 7.4e+18)
		tmp = fma(Float64(fma(fma(t, z, a), z, b) / fma(fma(fma(Float64(15.234687407 + z), z, 31.4690115749), z, 11.9400905721), z, 0.607771387771)), y, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[((-N[(N[((-N[(N[(N[((-N[(N[((-a) - N[(-15.234687407 * N[(457.9610022158428 + t), $MachinePrecision] + 1112.0901850848957), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]) + t), $MachinePrecision] + 457.9610022158428), $MachinePrecision] / z), $MachinePrecision]) + 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]) + 3.13060547623), $MachinePrecision] * y + x), $MachinePrecision]}, If[LessEqual[z, -4.3e+20], t$95$1, If[LessEqual[z, 7.4e+18], N[(N[(N[(N[(t * z + a), $MachinePrecision] * z + b), $MachinePrecision] / N[(N[(N[(N[(15.234687407 + z), $MachinePrecision] * z + 31.4690115749), $MachinePrecision] * z + 11.9400905721), $MachinePrecision] * z + 0.607771387771), $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.3e20 or 7.4e18 < z

   1. Initial program 58.2%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 65.6

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

   4. Applied rewrites 65.6%

      \[\leadsto x + \frac{y \cdot \color{blue}{\mathsf{fma}\left(a, z, b\right)}}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   5. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-+.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-+.f64 N/A

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

      10. associate-/l* N/A

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

   6. Applied rewrites 67.1%

      \[\leadsto x + \color{blue}{y \cdot \frac{\mathsf{fma}\left(a, z, b\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687407, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}} \]
   7. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 67.1

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

      6. lift-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 67.1

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

   8. Applied rewrites 67.1%

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

   9. Taylor expanded in z around -inf

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

   11. Applied rewrites 56.3%

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

   if -4.3e20 < z < 7.4e18

   1. Initial program 58.2%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 65.6

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

   4. Applied rewrites 65.6%

      \[\leadsto x + \frac{y \cdot \color{blue}{\mathsf{fma}\left(a, z, b\right)}}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   5. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-+.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-+.f64 N/A

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

      10. associate-/l* N/A

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

   6. Applied rewrites 67.1%

      \[\leadsto x + \color{blue}{y \cdot \frac{\mathsf{fma}\left(a, z, b\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687407, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}} \]
   7. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 67.1

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

      6. lift-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 67.1

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

   8. Applied rewrites 67.1%

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

   9. Taylor expanded in z around 0

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

       1. +-commutative N/A

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

       2. *-commutative N/A

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

       3. lower-fma.f64 N/A

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

       4. +-commutative N/A

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

       5. lower-fma.f64 63.2

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

   11. Applied rewrites 63.2%

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

Alternative 3: 97.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-\frac{\left(-\frac{457.9610022158428 + t}{z}\right) + 36.52704169880642}{z}\right) + 3.13060547623\\ \mathbf{if}\;z \leq -1.75 \cdot 10^{+25}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, y, x\right)\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+39}:\\ \;\;\;\;\mathsf{fma}\left(\frac{\mathsf{fma}\left(\mathsf{fma}\left(t, z, a\right), z, b\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(15.234687407 + z, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+
          (- (/ (+ (- (/ (+ 457.9610022158428 t) z)) 36.52704169880642) z))
          3.13060547623)))
   (if (<= z -1.75e+25)
     (fma t_1 y x)
     (if (<= z 1.05e+39)
       (fma
        (/
         (fma (fma t z a) z b)
         (fma
          (fma (fma (+ 15.234687407 z) z 31.4690115749) z 11.9400905721)
          z
          0.607771387771))
        y
        x)
       (+ x (* y t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -((-((457.9610022158428 + t) / z) + 36.52704169880642) / z) + 3.13060547623;
	double tmp;
	if (z <= -1.75e+25) {
		tmp = fma(t_1, y, x);
	} else if (z <= 1.05e+39) {
		tmp = fma((fma(fma(t, z, a), z, b) / fma(fma(fma((15.234687407 + z), z, 31.4690115749), z, 11.9400905721), z, 0.607771387771)), y, x);
	} else {
		tmp = x + (y * t_1);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(-Float64(Float64(Float64(-Float64(Float64(457.9610022158428 + t) / z)) + 36.52704169880642) / z)) + 3.13060547623)
	tmp = 0.0
	if (z <= -1.75e+25)
		tmp = fma(t_1, y, x);
	elseif (z <= 1.05e+39)
		tmp = fma(Float64(fma(fma(t, z, a), z, b) / fma(fma(fma(Float64(15.234687407 + z), z, 31.4690115749), z, 11.9400905721), z, 0.607771387771)), y, x);
	else
		tmp = Float64(x + Float64(y * t_1));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[((-N[(N[((-N[(N[(457.9610022158428 + t), $MachinePrecision] / z), $MachinePrecision]) + 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]) + 3.13060547623), $MachinePrecision]}, If[LessEqual[z, -1.75e+25], N[(t$95$1 * y + x), $MachinePrecision], If[LessEqual[z, 1.05e+39], N[(N[(N[(N[(t * z + a), $MachinePrecision] * z + b), $MachinePrecision] / N[(N[(N[(N[(15.234687407 + z), $MachinePrecision] * z + 31.4690115749), $MachinePrecision] * z + 11.9400905721), $MachinePrecision] * z + 0.607771387771), $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision], N[(x + N[(y * t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.75e25

   1. Initial program 58.2%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 65.6

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

   4. Applied rewrites 65.6%

      \[\leadsto x + \frac{y \cdot \color{blue}{\mathsf{fma}\left(a, z, b\right)}}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   5. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-+.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-+.f64 N/A

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

      10. associate-/l* N/A

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

   6. Applied rewrites 67.1%

      \[\leadsto x + \color{blue}{y \cdot \frac{\mathsf{fma}\left(a, z, b\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687407, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}} \]
   7. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 67.1

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

      6. lift-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 67.1

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

   8. Applied rewrites 67.1%

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

   9. Taylor expanded in z around -inf

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

       1. +-commutative N/A

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

       2. lower-+.f64 N/A

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

       3. mul-1-neg N/A

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

       4. lower-neg.f64 N/A

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

       5. lower-/.f64 N/A

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

       6. +-commutative N/A

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

       7. lower-+.f64 N/A

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

       8. mul-1-neg N/A

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

       9. lower-neg.f64 N/A

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

       10. lower-/.f64 N/A

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

       11. lower-+.f64 55.8

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

   11. Applied rewrites 55.8%

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

   if -1.75e25 < z < 1.0499999999999999e39

   1. Initial program 58.2%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 65.6

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

   4. Applied rewrites 65.6%

      \[\leadsto x + \frac{y \cdot \color{blue}{\mathsf{fma}\left(a, z, b\right)}}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   5. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-+.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-+.f64 N/A

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

      10. associate-/l* N/A

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

   6. Applied rewrites 67.1%

      \[\leadsto x + \color{blue}{y \cdot \frac{\mathsf{fma}\left(a, z, b\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687407, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}} \]
   7. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 67.1

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

      6. lift-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 67.1

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

   8. Applied rewrites 67.1%

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

   9. Taylor expanded in z around 0

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

       1. +-commutative N/A

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

       2. *-commutative N/A

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

       3. lower-fma.f64 N/A

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

       4. +-commutative N/A

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

       5. lower-fma.f64 63.2

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

   11. Applied rewrites 63.2%

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

   if 1.0499999999999999e39 < z

   1. Initial program 58.2%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 65.6

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

   4. Applied rewrites 65.6%

      \[\leadsto x + \frac{y \cdot \color{blue}{\mathsf{fma}\left(a, z, b\right)}}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   5. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-+.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-+.f64 N/A

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

      10. associate-/l* N/A

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

   6. Applied rewrites 67.1%

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

   7. Taylor expanded in z around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower-+.f64 55.8

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

   9. Applied rewrites 55.8%

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

Alternative 4: 95.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}\\ \mathbf{if}\;t\_1 \leq 10^{+307}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(\left(-\frac{\left(-\frac{\left(\left(-\frac{\left(-a\right) - \mathsf{fma}\left(-15.234687407, 457.9610022158428 + t, 1112.0901850848957\right)}{z}\right) + t\right) + 457.9610022158428}{z}\right) + 36.52704169880642}{z}\right) + 3.13060547623\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+
          x
          (/
           (*
            y
            (+
             (*
              (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a)
              z)
             b))
           (+
            (*
             (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721)
             z)
            0.607771387771)))))
   (if (<= t_1 1e+307)
     t_1
     (+
      x
      (*
       y
       (+
        (-
         (/
          (+
           (-
            (/
             (+
              (+
               (-
                (/
                 (-
                  (- a)
                  (fma
                   -15.234687407
                   (+ 457.9610022158428 t)
                   1112.0901850848957))
                 z))
               t)
              457.9610022158428)
             z))
           36.52704169880642)
          z))
        3.13060547623))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((y * ((((((((z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b)) / (((((((z + 15.234687407) * z) + 31.4690115749) * z) + 11.9400905721) * z) + 0.607771387771));
	double tmp;
	if (t_1 <= 1e+307) {
		tmp = t_1;
	} else {
		tmp = x + (y * (-((-(((-((-a - fma(-15.234687407, (457.9610022158428 + t), 1112.0901850848957)) / z) + t) + 457.9610022158428) / z) + 36.52704169880642) / z) + 3.13060547623));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(y * Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b)) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(z + 15.234687407) * z) + 31.4690115749) * z) + 11.9400905721) * z) + 0.607771387771)))
	tmp = 0.0
	if (t_1 <= 1e+307)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(y * Float64(Float64(-Float64(Float64(Float64(-Float64(Float64(Float64(Float64(-Float64(Float64(Float64(-a) - fma(-15.234687407, Float64(457.9610022158428 + t), 1112.0901850848957)) / z)) + t) + 457.9610022158428) / z)) + 36.52704169880642) / z)) + 3.13060547623)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(y * N[(N[(N[(N[(N[(N[(N[(N[(z * 3.13060547623), $MachinePrecision] + 11.1667541262), $MachinePrecision] * z), $MachinePrecision] + t), $MachinePrecision] * z), $MachinePrecision] + a), $MachinePrecision] * z), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(z + 15.234687407), $MachinePrecision] * z), $MachinePrecision] + 31.4690115749), $MachinePrecision] * z), $MachinePrecision] + 11.9400905721), $MachinePrecision] * z), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 1e+307], t$95$1, N[(x + N[(y * N[((-N[(N[((-N[(N[(N[((-N[(N[((-a) - N[(-15.234687407 * N[(457.9610022158428 + t), $MachinePrecision] + 1112.0901850848957), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]) + t), $MachinePrecision] + 457.9610022158428), $MachinePrecision] / z), $MachinePrecision]) + 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]) + 3.13060547623), $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)))) < 9.99999999999999986e306

   1. Initial program 58.2%

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

   if 9.99999999999999986e306 < (+.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 58.2%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 65.6

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

   4. Applied rewrites 65.6%

      \[\leadsto x + \frac{y \cdot \color{blue}{\mathsf{fma}\left(a, z, b\right)}}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   5. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-+.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-+.f64 N/A

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

      10. associate-/l* N/A

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

   6. Applied rewrites 67.1%

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

   7. Taylor expanded in z around -inf

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

   9. Applied rewrites 56.3%

      \[\leadsto x + y \cdot \color{blue}{\left(\left(-\frac{\left(-\frac{\left(\left(-\frac{\left(-a\right) - \mathsf{fma}\left(-15.234687407, 457.9610022158428 + t, 1112.0901850848957\right)}{z}\right) + t\right) + 457.9610022158428}{z}\right) + 36.52704169880642}{z}\right) + 3.13060547623\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 95.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-\frac{\left(-\frac{457.9610022158428 + t}{z}\right) + 36.52704169880642}{z}\right) + 3.13060547623\\ \mathbf{if}\;z \leq -55000:\\ \;\;\;\;\mathsf{fma}\left(t\_1, y, x\right)\\ \mathbf{elif}\;z \leq 56000000000000:\\ \;\;\;\;x + y \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(3.13060547623, z, 11.1667541262\right), z, t\right), z, a\right), z, b\right)}{\mathsf{fma}\left(11.9400905721, z, 0.607771387771\right)}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+
          (- (/ (+ (- (/ (+ 457.9610022158428 t) z)) 36.52704169880642) z))
          3.13060547623)))
   (if (<= z -55000.0)
     (fma t_1 y x)
     (if (<= z 56000000000000.0)
       (+
        x
        (*
         y
         (/
          (fma (fma (fma (fma 3.13060547623 z 11.1667541262) z t) z a) z b)
          (fma 11.9400905721 z 0.607771387771))))
       (+ x (* y t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -((-((457.9610022158428 + t) / z) + 36.52704169880642) / z) + 3.13060547623;
	double tmp;
	if (z <= -55000.0) {
		tmp = fma(t_1, y, x);
	} else if (z <= 56000000000000.0) {
		tmp = x + (y * (fma(fma(fma(fma(3.13060547623, z, 11.1667541262), z, t), z, a), z, b) / fma(11.9400905721, z, 0.607771387771)));
	} else {
		tmp = x + (y * t_1);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(-Float64(Float64(Float64(-Float64(Float64(457.9610022158428 + t) / z)) + 36.52704169880642) / z)) + 3.13060547623)
	tmp = 0.0
	if (z <= -55000.0)
		tmp = fma(t_1, y, x);
	elseif (z <= 56000000000000.0)
		tmp = Float64(x + Float64(y * Float64(fma(fma(fma(fma(3.13060547623, z, 11.1667541262), z, t), z, a), z, b) / fma(11.9400905721, z, 0.607771387771))));
	else
		tmp = Float64(x + Float64(y * t_1));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[((-N[(N[((-N[(N[(457.9610022158428 + t), $MachinePrecision] / z), $MachinePrecision]) + 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]) + 3.13060547623), $MachinePrecision]}, If[LessEqual[z, -55000.0], N[(t$95$1 * y + x), $MachinePrecision], If[LessEqual[z, 56000000000000.0], N[(x + N[(y * N[(N[(N[(N[(N[(3.13060547623 * z + 11.1667541262), $MachinePrecision] * z + t), $MachinePrecision] * z + a), $MachinePrecision] * z + b), $MachinePrecision] / N[(11.9400905721 * z + 0.607771387771), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -55000

   1. Initial program 58.2%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 65.6

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

   4. Applied rewrites 65.6%

      \[\leadsto x + \frac{y \cdot \color{blue}{\mathsf{fma}\left(a, z, b\right)}}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   5. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-+.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-+.f64 N/A

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

      10. associate-/l* N/A

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

   6. Applied rewrites 67.1%

      \[\leadsto x + \color{blue}{y \cdot \frac{\mathsf{fma}\left(a, z, b\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687407, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}} \]
   7. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 67.1

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

      6. lift-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 67.1

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

   8. Applied rewrites 67.1%

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

   9. Taylor expanded in z around -inf

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

       1. +-commutative N/A

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

       2. lower-+.f64 N/A

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

       3. mul-1-neg N/A

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

       4. lower-neg.f64 N/A

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

       5. lower-/.f64 N/A

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

       6. +-commutative N/A

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

       7. lower-+.f64 N/A

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

       8. mul-1-neg N/A

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

       9. lower-neg.f64 N/A

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

       10. lower-/.f64 N/A

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

       11. lower-+.f64 55.8

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

   11. Applied rewrites 55.8%

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

   if -55000 < z < 5.6e13

   1. Initial program 58.2%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 54.3

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

   4. Applied rewrites 54.3%

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

      1. lift-/.f64 N/A

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

   6. Applied rewrites 54.3%

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

   if 5.6e13 < z

   1. Initial program 58.2%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 65.6

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

   4. Applied rewrites 65.6%

      \[\leadsto x + \frac{y \cdot \color{blue}{\mathsf{fma}\left(a, z, b\right)}}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   5. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-+.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-+.f64 N/A

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

      10. associate-/l* N/A

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

   6. Applied rewrites 67.1%

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

   7. Taylor expanded in z around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower-+.f64 55.8

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

   9. Applied rewrites 55.8%

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

Alternative 6: 95.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-\frac{\left(-\frac{457.9610022158428 + t}{z}\right) + 36.52704169880642}{z}\right) + 3.13060547623\\ \mathbf{if}\;z \leq -55000:\\ \;\;\;\;\mathsf{fma}\left(t\_1, y, x\right)\\ \mathbf{elif}\;z \leq 56000000000000:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(11.1667541262, z, t\right), z, a\right), z, b\right)}{\mathsf{fma}\left(11.9400905721, z, 0.607771387771\right)}, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+
          (- (/ (+ (- (/ (+ 457.9610022158428 t) z)) 36.52704169880642) z))
          3.13060547623)))
   (if (<= z -55000.0)
     (fma t_1 y x)
     (if (<= z 56000000000000.0)
       (fma
        y
        (/
         (fma (fma (fma 11.1667541262 z t) z a) z b)
         (fma 11.9400905721 z 0.607771387771))
        x)
       (+ x (* y t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -((-((457.9610022158428 + t) / z) + 36.52704169880642) / z) + 3.13060547623;
	double tmp;
	if (z <= -55000.0) {
		tmp = fma(t_1, y, x);
	} else if (z <= 56000000000000.0) {
		tmp = fma(y, (fma(fma(fma(11.1667541262, z, t), z, a), z, b) / fma(11.9400905721, z, 0.607771387771)), x);
	} else {
		tmp = x + (y * t_1);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(-Float64(Float64(Float64(-Float64(Float64(457.9610022158428 + t) / z)) + 36.52704169880642) / z)) + 3.13060547623)
	tmp = 0.0
	if (z <= -55000.0)
		tmp = fma(t_1, y, x);
	elseif (z <= 56000000000000.0)
		tmp = fma(y, Float64(fma(fma(fma(11.1667541262, z, t), z, a), z, b) / fma(11.9400905721, z, 0.607771387771)), x);
	else
		tmp = Float64(x + Float64(y * t_1));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[((-N[(N[((-N[(N[(457.9610022158428 + t), $MachinePrecision] / z), $MachinePrecision]) + 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]) + 3.13060547623), $MachinePrecision]}, If[LessEqual[z, -55000.0], N[(t$95$1 * y + x), $MachinePrecision], If[LessEqual[z, 56000000000000.0], N[(y * N[(N[(N[(N[(11.1667541262 * z + t), $MachinePrecision] * z + a), $MachinePrecision] * z + b), $MachinePrecision] / N[(11.9400905721 * z + 0.607771387771), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(x + N[(y * t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -55000

   1. Initial program 58.2%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 65.6

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

   4. Applied rewrites 65.6%

      \[\leadsto x + \frac{y \cdot \color{blue}{\mathsf{fma}\left(a, z, b\right)}}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   5. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-+.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-+.f64 N/A

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

      10. associate-/l* N/A

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

   6. Applied rewrites 67.1%

      \[\leadsto x + \color{blue}{y \cdot \frac{\mathsf{fma}\left(a, z, b\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687407, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}} \]
   7. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 67.1

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

      6. lift-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 67.1

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

   8. Applied rewrites 67.1%

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

   9. Taylor expanded in z around -inf

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

       1. +-commutative N/A

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

       2. lower-+.f64 N/A

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

       3. mul-1-neg N/A

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

       4. lower-neg.f64 N/A

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

       5. lower-/.f64 N/A

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

       6. +-commutative N/A

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

       7. lower-+.f64 N/A

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

       8. mul-1-neg N/A

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

       9. lower-neg.f64 N/A

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

       10. lower-/.f64 N/A

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

       11. lower-+.f64 55.8

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

   11. Applied rewrites 55.8%

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

   if -55000 < z < 5.6e13

   1. Initial program 58.2%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 54.3

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

   4. Applied rewrites 54.3%

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

   5. Taylor expanded in z around 0

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

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

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

      2. lower--.f64 N/A

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

      3. metadata-eval N/A

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

      4. lower-*.f64 55.3

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

   7. Applied rewrites 55.3%

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

   9. Applied rewrites 55.3%

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

   if 5.6e13 < z

   1. Initial program 58.2%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 65.6

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

   4. Applied rewrites 65.6%

      \[\leadsto x + \frac{y \cdot \color{blue}{\mathsf{fma}\left(a, z, b\right)}}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   5. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-+.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-+.f64 N/A

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

      10. associate-/l* N/A

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

   6. Applied rewrites 67.1%

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

   7. Taylor expanded in z around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower-+.f64 55.8

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

   9. Applied rewrites 55.8%

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

Alternative 7: 95.6% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-\frac{\left(-\frac{457.9610022158428 + t}{z}\right) + 36.52704169880642}{z}\right) + 3.13060547623\\ \mathbf{if}\;z \leq -55000:\\ \;\;\;\;\mathsf{fma}\left(t\_1, y, x\right)\\ \mathbf{elif}\;z \leq 58000000000000:\\ \;\;\;\;x + \frac{y \cdot \left(\mathsf{fma}\left(t, z, a\right) \cdot z + b\right)}{\mathsf{fma}\left(11.9400905721, z, 0.607771387771\right)}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+
          (- (/ (+ (- (/ (+ 457.9610022158428 t) z)) 36.52704169880642) z))
          3.13060547623)))
   (if (<= z -55000.0)
     (fma t_1 y x)
     (if (<= z 58000000000000.0)
       (+
        x
        (/ (* y (+ (* (fma t z a) z) b)) (fma 11.9400905721 z 0.607771387771)))
       (+ x (* y t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -((-((457.9610022158428 + t) / z) + 36.52704169880642) / z) + 3.13060547623;
	double tmp;
	if (z <= -55000.0) {
		tmp = fma(t_1, y, x);
	} else if (z <= 58000000000000.0) {
		tmp = x + ((y * ((fma(t, z, a) * z) + b)) / fma(11.9400905721, z, 0.607771387771));
	} else {
		tmp = x + (y * t_1);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(-Float64(Float64(Float64(-Float64(Float64(457.9610022158428 + t) / z)) + 36.52704169880642) / z)) + 3.13060547623)
	tmp = 0.0
	if (z <= -55000.0)
		tmp = fma(t_1, y, x);
	elseif (z <= 58000000000000.0)
		tmp = Float64(x + Float64(Float64(y * Float64(Float64(fma(t, z, a) * z) + b)) / fma(11.9400905721, z, 0.607771387771)));
	else
		tmp = Float64(x + Float64(y * t_1));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[((-N[(N[((-N[(N[(457.9610022158428 + t), $MachinePrecision] / z), $MachinePrecision]) + 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]) + 3.13060547623), $MachinePrecision]}, If[LessEqual[z, -55000.0], N[(t$95$1 * y + x), $MachinePrecision], If[LessEqual[z, 58000000000000.0], N[(x + N[(N[(y * N[(N[(N[(t * z + a), $MachinePrecision] * z), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(11.9400905721 * z + 0.607771387771), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -55000

   1. Initial program 58.2%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 65.6

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

   4. Applied rewrites 65.6%

      \[\leadsto x + \frac{y \cdot \color{blue}{\mathsf{fma}\left(a, z, b\right)}}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   5. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-+.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-+.f64 N/A

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

      10. associate-/l* N/A

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

   6. Applied rewrites 67.1%

      \[\leadsto x + \color{blue}{y \cdot \frac{\mathsf{fma}\left(a, z, b\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687407, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}} \]
   7. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 67.1

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

      6. lift-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 67.1

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

   8. Applied rewrites 67.1%

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

   9. Taylor expanded in z around -inf

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

       1. +-commutative N/A

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

       2. lower-+.f64 N/A

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

       3. mul-1-neg N/A

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

       4. lower-neg.f64 N/A

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

       5. lower-/.f64 N/A

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

       6. +-commutative N/A

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

       7. lower-+.f64 N/A

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

       8. mul-1-neg N/A

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

       9. lower-neg.f64 N/A

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

       10. lower-/.f64 N/A

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

       11. lower-+.f64 55.8

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

   11. Applied rewrites 55.8%

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

   if -55000 < z < 5.8e13

   1. Initial program 58.2%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 54.3

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

   4. Applied rewrites 54.3%

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

   5. Taylor expanded in z around 0

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

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

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

      2. lower--.f64 N/A

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

      3. metadata-eval N/A

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

      4. lower-*.f64 55.3

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

   7. Applied rewrites 55.3%

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

   8. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 58.2

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

   10. Applied rewrites 58.2%

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

   if 5.8e13 < z

   1. Initial program 58.2%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 65.6

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

   4. Applied rewrites 65.6%

      \[\leadsto x + \frac{y \cdot \color{blue}{\mathsf{fma}\left(a, z, b\right)}}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   5. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-+.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-+.f64 N/A

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

      10. associate-/l* N/A

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

   6. Applied rewrites 67.1%

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

   7. Taylor expanded in z around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower-+.f64 55.8

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

   9. Applied rewrites 55.8%

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

Alternative 8: 95.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-\frac{\left(-\frac{457.9610022158428 + t}{z}\right) + 36.52704169880642}{z}\right) + 3.13060547623\\ \mathbf{if}\;z \leq -3.3 \cdot 10^{+18}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, y, x\right)\\ \mathbf{elif}\;z \leq 56000000000000:\\ \;\;\;\;x + y \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(11.1667541262, z, t\right), z, a\right), z, b\right)}{0.607771387771}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+
          (- (/ (+ (- (/ (+ 457.9610022158428 t) z)) 36.52704169880642) z))
          3.13060547623)))
   (if (<= z -3.3e+18)
     (fma t_1 y x)
     (if (<= z 56000000000000.0)
       (+
        x
        (* y (/ (fma (fma (fma 11.1667541262 z t) z a) z b) 0.607771387771)))
       (+ x (* y t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -((-((457.9610022158428 + t) / z) + 36.52704169880642) / z) + 3.13060547623;
	double tmp;
	if (z <= -3.3e+18) {
		tmp = fma(t_1, y, x);
	} else if (z <= 56000000000000.0) {
		tmp = x + (y * (fma(fma(fma(11.1667541262, z, t), z, a), z, b) / 0.607771387771));
	} else {
		tmp = x + (y * t_1);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(-Float64(Float64(Float64(-Float64(Float64(457.9610022158428 + t) / z)) + 36.52704169880642) / z)) + 3.13060547623)
	tmp = 0.0
	if (z <= -3.3e+18)
		tmp = fma(t_1, y, x);
	elseif (z <= 56000000000000.0)
		tmp = Float64(x + Float64(y * Float64(fma(fma(fma(11.1667541262, z, t), z, a), z, b) / 0.607771387771)));
	else
		tmp = Float64(x + Float64(y * t_1));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[((-N[(N[((-N[(N[(457.9610022158428 + t), $MachinePrecision] / z), $MachinePrecision]) + 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]) + 3.13060547623), $MachinePrecision]}, If[LessEqual[z, -3.3e+18], N[(t$95$1 * y + x), $MachinePrecision], If[LessEqual[z, 56000000000000.0], N[(x + N[(y * N[(N[(N[(N[(11.1667541262 * z + t), $MachinePrecision] * z + a), $MachinePrecision] * z + b), $MachinePrecision] / 0.607771387771), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.3e18

   1. Initial program 58.2%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 65.6

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

   4. Applied rewrites 65.6%

      \[\leadsto x + \frac{y \cdot \color{blue}{\mathsf{fma}\left(a, z, b\right)}}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   5. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-+.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-+.f64 N/A

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

      10. associate-/l* N/A

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

   6. Applied rewrites 67.1%

      \[\leadsto x + \color{blue}{y \cdot \frac{\mathsf{fma}\left(a, z, b\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687407, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}} \]
   7. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 67.1

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

      6. lift-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 67.1

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

   8. Applied rewrites 67.1%

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

   9. Taylor expanded in z around -inf

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

       1. +-commutative N/A

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

       2. lower-+.f64 N/A

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

       3. mul-1-neg N/A

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

       4. lower-neg.f64 N/A

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

       5. lower-/.f64 N/A

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

       6. +-commutative N/A

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

       7. lower-+.f64 N/A

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

       8. mul-1-neg N/A

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

       9. lower-neg.f64 N/A

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

       10. lower-/.f64 N/A

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

       11. lower-+.f64 55.8

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

   11. Applied rewrites 55.8%

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

   if -3.3e18 < z < 5.6e13

   1. Initial program 58.2%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 65.6

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

   4. Applied rewrites 65.6%

      \[\leadsto x + \frac{y \cdot \color{blue}{\mathsf{fma}\left(a, z, b\right)}}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   5. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-+.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-+.f64 N/A

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

      10. associate-/l* N/A

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

   6. Applied rewrites 67.1%

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

   7. Taylor expanded in z around 0

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

   9. Applied rewrites 59.8%

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

   10. Taylor expanded in z around 0

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

       1. +-commutative N/A

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

       2. *-commutative N/A

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

       3. lower-fma.f64 N/A

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

       4. +-commutative N/A

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

       5. metadata-eval N/A

          \[\leadsto x + y \cdot \frac{\mathsf{fma}\left(z \cdot \left(t + \left(\mathsf{neg}\left(\frac{-55833770631}{5000000000}\right)\right) \cdot z\right) + a, z, b\right)}{\frac{607771387771}{1000000000000}} \]

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

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

       7. *-commutative N/A

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

       8. lower-fma.f64 N/A

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

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

          \[\leadsto x + y \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(t + \left(\mathsf{neg}\left(\frac{-55833770631}{5000000000}\right)\right) \cdot z, z, a\right), z, b\right)}{\frac{607771387771}{1000000000000}} \]

       10. metadata-eval N/A

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

       11. +-commutative N/A

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

       12. lower-fma.f64 55.1

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

   12. Applied rewrites 55.1%

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

   if 5.6e13 < z

   1. Initial program 58.2%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 65.6

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

   4. Applied rewrites 65.6%

      \[\leadsto x + \frac{y \cdot \color{blue}{\mathsf{fma}\left(a, z, b\right)}}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   5. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-+.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-+.f64 N/A

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

      10. associate-/l* N/A

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

   6. Applied rewrites 67.1%

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

   7. Taylor expanded in z around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower-+.f64 55.8

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

   9. Applied rewrites 55.8%

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

Alternative 9: 95.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-\frac{\left(-\frac{457.9610022158428 + t}{z}\right) + 36.52704169880642}{z}\right) + 3.13060547623\\ \mathbf{if}\;z \leq -3.3 \cdot 10^{+18}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, y, x\right)\\ \mathbf{elif}\;z \leq 58000000000000:\\ \;\;\;\;x + y \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(t, z, a\right), z, b\right)}{0.607771387771}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+
          (- (/ (+ (- (/ (+ 457.9610022158428 t) z)) 36.52704169880642) z))
          3.13060547623)))
   (if (<= z -3.3e+18)
     (fma t_1 y x)
     (if (<= z 58000000000000.0)
       (+ x (* y (/ (fma (fma t z a) z b) 0.607771387771)))
       (+ x (* y t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -((-((457.9610022158428 + t) / z) + 36.52704169880642) / z) + 3.13060547623;
	double tmp;
	if (z <= -3.3e+18) {
		tmp = fma(t_1, y, x);
	} else if (z <= 58000000000000.0) {
		tmp = x + (y * (fma(fma(t, z, a), z, b) / 0.607771387771));
	} else {
		tmp = x + (y * t_1);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(-Float64(Float64(Float64(-Float64(Float64(457.9610022158428 + t) / z)) + 36.52704169880642) / z)) + 3.13060547623)
	tmp = 0.0
	if (z <= -3.3e+18)
		tmp = fma(t_1, y, x);
	elseif (z <= 58000000000000.0)
		tmp = Float64(x + Float64(y * Float64(fma(fma(t, z, a), z, b) / 0.607771387771)));
	else
		tmp = Float64(x + Float64(y * t_1));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[((-N[(N[((-N[(N[(457.9610022158428 + t), $MachinePrecision] / z), $MachinePrecision]) + 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]) + 3.13060547623), $MachinePrecision]}, If[LessEqual[z, -3.3e+18], N[(t$95$1 * y + x), $MachinePrecision], If[LessEqual[z, 58000000000000.0], N[(x + N[(y * N[(N[(N[(t * z + a), $MachinePrecision] * z + b), $MachinePrecision] / 0.607771387771), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.3e18

   1. Initial program 58.2%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 65.6

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

   4. Applied rewrites 65.6%

      \[\leadsto x + \frac{y \cdot \color{blue}{\mathsf{fma}\left(a, z, b\right)}}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   5. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-+.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-+.f64 N/A

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

      10. associate-/l* N/A

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

   6. Applied rewrites 67.1%

      \[\leadsto x + \color{blue}{y \cdot \frac{\mathsf{fma}\left(a, z, b\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687407, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}} \]
   7. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 67.1

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

      6. lift-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 67.1

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

   8. Applied rewrites 67.1%

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

   9. Taylor expanded in z around -inf

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

       1. +-commutative N/A

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

       2. lower-+.f64 N/A

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

       3. mul-1-neg N/A

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

       4. lower-neg.f64 N/A

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

       5. lower-/.f64 N/A

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

       6. +-commutative N/A

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

       7. lower-+.f64 N/A

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

       8. mul-1-neg N/A

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

       9. lower-neg.f64 N/A

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

       10. lower-/.f64 N/A

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

       11. lower-+.f64 55.8

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

   11. Applied rewrites 55.8%

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

   if -3.3e18 < z < 5.8e13

   1. Initial program 58.2%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 65.6

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

   4. Applied rewrites 65.6%

      \[\leadsto x + \frac{y \cdot \color{blue}{\mathsf{fma}\left(a, z, b\right)}}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   5. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-+.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-+.f64 N/A

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

      10. associate-/l* N/A

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

   6. Applied rewrites 67.1%

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

   7. Taylor expanded in z around 0

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

   9. Applied rewrites 59.8%

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

   10. Taylor expanded in z around 0

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

       1. +-commutative N/A

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

       2. *-commutative N/A

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

       3. lower-fma.f64 N/A

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

       4. +-commutative N/A

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

       5. lower-fma.f64 57.0

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

   12. Applied rewrites 57.0%

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

   if 5.8e13 < z

   1. Initial program 58.2%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 65.6

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

   4. Applied rewrites 65.6%

      \[\leadsto x + \frac{y \cdot \color{blue}{\mathsf{fma}\left(a, z, b\right)}}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   5. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-+.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-+.f64 N/A

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

      10. associate-/l* N/A

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

   6. Applied rewrites 67.1%

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

   7. Taylor expanded in z around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower-+.f64 55.8

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

   9. Applied rewrites 55.8%

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

Alternative 10: 95.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\left(-\frac{\left(-\frac{457.9610022158428 + t}{z}\right) + 36.52704169880642}{z}\right) + 3.13060547623, y, x\right)\\ \mathbf{if}\;z \leq -3.3 \cdot 10^{+18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 58000000000000:\\ \;\;\;\;x + y \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(t, z, a\right), z, b\right)}{0.607771387771}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (fma
          (+
           (- (/ (+ (- (/ (+ 457.9610022158428 t) z)) 36.52704169880642) z))
           3.13060547623)
          y
          x)))
   (if (<= z -3.3e+18)
     t_1
     (if (<= z 58000000000000.0)
       (+ x (* y (/ (fma (fma t z a) z b) 0.607771387771)))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma((-((-((457.9610022158428 + t) / z) + 36.52704169880642) / z) + 3.13060547623), y, x);
	double tmp;
	if (z <= -3.3e+18) {
		tmp = t_1;
	} else if (z <= 58000000000000.0) {
		tmp = x + (y * (fma(fma(t, z, a), z, b) / 0.607771387771));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(Float64(Float64(-Float64(Float64(Float64(-Float64(Float64(457.9610022158428 + t) / z)) + 36.52704169880642) / z)) + 3.13060547623), y, x)
	tmp = 0.0
	if (z <= -3.3e+18)
		tmp = t_1;
	elseif (z <= 58000000000000.0)
		tmp = Float64(x + Float64(y * Float64(fma(fma(t, z, a), z, b) / 0.607771387771)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[((-N[(N[((-N[(N[(457.9610022158428 + t), $MachinePrecision] / z), $MachinePrecision]) + 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]) + 3.13060547623), $MachinePrecision] * y + x), $MachinePrecision]}, If[LessEqual[z, -3.3e+18], t$95$1, If[LessEqual[z, 58000000000000.0], N[(x + N[(y * N[(N[(N[(t * z + a), $MachinePrecision] * z + b), $MachinePrecision] / 0.607771387771), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.3e18 or 5.8e13 < z

   1. Initial program 58.2%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 65.6

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

   4. Applied rewrites 65.6%

      \[\leadsto x + \frac{y \cdot \color{blue}{\mathsf{fma}\left(a, z, b\right)}}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   5. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-+.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-+.f64 N/A

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

      10. associate-/l* N/A

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

   6. Applied rewrites 67.1%

      \[\leadsto x + \color{blue}{y \cdot \frac{\mathsf{fma}\left(a, z, b\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687407, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}} \]
   7. Step-by-step derivation

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 67.1

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

      6. lift-+.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 67.1

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

   8. Applied rewrites 67.1%

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

   9. Taylor expanded in z around -inf

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

       1. +-commutative N/A

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

       2. lower-+.f64 N/A

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

       3. mul-1-neg N/A

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

       4. lower-neg.f64 N/A

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

       5. lower-/.f64 N/A

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

       6. +-commutative N/A

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

       7. lower-+.f64 N/A

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

       8. mul-1-neg N/A

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

       9. lower-neg.f64 N/A

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

       10. lower-/.f64 N/A

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

       11. lower-+.f64 55.8

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

   11. Applied rewrites 55.8%

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

   if -3.3e18 < z < 5.8e13

   1. Initial program 58.2%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 65.6

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

   4. Applied rewrites 65.6%

      \[\leadsto x + \frac{y \cdot \color{blue}{\mathsf{fma}\left(a, z, b\right)}}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   5. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-+.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-+.f64 N/A

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

      10. associate-/l* N/A

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

   6. Applied rewrites 67.1%

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

   7. Taylor expanded in z around 0

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

   9. Applied rewrites 59.8%

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

   10. Taylor expanded in z around 0

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

       1. +-commutative N/A

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

       2. *-commutative N/A

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

       3. lower-fma.f64 N/A

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

       4. +-commutative N/A

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

       5. lower-fma.f64 57.0

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

   12. Applied rewrites 57.0%

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

Alternative 11: 92.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+22}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \mathbf{elif}\;z \leq 1.26 \cdot 10^{+14}:\\ \;\;\;\;x + y \cdot \frac{\mathsf{fma}\left(\mathsf{fma}\left(t, z, a\right), z, b\right)}{0.607771387771}\\ \mathbf{else}:\\ \;\;\;\;x + \mathsf{fma}\left(3.13060547623, y, -\frac{y \cdot 36.52704169880642}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.45e+22)
   (fma 3.13060547623 y x)
   (if (<= z 1.26e+14)
     (+ x (* y (/ (fma (fma t z a) z b) 0.607771387771)))
     (+ x (fma 3.13060547623 y (- (/ (* y 36.52704169880642) z)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.45e+22) {
		tmp = fma(3.13060547623, y, x);
	} else if (z <= 1.26e+14) {
		tmp = x + (y * (fma(fma(t, z, a), z, b) / 0.607771387771));
	} else {
		tmp = x + fma(3.13060547623, y, -((y * 36.52704169880642) / z));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.45e+22)
		tmp = fma(3.13060547623, y, x);
	elseif (z <= 1.26e+14)
		tmp = Float64(x + Float64(y * Float64(fma(fma(t, z, a), z, b) / 0.607771387771)));
	else
		tmp = Float64(x + fma(3.13060547623, y, Float64(-Float64(Float64(y * 36.52704169880642) / z))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.45e+22], N[(3.13060547623 * y + x), $MachinePrecision], If[LessEqual[z, 1.26e+14], N[(x + N[(y * N[(N[(N[(t * z + a), $MachinePrecision] * z + b), $MachinePrecision] / 0.607771387771), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(3.13060547623 * y + (-N[(N[(y * 36.52704169880642), $MachinePrecision] / z), $MachinePrecision])), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.45e22

   1. Initial program 58.2%

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

   2. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-fma.f64 62.4

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

   4. Applied rewrites 62.4%

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

   if -1.45e22 < z < 1.26e14

   1. Initial program 58.2%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 65.6

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

   4. Applied rewrites 65.6%

      \[\leadsto x + \frac{y \cdot \color{blue}{\mathsf{fma}\left(a, z, b\right)}}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   5. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-+.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-+.f64 N/A

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

      10. associate-/l* N/A

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

   6. Applied rewrites 67.1%

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

   7. Taylor expanded in z around 0

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

   9. Applied rewrites 59.8%

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

   10. Taylor expanded in z around 0

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

       1. +-commutative N/A

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

       2. *-commutative N/A

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

       3. lower-fma.f64 N/A

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

       4. +-commutative N/A

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

       5. lower-fma.f64 57.0

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

   12. Applied rewrites 57.0%

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

   if 1.26e14 < z

   1. Initial program 58.2%

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

   2. Taylor expanded in z around -inf

      \[\leadsto x + \color{blue}{\left(-1 \cdot \frac{\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y}{z} + \frac{313060547623}{100000000000} \cdot y\right)} \]
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto x + \left(\frac{313060547623}{100000000000} \cdot y + \color{blue}{-1 \cdot \frac{\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y}{z}}\right) \]

      2. lower-fma.f64 N/A

         \[\leadsto x + \mathsf{fma}\left(\frac{313060547623}{100000000000}, \color{blue}{y}, -1 \cdot \frac{\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y}{z}\right) \]

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

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

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

      7. lower-*.f64 N/A

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

      8. metadata-eval 58.8

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

   4. Applied rewrites 58.8%

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

Alternative 12: 90.0% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+22}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{+14}:\\ \;\;\;\;\mathsf{fma}\left(\frac{\mathsf{fma}\left(a, z, b\right)}{0.607771387771}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;x - -3.13060547623 \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.45e+22)
   (fma 3.13060547623 y x)
   (if (<= z 4.7e+14)
     (fma (/ (fma a z b) 0.607771387771) y x)
     (- x (* -3.13060547623 y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.45e+22) {
		tmp = fma(3.13060547623, y, x);
	} else if (z <= 4.7e+14) {
		tmp = fma((fma(a, z, b) / 0.607771387771), y, x);
	} else {
		tmp = x - (-3.13060547623 * y);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.45e+22)
		tmp = fma(3.13060547623, y, x);
	elseif (z <= 4.7e+14)
		tmp = fma(Float64(fma(a, z, b) / 0.607771387771), y, x);
	else
		tmp = Float64(x - Float64(-3.13060547623 * y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.45e+22], N[(3.13060547623 * y + x), $MachinePrecision], If[LessEqual[z, 4.7e+14], N[(N[(N[(a * z + b), $MachinePrecision] / 0.607771387771), $MachinePrecision] * y + x), $MachinePrecision], N[(x - N[(-3.13060547623 * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.45e22

   1. Initial program 58.2%

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

   2. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-fma.f64 62.4

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

   4. Applied rewrites 62.4%

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

   if -1.45e22 < z < 4.7e14

   1. Initial program 58.2%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 65.6

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

   4. Applied rewrites 65.6%

      \[\leadsto x + \frac{y \cdot \color{blue}{\mathsf{fma}\left(a, z, b\right)}}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   5. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift-+.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. lift-+.f64 N/A

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

      10. associate-/l* N/A

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

   6. Applied rewrites 67.1%

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

   7. Taylor expanded in z around 0

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

   9. Applied rewrites 59.8%

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

       1. lift-+.f64 N/A

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

       2. +-commutative N/A

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

       3. lift-*.f64 N/A

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

       4. *-commutative N/A

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

       5. lower-fma.f64 59.8

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

   11. Applied rewrites 59.8%

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

   if 4.7e14 < z

   1. Initial program 58.2%

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

   2. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-fma.f64 62.4

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

   4. Applied rewrites 62.4%

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

   5. Taylor expanded in x around 0

      \[\leadsto x + \color{blue}{\frac{313060547623}{100000000000} \cdot y} \]
   6. Step-by-step derivation

      1. fp-cancel-sign-sub-inv N/A

         \[\leadsto x - \left(\mathsf{neg}\left(\frac{313060547623}{100000000000}\right)\right) \cdot \color{blue}{y} \]

      2. lower--.f64 N/A

         \[\leadsto x - \left(\mathsf{neg}\left(\frac{313060547623}{100000000000}\right)\right) \cdot \color{blue}{y} \]

      3. metadata-eval N/A

         \[\leadsto x - \frac{-313060547623}{100000000000} \cdot y \]

      4. lower-*.f64 62.4

         \[\leadsto x - -3.13060547623 \cdot y \]

   7. Applied rewrites 62.4%

      \[\leadsto x - \color{blue}{-3.13060547623 \cdot y} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 13: 89.9% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+22}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{+14}:\\ \;\;\;\;\mathsf{fma}\left(\frac{\mathsf{fma}\left(a, z, b\right)}{0.607771387771}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \mathsf{fma}\left(3.13060547623, y, -\frac{y \cdot 36.52704169880642}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.45e+22)
   (fma 3.13060547623 y x)
   (if (<= z 4.7e+14)
     (fma (/ (fma a z b) 0.607771387771) y x)
     (+ x (fma 3.13060547623 y (- (/ (* y 36.52704169880642) z)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.45e+22) {
		tmp = fma(3.13060547623, y, x);
	} else if (z <= 4.7e+14) {
		tmp = fma((fma(a, z, b) / 0.607771387771), y, x);
	} else {
		tmp = x + fma(3.13060547623, y, -((y * 36.52704169880642) / z));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.45e+22)
		tmp = fma(3.13060547623, y, x);
	elseif (z <= 4.7e+14)
		tmp = fma(Float64(fma(a, z, b) / 0.607771387771), y, x);
	else
		tmp = Float64(x + fma(3.13060547623, y, Float64(-Float64(Float64(y * 36.52704169880642) / z))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.45e+22], N[(3.13060547623 * y + x), $MachinePrecision], If[LessEqual[z, 4.7e+14], N[(N[(N[(a * z + b), $MachinePrecision] / 0.607771387771), $MachinePrecision] * y + x), $MachinePrecision], N[(x + N[(3.13060547623 * y + (-N[(N[(y * 36.52704169880642), $MachinePrecision] / z), $MachinePrecision])), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.45e22

   1. Initial program 58.2%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{x + \frac{313060547623}{100000000000} \cdot y} \]
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \frac{313060547623}{100000000000} \cdot y + \color{blue}{x} \]

      2. lower-fma.f64 62.4

         \[\leadsto \mathsf{fma}\left(3.13060547623, \color{blue}{y}, x\right) \]

   4. Applied rewrites 62.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(3.13060547623, y, x\right)} \]

   if -1.45e22 < z < 4.7e14

   1. Initial program 58.2%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

   2. Taylor expanded in z around 0

      \[\leadsto x + \frac{y \cdot \color{blue}{\left(b + a \cdot z\right)}}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto x + \frac{y \cdot \left(a \cdot z + \color{blue}{b}\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      2. lower-fma.f64 65.6

         \[\leadsto x + \frac{y \cdot \mathsf{fma}\left(a, \color{blue}{z}, b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

   4. Applied rewrites 65.6%

      \[\leadsto x + \frac{y \cdot \color{blue}{\mathsf{fma}\left(a, z, b\right)}}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   5. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto x + \color{blue}{\frac{y \cdot \mathsf{fma}\left(a, z, b\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}}} \]

      2. lift-*.f64 N/A

         \[\leadsto x + \frac{\color{blue}{y \cdot \mathsf{fma}\left(a, z, b\right)}}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      3. lift-+.f64 N/A

         \[\leadsto x + \frac{y \cdot \mathsf{fma}\left(a, z, b\right)}{\color{blue}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}}} \]

      4. lift-*.f64 N/A

         \[\leadsto x + \frac{y \cdot \mathsf{fma}\left(a, z, b\right)}{\color{blue}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z} + \frac{607771387771}{1000000000000}} \]

      5. lift-+.f64 N/A

         \[\leadsto x + \frac{y \cdot \mathsf{fma}\left(a, z, b\right)}{\color{blue}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right)} \cdot z + \frac{607771387771}{1000000000000}} \]

      6. lift-*.f64 N/A

         \[\leadsto x + \frac{y \cdot \mathsf{fma}\left(a, z, b\right)}{\left(\color{blue}{\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z} + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      7. lift-+.f64 N/A

         \[\leadsto x + \frac{y \cdot \mathsf{fma}\left(a, z, b\right)}{\left(\color{blue}{\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right)} \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      8. lift-*.f64 N/A

         \[\leadsto x + \frac{y \cdot \mathsf{fma}\left(a, z, b\right)}{\left(\left(\color{blue}{\left(z + \frac{15234687407}{1000000000}\right) \cdot z} + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      9. lift-+.f64 N/A

         \[\leadsto x + \frac{y \cdot \mathsf{fma}\left(a, z, b\right)}{\left(\left(\color{blue}{\left(z + \frac{15234687407}{1000000000}\right)} \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \]

      10. associate-/l* N/A

          \[\leadsto x + \color{blue}{y \cdot \frac{\mathsf{fma}\left(a, z, b\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}}} \]

   6. Applied rewrites 67.1%

      \[\leadsto x + \color{blue}{y \cdot \frac{\mathsf{fma}\left(a, z, b\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687407, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}} \]

   7. Taylor expanded in z around 0

      \[\leadsto x + y \cdot \frac{\mathsf{fma}\left(a, z, b\right)}{\color{blue}{\frac{607771387771}{1000000000000}}} \]
   8. Step-by-step derivation

   9. Applied rewrites 59.8%

      \[\leadsto x + y \cdot \frac{\mathsf{fma}\left(a, z, b\right)}{\color{blue}{0.607771387771}} \]
   10. Step-by-step derivation

       1. lift-+.f64 N/A

          \[\leadsto \color{blue}{x + y \cdot \frac{\mathsf{fma}\left(a, z, b\right)}{\frac{607771387771}{1000000000000}}} \]

       2. +-commutative N/A

          \[\leadsto \color{blue}{y \cdot \frac{\mathsf{fma}\left(a, z, b\right)}{\frac{607771387771}{1000000000000}} + x} \]

       3. lift-*.f64 N/A

          \[\leadsto \color{blue}{y \cdot \frac{\mathsf{fma}\left(a, z, b\right)}{\frac{607771387771}{1000000000000}}} + x \]

       4. *-commutative N/A

          \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(a, z, b\right)}{\frac{607771387771}{1000000000000}} \cdot y} + x \]

       5. lower-fma.f64 59.8

          \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(a, z, b\right)}{0.607771387771}, y, x\right)} \]

   11. Applied rewrites 59.8%

       \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(a, z, b\right)}{0.607771387771}, y, x\right)} \]

   if 4.7e14 < z

   1. Initial program 58.2%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

   2. Taylor expanded in z around -inf

      \[\leadsto x + \color{blue}{\left(-1 \cdot \frac{\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y}{z} + \frac{313060547623}{100000000000} \cdot y\right)} \]
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto x + \left(\frac{313060547623}{100000000000} \cdot y + \color{blue}{-1 \cdot \frac{\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y}{z}}\right) \]

      2. lower-fma.f64 N/A

         \[\leadsto x + \mathsf{fma}\left(\frac{313060547623}{100000000000}, \color{blue}{y}, -1 \cdot \frac{\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y}{z}\right) \]

      3. mul-1-neg N/A

         \[\leadsto x + \mathsf{fma}\left(\frac{313060547623}{100000000000}, y, \mathsf{neg}\left(\frac{\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y}{z}\right)\right) \]

      4. lower-neg.f64 N/A

         \[\leadsto x + \mathsf{fma}\left(\frac{313060547623}{100000000000}, y, -\frac{\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y}{z}\right) \]

      5. lower-/.f64 N/A

         \[\leadsto x + \mathsf{fma}\left(\frac{313060547623}{100000000000}, y, -\frac{\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y}{z}\right) \]

      6. distribute-rgt-out-- N/A

         \[\leadsto x + \mathsf{fma}\left(\frac{313060547623}{100000000000}, y, -\frac{y \cdot \left(\frac{-55833770631}{5000000000} - \frac{-4769379582500641883561}{100000000000000000000}\right)}{z}\right) \]

      7. lower-*.f64 N/A

         \[\leadsto x + \mathsf{fma}\left(\frac{313060547623}{100000000000}, y, -\frac{y \cdot \left(\frac{-55833770631}{5000000000} - \frac{-4769379582500641883561}{100000000000000000000}\right)}{z}\right) \]

      8. metadata-eval 58.8

         \[\leadsto x + \mathsf{fma}\left(3.13060547623, y, -\frac{y \cdot 36.52704169880642}{z}\right) \]

   4. Applied rewrites 58.8%

      \[\leadsto x + \color{blue}{\mathsf{fma}\left(3.13060547623, y, -\frac{y \cdot 36.52704169880642}{z}\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 14: 83.3% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+15}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-10}:\\ \;\;\;\;\mathsf{fma}\left(b \cdot y, 1.6453555072203998, x\right)\\ \mathbf{else}:\\ \;\;\;\;x - -3.13060547623 \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.05e+15)
   (fma 3.13060547623 y x)
   (if (<= z 4.6e-10)
     (fma (* b y) 1.6453555072203998 x)
     (- x (* -3.13060547623 y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.05e+15) {
		tmp = fma(3.13060547623, y, x);
	} else if (z <= 4.6e-10) {
		tmp = fma((b * y), 1.6453555072203998, x);
	} else {
		tmp = x - (-3.13060547623 * y);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.05e+15)
		tmp = fma(3.13060547623, y, x);
	elseif (z <= 4.6e-10)
		tmp = fma(Float64(b * y), 1.6453555072203998, x);
	else
		tmp = Float64(x - Float64(-3.13060547623 * y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.05e+15], N[(3.13060547623 * y + x), $MachinePrecision], If[LessEqual[z, 4.6e-10], N[(N[(b * y), $MachinePrecision] * 1.6453555072203998 + x), $MachinePrecision], N[(x - N[(-3.13060547623 * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.05e15

   1. Initial program 58.2%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{x + \frac{313060547623}{100000000000} \cdot y} \]
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \frac{313060547623}{100000000000} \cdot y + \color{blue}{x} \]

      2. lower-fma.f64 62.4

         \[\leadsto \mathsf{fma}\left(3.13060547623, \color{blue}{y}, x\right) \]

   4. Applied rewrites 62.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(3.13060547623, y, x\right)} \]

   if -1.05e15 < z < 4.60000000000000014e-10

   1. Initial program 58.2%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

   2. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + \frac{1000000000000}{607771387771} \cdot \left(b \cdot y\right)} \]
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \frac{1000000000000}{607771387771} \cdot \left(b \cdot y\right) + \color{blue}{x} \]

      2. *-commutative N/A

         \[\leadsto \left(b \cdot y\right) \cdot \frac{1000000000000}{607771387771} + x \]

      3. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(b \cdot y, \color{blue}{\frac{1000000000000}{607771387771}}, x\right) \]

      4. lower-*.f64 60.0

         \[\leadsto \mathsf{fma}\left(b \cdot y, 1.6453555072203998, x\right) \]

   4. Applied rewrites 60.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(b \cdot y, 1.6453555072203998, x\right)} \]

   if 4.60000000000000014e-10 < z

   1. Initial program 58.2%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{x + \frac{313060547623}{100000000000} \cdot y} \]
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \frac{313060547623}{100000000000} \cdot y + \color{blue}{x} \]

      2. lower-fma.f64 62.4

         \[\leadsto \mathsf{fma}\left(3.13060547623, \color{blue}{y}, x\right) \]

   4. Applied rewrites 62.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(3.13060547623, y, x\right)} \]

   5. Taylor expanded in x around 0

      \[\leadsto x + \color{blue}{\frac{313060547623}{100000000000} \cdot y} \]
   6. Step-by-step derivation

      1. fp-cancel-sign-sub-inv N/A

         \[\leadsto x - \left(\mathsf{neg}\left(\frac{313060547623}{100000000000}\right)\right) \cdot \color{blue}{y} \]

      2. lower--.f64 N/A

         \[\leadsto x - \left(\mathsf{neg}\left(\frac{313060547623}{100000000000}\right)\right) \cdot \color{blue}{y} \]

      3. metadata-eval N/A

         \[\leadsto x - \frac{-313060547623}{100000000000} \cdot y \]

      4. lower-*.f64 62.4

         \[\leadsto x - -3.13060547623 \cdot y \]

   7. Applied rewrites 62.4%

      \[\leadsto x - \color{blue}{-3.13060547623 \cdot y} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 15: 83.3% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+15}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-10}:\\ \;\;\;\;\mathsf{fma}\left(y, 1.6453555072203998 \cdot b, x\right)\\ \mathbf{else}:\\ \;\;\;\;x - -3.13060547623 \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.05e+15)
   (fma 3.13060547623 y x)
   (if (<= z 4.6e-10)
     (fma y (* 1.6453555072203998 b) x)
     (- x (* -3.13060547623 y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.05e+15) {
		tmp = fma(3.13060547623, y, x);
	} else if (z <= 4.6e-10) {
		tmp = fma(y, (1.6453555072203998 * b), x);
	} else {
		tmp = x - (-3.13060547623 * y);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.05e+15)
		tmp = fma(3.13060547623, y, x);
	elseif (z <= 4.6e-10)
		tmp = fma(y, Float64(1.6453555072203998 * b), x);
	else
		tmp = Float64(x - Float64(-3.13060547623 * y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.05e+15], N[(3.13060547623 * y + x), $MachinePrecision], If[LessEqual[z, 4.6e-10], N[(y * N[(1.6453555072203998 * b), $MachinePrecision] + x), $MachinePrecision], N[(x - N[(-3.13060547623 * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.05e15

   1. Initial program 58.2%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{x + \frac{313060547623}{100000000000} \cdot y} \]
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \frac{313060547623}{100000000000} \cdot y + \color{blue}{x} \]

      2. lower-fma.f64 62.4

         \[\leadsto \mathsf{fma}\left(3.13060547623, \color{blue}{y}, x\right) \]

   4. Applied rewrites 62.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(3.13060547623, y, x\right)} \]

   if -1.05e15 < z < 4.60000000000000014e-10

   1. Initial program 58.2%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

   2. Taylor expanded in t around 0

      \[\leadsto \color{blue}{x + \frac{y \cdot \left(b + z \cdot \left(a + {z}^{2} \cdot \left(\frac{55833770631}{5000000000} + \frac{313060547623}{100000000000} \cdot z\right)\right)\right)}{\frac{607771387771}{1000000000000} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)}} \]

   4. Applied rewrites 56.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{\mathsf{fma}\left(\mathsf{fma}\left(z \cdot z, \mathsf{fma}\left(3.13060547623, z, 11.1667541262\right), a\right), z, b\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(15.234687407 + z, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}, x\right)} \]

   5. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(y, \frac{1000000000000}{607771387771} \cdot \color{blue}{b}, x\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 60.0

         \[\leadsto \mathsf{fma}\left(y, 1.6453555072203998 \cdot b, x\right) \]

   7. Applied rewrites 60.0%

      \[\leadsto \mathsf{fma}\left(y, 1.6453555072203998 \cdot \color{blue}{b}, x\right) \]

   if 4.60000000000000014e-10 < z

   1. Initial program 58.2%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{x + \frac{313060547623}{100000000000} \cdot y} \]
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \frac{313060547623}{100000000000} \cdot y + \color{blue}{x} \]

      2. lower-fma.f64 62.4

         \[\leadsto \mathsf{fma}\left(3.13060547623, \color{blue}{y}, x\right) \]

   4. Applied rewrites 62.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(3.13060547623, y, x\right)} \]

   5. Taylor expanded in x around 0

      \[\leadsto x + \color{blue}{\frac{313060547623}{100000000000} \cdot y} \]
   6. Step-by-step derivation

      1. fp-cancel-sign-sub-inv N/A

         \[\leadsto x - \left(\mathsf{neg}\left(\frac{313060547623}{100000000000}\right)\right) \cdot \color{blue}{y} \]

      2. lower--.f64 N/A

         \[\leadsto x - \left(\mathsf{neg}\left(\frac{313060547623}{100000000000}\right)\right) \cdot \color{blue}{y} \]

      3. metadata-eval N/A

         \[\leadsto x - \frac{-313060547623}{100000000000} \cdot y \]

      4. lower-*.f64 62.4

         \[\leadsto x - -3.13060547623 \cdot y \]

   7. Applied rewrites 62.4%

      \[\leadsto x - \color{blue}{-3.13060547623 \cdot y} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 16: 66.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \leq -1.5 \cdot 10^{+45}:\\ \;\;\;\;b \cdot \left(1.6453555072203998 \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x - -3.13060547623 \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<=
      (/
       (*
        y
        (+
         (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z)
         b))
       (+
        (*
         (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721)
         z)
        0.607771387771))
      -1.5e+45)
   (* b (* 1.6453555072203998 y))
   (- x (* -3.13060547623 y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((y * ((((((((z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b)) / (((((((z + 15.234687407) * z) + 31.4690115749) * z) + 11.9400905721) * z) + 0.607771387771)) <= -1.5e+45) {
		tmp = b * (1.6453555072203998 * y);
	} else {
		tmp = x - (-3.13060547623 * y);
	}
	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 * ((((((((z * 3.13060547623d0) + 11.1667541262d0) * z) + t) * z) + a) * z) + b)) / (((((((z + 15.234687407d0) * z) + 31.4690115749d0) * z) + 11.9400905721d0) * z) + 0.607771387771d0)) <= (-1.5d+45)) then
        tmp = b * (1.6453555072203998d0 * y)
    else
        tmp = x - ((-3.13060547623d0) * y)
    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 * ((((((((z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b)) / (((((((z + 15.234687407) * z) + 31.4690115749) * z) + 11.9400905721) * z) + 0.607771387771)) <= -1.5e+45) {
		tmp = b * (1.6453555072203998 * y);
	} else {
		tmp = x - (-3.13060547623 * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if ((y * ((((((((z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b)) / (((((((z + 15.234687407) * z) + 31.4690115749) * z) + 11.9400905721) * z) + 0.607771387771)) <= -1.5e+45:
		tmp = b * (1.6453555072203998 * y)
	else:
		tmp = x - (-3.13060547623 * y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(Float64(y * Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b)) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(z + 15.234687407) * z) + 31.4690115749) * z) + 11.9400905721) * z) + 0.607771387771)) <= -1.5e+45)
		tmp = Float64(b * Float64(1.6453555072203998 * y));
	else
		tmp = Float64(x - Float64(-3.13060547623 * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (((y * ((((((((z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b)) / (((((((z + 15.234687407) * z) + 31.4690115749) * z) + 11.9400905721) * z) + 0.607771387771)) <= -1.5e+45)
		tmp = b * (1.6453555072203998 * y);
	else
		tmp = x - (-3.13060547623 * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(N[(y * N[(N[(N[(N[(N[(N[(N[(N[(z * 3.13060547623), $MachinePrecision] + 11.1667541262), $MachinePrecision] * z), $MachinePrecision] + t), $MachinePrecision] * z), $MachinePrecision] + a), $MachinePrecision] * z), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(z + 15.234687407), $MachinePrecision] * z), $MachinePrecision] + 31.4690115749), $MachinePrecision] * z), $MachinePrecision] + 11.9400905721), $MachinePrecision] * z), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision], -1.5e+45], N[(b * N[(1.6453555072203998 * y), $MachinePrecision]), $MachinePrecision], N[(x - N[(-3.13060547623 * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z #s(literal 313060547623/100000000000 binary64)) #s(literal 55833770631/5000000000 binary64)) z) t) z) a) z) b)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z #s(literal 15234687407/1000000000 binary64)) z) #s(literal 314690115749/10000000000 binary64)) z) #s(literal 119400905721/10000000000 binary64)) z) #s(literal 607771387771/1000000000000 binary64))) < -1.50000000000000005e45

   1. Initial program 58.2%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

   2. Taylor expanded in b around inf

      \[\leadsto \color{blue}{\frac{b \cdot y}{\frac{607771387771}{1000000000000} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)}} \]
   3. Step-by-step derivation

      1. associate-/l* N/A

         \[\leadsto b \cdot \color{blue}{\frac{y}{\frac{607771387771}{1000000000000} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)}} \]

      2. lower-*.f64 N/A

         \[\leadsto b \cdot \color{blue}{\frac{y}{\frac{607771387771}{1000000000000} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)}} \]

      3. lower-/.f64 N/A

         \[\leadsto b \cdot \frac{y}{\color{blue}{\frac{607771387771}{1000000000000} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)}} \]

      4. *-commutative N/A

         \[\leadsto b \cdot \frac{y}{\frac{607771387771}{1000000000000} + \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right) \cdot \color{blue}{z}} \]

      5. +-commutative N/A

         \[\leadsto b \cdot \frac{y}{\frac{607771387771}{1000000000000} + \left(z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right) + \frac{119400905721}{10000000000}\right) \cdot z} \]

      6. *-commutative N/A

         \[\leadsto b \cdot \frac{y}{\frac{607771387771}{1000000000000} + \left(\left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z} \]

      7. +-commutative N/A

         \[\leadsto b \cdot \frac{y}{\frac{607771387771}{1000000000000} + \left(\left(\frac{314690115749}{10000000000} + z \cdot \left(z + \frac{15234687407}{1000000000}\right)\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z} \]

      8. *-commutative N/A

         \[\leadsto b \cdot \frac{y}{\frac{607771387771}{1000000000000} + \left(\left(\frac{314690115749}{10000000000} + \left(z + \frac{15234687407}{1000000000}\right) \cdot z\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z} \]

      9. +-commutative N/A

         \[\leadsto b \cdot \frac{y}{\frac{607771387771}{1000000000000} + \left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z} \]

      10. +-commutative N/A

          \[\leadsto b \cdot \frac{y}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \color{blue}{\frac{607771387771}{1000000000000}}} \]

   4. Applied rewrites 22.4%

      \[\leadsto \color{blue}{b \cdot \frac{y}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(15.234687407 + z, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}} \]

   5. Taylor expanded in z around 0

      \[\leadsto b \cdot \left(\frac{1000000000000}{607771387771} \cdot \color{blue}{y}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 22.0

         \[\leadsto b \cdot \left(1.6453555072203998 \cdot y\right) \]

   7. Applied rewrites 22.0%

      \[\leadsto b \cdot \left(1.6453555072203998 \cdot \color{blue}{y}\right) \]

   if -1.50000000000000005e45 < (/.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 58.2%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{x + \frac{313060547623}{100000000000} \cdot y} \]
   3. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \frac{313060547623}{100000000000} \cdot y + \color{blue}{x} \]

      2. lower-fma.f64 62.4

         \[\leadsto \mathsf{fma}\left(3.13060547623, \color{blue}{y}, x\right) \]

   4. Applied rewrites 62.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(3.13060547623, y, x\right)} \]

   5. Taylor expanded in x around 0

      \[\leadsto x + \color{blue}{\frac{313060547623}{100000000000} \cdot y} \]
   6. Step-by-step derivation

      1. fp-cancel-sign-sub-inv N/A

         \[\leadsto x - \left(\mathsf{neg}\left(\frac{313060547623}{100000000000}\right)\right) \cdot \color{blue}{y} \]

      2. lower--.f64 N/A

         \[\leadsto x - \left(\mathsf{neg}\left(\frac{313060547623}{100000000000}\right)\right) \cdot \color{blue}{y} \]

      3. metadata-eval N/A

         \[\leadsto x - \frac{-313060547623}{100000000000} \cdot y \]

      4. lower-*.f64 62.4

         \[\leadsto x - -3.13060547623 \cdot y \]

   7. Applied rewrites 62.4%

      \[\leadsto x - \color{blue}{-3.13060547623 \cdot y} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 17: 62.4% accurate, 8.0× speedup

Math

\[\begin{array}{l} \\ x - -3.13060547623 \cdot y \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (- x (* -3.13060547623 y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return x - (-3.13060547623 * y);
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a, b)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = x - ((-3.13060547623d0) * y)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x - (-3.13060547623 * y);
}

Python

def code(x, y, z, t, a, b):
	return x - (-3.13060547623 * y)

Julia

function code(x, y, z, t, a, b)
	return Float64(x - Float64(-3.13060547623 * y))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x - (-3.13060547623 * y);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x - N[(-3.13060547623 * y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 58.2%

   \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

2. Taylor expanded in z around inf

   \[\leadsto \color{blue}{x + \frac{313060547623}{100000000000} \cdot y} \]
3. Step-by-step derivation

   1. +-commutative N/A

      \[\leadsto \frac{313060547623}{100000000000} \cdot y + \color{blue}{x} \]

   2. lower-fma.f64 62.4

      \[\leadsto \mathsf{fma}\left(3.13060547623, \color{blue}{y}, x\right) \]

4. Applied rewrites 62.4%

   \[\leadsto \color{blue}{\mathsf{fma}\left(3.13060547623, y, x\right)} \]

5. Taylor expanded in x around 0

   \[\leadsto x + \color{blue}{\frac{313060547623}{100000000000} \cdot y} \]
6. Step-by-step derivation

   1. fp-cancel-sign-sub-inv N/A

      \[\leadsto x - \left(\mathsf{neg}\left(\frac{313060547623}{100000000000}\right)\right) \cdot \color{blue}{y} \]

   2. lower--.f64 N/A

      \[\leadsto x - \left(\mathsf{neg}\left(\frac{313060547623}{100000000000}\right)\right) \cdot \color{blue}{y} \]

   3. metadata-eval N/A

      \[\leadsto x - \frac{-313060547623}{100000000000} \cdot y \]

   4. lower-*.f64 62.4

      \[\leadsto x - -3.13060547623 \cdot y \]

7. Applied rewrites 62.4%

   \[\leadsto x - \color{blue}{-3.13060547623 \cdot y} \]
8. Add Preprocessing

Alternative 18: 62.4% accurate, 8.8× 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 58.2%

   \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

2. Taylor expanded in z around inf

   \[\leadsto \color{blue}{x + \frac{313060547623}{100000000000} \cdot y} \]
3. Step-by-step derivation

   1. +-commutative N/A

      \[\leadsto \frac{313060547623}{100000000000} \cdot y + \color{blue}{x} \]

   2. lower-fma.f64 62.4

      \[\leadsto \mathsf{fma}\left(3.13060547623, \color{blue}{y}, x\right) \]

4. Applied rewrites 62.4%

   \[\leadsto \color{blue}{\mathsf{fma}\left(3.13060547623, y, x\right)} \]
5. Add Preprocessing

Alternative 19: 22.5% accurate, 13.3× 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 58.2%

   \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

2. Taylor expanded in z around inf

   \[\leadsto \color{blue}{x + \frac{313060547623}{100000000000} \cdot y} \]
3. Step-by-step derivation

   1. +-commutative N/A

      \[\leadsto \frac{313060547623}{100000000000} \cdot y + \color{blue}{x} \]

   2. lower-fma.f64 62.4

      \[\leadsto \mathsf{fma}\left(3.13060547623, \color{blue}{y}, x\right) \]

4. Applied rewrites 62.4%

   \[\leadsto \color{blue}{\mathsf{fma}\left(3.13060547623, y, x\right)} \]

5. Taylor expanded in x around 0

   \[\leadsto \frac{313060547623}{100000000000} \cdot \color{blue}{y} \]
6. Step-by-step derivation

   1. lower-*.f64 22.5

      \[\leadsto 3.13060547623 \cdot y \]

7. Applied rewrites 22.5%

   \[\leadsto 3.13060547623 \cdot \color{blue}{y} \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2025127 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, D"
  :precision binary64
  (+ x (/ (* y (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b)) (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))))