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

Percentage Accurate: 57.5% → 97.6%

Time: 5.6s

Alternatives: 15

Speedup: 3.2×

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: 57.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+31}:\\ \;\;\;\;\mathsf{fma}\left(y, \left(-\frac{\frac{-t}{z}}{z}\right) + 3.13060547623, x\right)\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+43}:\\ \;\;\;\;x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \left(-\frac{\left(-\left(\frac{457.9610022158428}{t \cdot z} + \frac{1}{z}\right) \cdot t\right) + 36.52704169880642}{z}\right) + 3.13060547623, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -4.4e+31)
   (fma y (+ (- (/ (/ (- t) z) z)) 3.13060547623) x)
   (if (<= z 6.5e+43)
     (+
      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)))
     (fma
      y
      (+
       (-
        (/
         (+
          (- (* (+ (/ 457.9610022158428 (* t z)) (/ 1.0 z)) t))
          36.52704169880642)
         z))
       3.13060547623)
      x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -4.4e+31) {
		tmp = fma(y, (-((-t / z) / z) + 3.13060547623), x);
	} else if (z <= 6.5e+43) {
		tmp = x + ((y * ((((((((z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b)) / (((((((z + 15.234687407) * z) + 31.4690115749) * z) + 11.9400905721) * z) + 0.607771387771));
	} else {
		tmp = fma(y, (-((-(((457.9610022158428 / (t * z)) + (1.0 / z)) * t) + 36.52704169880642) / z) + 3.13060547623), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -4.4e+31)
		tmp = fma(y, Float64(Float64(-Float64(Float64(Float64(-t) / z) / z)) + 3.13060547623), x);
	elseif (z <= 6.5e+43)
		tmp = Float64(x + Float64(Float64(y * Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b)) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(z + 15.234687407) * z) + 31.4690115749) * z) + 11.9400905721) * z) + 0.607771387771)));
	else
		tmp = fma(y, Float64(Float64(-Float64(Float64(Float64(-Float64(Float64(Float64(457.9610022158428 / Float64(t * z)) + Float64(1.0 / z)) * t)) + 36.52704169880642) / z)) + 3.13060547623), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -4.4e+31], N[(y * N[((-N[(N[((-t) / z), $MachinePrecision] / z), $MachinePrecision]) + 3.13060547623), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[z, 6.5e+43], 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], N[(y * N[((-N[(N[((-N[(N[(N[(457.9610022158428 / N[(t * z), $MachinePrecision]), $MachinePrecision] + N[(1.0 / z), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]) + 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]) + 3.13060547623), $MachinePrecision] + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.4000000000000002e31

   1. Initial program 8.1%

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

   2. Taylor expanded in a around 0

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

   4. Applied rewrites 12.4%

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

   5. Taylor expanded in z around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower-+.f64 97.0

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

   7. Applied rewrites 97.0%

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

   8. Taylor expanded in t around inf

      \[\leadsto \mathsf{fma}\left(y, \left(-\frac{-1 \cdot \frac{t}{z}}{z}\right) + \frac{313060547623}{100000000000}, x\right) \]
   9. Step-by-step derivation

      1. associate-*r/ N/A

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

      2. mul-1-neg N/A

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

      3. lower-/.f64 N/A

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

      4. lower-neg.f64 97.0

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

   10. Applied rewrites 97.0%

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

   if -4.4000000000000002e31 < z < 6.4999999999999998e43

   1. Initial program 97.8%

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

   if 6.4999999999999998e43 < z

   1. Initial program 6.8%

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

   2. Taylor expanded in a around 0

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

   4. Applied rewrites 10.1%

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

   5. Taylor expanded in z around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower-+.f64 97.6

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

   7. Applied rewrites 97.6%

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

   8. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. associate-*r/ N/A

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

      3. metadata-eval N/A

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

      4. lower-*.f64 N/A

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

      5. metadata-eval N/A

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

      6. associate-*r/ N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. lower-/.f64 N/A

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

      12. lower-*.f64 N/A

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

      13. lower-/.f64 97.6

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

   10. Applied rewrites 97.6%

       \[\leadsto \mathsf{fma}\left(y, \left(-\frac{\left(-\left(\frac{457.9610022158428}{t \cdot z} + \frac{1}{z}\right) \cdot t\right) + 36.52704169880642}{z}\right) + 3.13060547623, x\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 2: 95.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.45 \cdot 10^{+19}:\\ \;\;\;\;\mathsf{fma}\left(y, \left(-\frac{\frac{-t}{z}}{z}\right) + 3.13060547623, x\right)\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-29}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(3.13060547623, z, 11.1667541262\right), z, t\right), z, a\right), z, b\right)}{0.607771387771}, x\right)\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+26}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{\mathsf{fma}\left(z \cdot z, t, b\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(15.234687407 + z, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \left(-\frac{\left(-\left(\frac{457.9610022158428}{t \cdot z} + \frac{1}{z}\right) \cdot t\right) + 36.52704169880642}{z}\right) + 3.13060547623, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -3.45e+19)
   (fma y (+ (- (/ (/ (- t) z) z)) 3.13060547623) x)
   (if (<= z 3.5e-29)
     (fma
      y
      (/
       (fma (fma (fma (fma 3.13060547623 z 11.1667541262) z t) z a) z b)
       0.607771387771)
      x)
     (if (<= z 3.5e+26)
       (fma
        y
        (/
         (fma (* z z) t b)
         (fma
          (fma (fma (+ 15.234687407 z) z 31.4690115749) z 11.9400905721)
          z
          0.607771387771))
        x)
       (fma
        y
        (+
         (-
          (/
           (+
            (- (* (+ (/ 457.9610022158428 (* t z)) (/ 1.0 z)) t))
            36.52704169880642)
           z))
         3.13060547623)
        x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -3.45e+19) {
		tmp = fma(y, (-((-t / z) / z) + 3.13060547623), x);
	} else if (z <= 3.5e-29) {
		tmp = fma(y, (fma(fma(fma(fma(3.13060547623, z, 11.1667541262), z, t), z, a), z, b) / 0.607771387771), x);
	} else if (z <= 3.5e+26) {
		tmp = fma(y, (fma((z * z), t, b) / fma(fma(fma((15.234687407 + z), z, 31.4690115749), z, 11.9400905721), z, 0.607771387771)), x);
	} else {
		tmp = fma(y, (-((-(((457.9610022158428 / (t * z)) + (1.0 / z)) * t) + 36.52704169880642) / z) + 3.13060547623), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -3.45e+19)
		tmp = fma(y, Float64(Float64(-Float64(Float64(Float64(-t) / z) / z)) + 3.13060547623), x);
	elseif (z <= 3.5e-29)
		tmp = fma(y, Float64(fma(fma(fma(fma(3.13060547623, z, 11.1667541262), z, t), z, a), z, b) / 0.607771387771), x);
	elseif (z <= 3.5e+26)
		tmp = fma(y, Float64(fma(Float64(z * z), t, b) / fma(fma(fma(Float64(15.234687407 + z), z, 31.4690115749), z, 11.9400905721), z, 0.607771387771)), x);
	else
		tmp = fma(y, Float64(Float64(-Float64(Float64(Float64(-Float64(Float64(Float64(457.9610022158428 / Float64(t * z)) + Float64(1.0 / z)) * t)) + 36.52704169880642) / z)) + 3.13060547623), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -3.45e+19], N[(y * N[((-N[(N[((-t) / z), $MachinePrecision] / z), $MachinePrecision]) + 3.13060547623), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[z, 3.5e-29], N[(y * N[(N[(N[(N[(N[(3.13060547623 * z + 11.1667541262), $MachinePrecision] * z + t), $MachinePrecision] * z + a), $MachinePrecision] * z + b), $MachinePrecision] / 0.607771387771), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[z, 3.5e+26], N[(y * N[(N[(N[(z * z), $MachinePrecision] * t + b), $MachinePrecision] / N[(N[(N[(N[(15.234687407 + z), $MachinePrecision] * z + 31.4690115749), $MachinePrecision] * z + 11.9400905721), $MachinePrecision] * z + 0.607771387771), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(y * N[((-N[(N[((-N[(N[(N[(457.9610022158428 / N[(t * z), $MachinePrecision]), $MachinePrecision] + N[(1.0 / z), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]) + 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]) + 3.13060547623), $MachinePrecision] + x), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.45e19

   1. Initial program 11.2%

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

   2. Taylor expanded in a around 0

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

   4. Applied rewrites 15.6%

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

   5. Taylor expanded in z around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower-+.f64 96.0

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

   7. Applied rewrites 96.0%

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

   8. Taylor expanded in t around inf

      \[\leadsto \mathsf{fma}\left(y, \left(-\frac{-1 \cdot \frac{t}{z}}{z}\right) + \frac{313060547623}{100000000000}, x\right) \]
   9. Step-by-step derivation

      1. associate-*r/ N/A

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

      2. mul-1-neg N/A

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

      3. lower-/.f64 N/A

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

      4. lower-neg.f64 96.0

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

   10. Applied rewrites 96.0%

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

   if -3.45e19 < z < 3.4999999999999997e-29

   1. Initial program 99.4%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 97.7%

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

   6. Applied rewrites 97.7%

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

   if 3.4999999999999997e-29 < z < 3.4999999999999999e26

   1. Initial program 94.2%

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

   2. Taylor expanded in a around 0

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

   4. Applied rewrites 80.5%

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

   5. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. pow2 N/A

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

      5. lift-*.f64 75.2

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

   7. Applied rewrites 75.2%

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

   if 3.4999999999999999e26 < z

   1. Initial program 10.5%

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

   2. Taylor expanded in a around 0

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

   4. Applied rewrites 13.6%

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

   5. Taylor expanded in z around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower-+.f64 95.9

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

   7. Applied rewrites 95.9%

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

   8. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. associate-*r/ N/A

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

      3. metadata-eval N/A

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

      4. lower-*.f64 N/A

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

      5. metadata-eval N/A

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

      6. associate-*r/ N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. lower-/.f64 N/A

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

      12. lower-*.f64 N/A

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

      13. lower-/.f64 95.9

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

   10. Applied rewrites 95.9%

       \[\leadsto \mathsf{fma}\left(y, \left(-\frac{\left(-\left(\frac{457.9610022158428}{t \cdot z} + \frac{1}{z}\right) \cdot t\right) + 36.52704169880642}{z}\right) + 3.13060547623, x\right) \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 3: 95.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.45 \cdot 10^{+19}:\\ \;\;\;\;\mathsf{fma}\left(y, \left(-\frac{\frac{-t}{z}}{z}\right) + 3.13060547623, x\right)\\ \mathbf{elif}\;z \leq 1.35:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(3.13060547623, z, 11.1667541262\right), z, t\right), z, a\right), z, b\right)}{0.607771387771}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \left(-\frac{\left(-\left(\frac{457.9610022158428}{t \cdot z} + \frac{1}{z}\right) \cdot t\right) + 36.52704169880642}{z}\right) + 3.13060547623, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -3.45e+19)
   (fma y (+ (- (/ (/ (- t) z) z)) 3.13060547623) x)
   (if (<= z 1.35)
     (fma
      y
      (/
       (fma (fma (fma (fma 3.13060547623 z 11.1667541262) z t) z a) z b)
       0.607771387771)
      x)
     (fma
      y
      (+
       (-
        (/
         (+
          (- (* (+ (/ 457.9610022158428 (* t z)) (/ 1.0 z)) t))
          36.52704169880642)
         z))
       3.13060547623)
      x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -3.45e+19) {
		tmp = fma(y, (-((-t / z) / z) + 3.13060547623), x);
	} else if (z <= 1.35) {
		tmp = fma(y, (fma(fma(fma(fma(3.13060547623, z, 11.1667541262), z, t), z, a), z, b) / 0.607771387771), x);
	} else {
		tmp = fma(y, (-((-(((457.9610022158428 / (t * z)) + (1.0 / z)) * t) + 36.52704169880642) / z) + 3.13060547623), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -3.45e+19)
		tmp = fma(y, Float64(Float64(-Float64(Float64(Float64(-t) / z) / z)) + 3.13060547623), x);
	elseif (z <= 1.35)
		tmp = fma(y, Float64(fma(fma(fma(fma(3.13060547623, z, 11.1667541262), z, t), z, a), z, b) / 0.607771387771), x);
	else
		tmp = fma(y, Float64(Float64(-Float64(Float64(Float64(-Float64(Float64(Float64(457.9610022158428 / Float64(t * z)) + Float64(1.0 / z)) * t)) + 36.52704169880642) / z)) + 3.13060547623), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -3.45e+19], N[(y * N[((-N[(N[((-t) / z), $MachinePrecision] / z), $MachinePrecision]) + 3.13060547623), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[z, 1.35], N[(y * N[(N[(N[(N[(N[(3.13060547623 * z + 11.1667541262), $MachinePrecision] * z + t), $MachinePrecision] * z + a), $MachinePrecision] * z + b), $MachinePrecision] / 0.607771387771), $MachinePrecision] + x), $MachinePrecision], N[(y * N[((-N[(N[((-N[(N[(N[(457.9610022158428 / N[(t * z), $MachinePrecision]), $MachinePrecision] + N[(1.0 / z), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]) + 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]) + 3.13060547623), $MachinePrecision] + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.45e19

   1. Initial program 11.2%

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

   2. Taylor expanded in a around 0

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

   4. Applied rewrites 15.6%

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

   5. Taylor expanded in z around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower-+.f64 96.0

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

   7. Applied rewrites 96.0%

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

   8. Taylor expanded in t around inf

      \[\leadsto \mathsf{fma}\left(y, \left(-\frac{-1 \cdot \frac{t}{z}}{z}\right) + \frac{313060547623}{100000000000}, x\right) \]
   9. Step-by-step derivation

      1. associate-*r/ N/A

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

      2. mul-1-neg N/A

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

      3. lower-/.f64 N/A

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

      4. lower-neg.f64 96.0

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

   10. Applied rewrites 96.0%

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

   if -3.45e19 < z < 1.3500000000000001

   1. Initial program 99.5%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 97.3%

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

   6. Applied rewrites 97.3%

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

   if 1.3500000000000001 < z

   1. Initial program 16.9%

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

   2. Taylor expanded in a around 0

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

   4. Applied rewrites 19.4%

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

   5. Taylor expanded in z around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower-+.f64 93.0

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

   7. Applied rewrites 93.0%

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

   8. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. associate-*r/ N/A

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

      3. metadata-eval N/A

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

      4. lower-*.f64 N/A

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

      5. metadata-eval N/A

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

      6. associate-*r/ N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. lower-/.f64 N/A

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

      12. lower-*.f64 N/A

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

      13. lower-/.f64 93.0

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

   10. Applied rewrites 93.0%

       \[\leadsto \mathsf{fma}\left(y, \left(-\frac{\left(-\left(\frac{457.9610022158428}{t \cdot z} + \frac{1}{z}\right) \cdot t\right) + 36.52704169880642}{z}\right) + 3.13060547623, x\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 4: 95.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y, \left(-\frac{\frac{-t}{z}}{z}\right) + 3.13060547623, x\right)\\ \mathbf{if}\;z \leq -3.45 \cdot 10^{+19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.35:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(3.13060547623, z, 11.1667541262\right), z, t\right), z, a\right), z, b\right)}{0.607771387771}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma y (+ (- (/ (/ (- t) z) z)) 3.13060547623) x)))
   (if (<= z -3.45e+19)
     t_1
     (if (<= z 1.35)
       (fma
        y
        (/
         (fma (fma (fma (fma 3.13060547623 z 11.1667541262) z t) z a) z b)
         0.607771387771)
        x)
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(y, (-((-t / z) / z) + 3.13060547623), x);
	double tmp;
	if (z <= -3.45e+19) {
		tmp = t_1;
	} else if (z <= 1.35) {
		tmp = fma(y, (fma(fma(fma(fma(3.13060547623, z, 11.1667541262), z, t), z, a), z, b) / 0.607771387771), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(y, Float64(Float64(-Float64(Float64(Float64(-t) / z) / z)) + 3.13060547623), x)
	tmp = 0.0
	if (z <= -3.45e+19)
		tmp = t_1;
	elseif (z <= 1.35)
		tmp = fma(y, Float64(fma(fma(fma(fma(3.13060547623, z, 11.1667541262), z, t), z, a), z, b) / 0.607771387771), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[((-N[(N[((-t) / z), $MachinePrecision] / z), $MachinePrecision]) + 3.13060547623), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[z, -3.45e+19], t$95$1, If[LessEqual[z, 1.35], N[(y * N[(N[(N[(N[(N[(3.13060547623 * z + 11.1667541262), $MachinePrecision] * z + t), $MachinePrecision] * z + a), $MachinePrecision] * z + b), $MachinePrecision] / 0.607771387771), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.45e19 or 1.3500000000000001 < z

   1. Initial program 14.2%

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

   2. Taylor expanded in a around 0

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

   4. Applied rewrites 17.6%

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

   5. Taylor expanded in z around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower-+.f64 94.4

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

   7. Applied rewrites 94.4%

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

   8. Taylor expanded in t around inf

      \[\leadsto \mathsf{fma}\left(y, \left(-\frac{-1 \cdot \frac{t}{z}}{z}\right) + \frac{313060547623}{100000000000}, x\right) \]
   9. Step-by-step derivation

      1. associate-*r/ N/A

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

      2. mul-1-neg N/A

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

      3. lower-/.f64 N/A

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

      4. lower-neg.f64 94.4

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

   10. Applied rewrites 94.4%

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

   if -3.45e19 < z < 1.3500000000000001

   1. Initial program 99.5%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 97.3%

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

   6. Applied rewrites 97.3%

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

Alternative 5: 93.1% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -28:\\ \;\;\;\;\mathsf{fma}\left(y, \left(-\frac{\frac{-t}{z}}{z}\right) + 3.13060547623, x\right)\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-18}:\\ \;\;\;\;\mathsf{fma}\left(y, \mathsf{fma}\left(\mathsf{fma}\left(1.6453555072203998, a, -32.324150453290734 \cdot b\right), z, 1.6453555072203998 \cdot b\right), x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \left(-\frac{\left(-\frac{457.9610022158428 + t}{z}\right) + 36.52704169880642}{z}\right) + 3.13060547623, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -28.0)
   (fma y (+ (- (/ (/ (- t) z) z)) 3.13060547623) x)
   (if (<= z 1.4e-18)
     (fma
      y
      (fma
       (fma 1.6453555072203998 a (* -32.324150453290734 b))
       z
       (* 1.6453555072203998 b))
      x)
     (fma
      y
      (+
       (- (/ (+ (- (/ (+ 457.9610022158428 t) z)) 36.52704169880642) z))
       3.13060547623)
      x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -28.0) {
		tmp = fma(y, (-((-t / z) / z) + 3.13060547623), x);
	} else if (z <= 1.4e-18) {
		tmp = fma(y, fma(fma(1.6453555072203998, a, (-32.324150453290734 * b)), z, (1.6453555072203998 * b)), x);
	} else {
		tmp = fma(y, (-((-((457.9610022158428 + t) / z) + 36.52704169880642) / z) + 3.13060547623), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -28.0)
		tmp = fma(y, Float64(Float64(-Float64(Float64(Float64(-t) / z) / z)) + 3.13060547623), x);
	elseif (z <= 1.4e-18)
		tmp = fma(y, fma(fma(1.6453555072203998, a, Float64(-32.324150453290734 * b)), z, Float64(1.6453555072203998 * b)), x);
	else
		tmp = fma(y, Float64(Float64(-Float64(Float64(Float64(-Float64(Float64(457.9610022158428 + t) / z)) + 36.52704169880642) / z)) + 3.13060547623), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -28.0], N[(y * N[((-N[(N[((-t) / z), $MachinePrecision] / z), $MachinePrecision]) + 3.13060547623), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[z, 1.4e-18], N[(y * N[(N[(1.6453555072203998 * a + N[(-32.324150453290734 * b), $MachinePrecision]), $MachinePrecision] * z + N[(1.6453555072203998 * b), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(y * N[((-N[(N[((-N[(N[(457.9610022158428 + t), $MachinePrecision] / z), $MachinePrecision]) + 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]) + 3.13060547623), $MachinePrecision] + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -28

   1. Initial program 16.1%

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

   2. Taylor expanded in a around 0

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

   4. Applied rewrites 19.6%

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

   5. Taylor expanded in z around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower-+.f64 93.8

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

   7. Applied rewrites 93.8%

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

   8. Taylor expanded in t around inf

      \[\leadsto \mathsf{fma}\left(y, \left(-\frac{-1 \cdot \frac{t}{z}}{z}\right) + \frac{313060547623}{100000000000}, x\right) \]
   9. Step-by-step derivation

      1. associate-*r/ N/A

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

      2. mul-1-neg N/A

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

      3. lower-/.f64 N/A

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

      4. lower-neg.f64 93.7

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

   10. Applied rewrites 93.7%

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

   if -28 < z < 1.40000000000000006e-18

   1. Initial program 99.7%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 81.3%

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

   6. Applied rewrites 81.3%

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

   7. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

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

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

      5. lower-fma.f64 N/A

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

      6. metadata-eval N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 93.8

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

   9. Applied rewrites 93.8%

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

   if 1.40000000000000006e-18 < z

   1. Initial program 21.1%

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

   2. Taylor expanded in a around 0

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

   4. Applied rewrites 22.4%

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

   5. Taylor expanded in z around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower-+.f64 90.7

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

   7. Applied rewrites 90.7%

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

Alternative 6: 93.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y, \left(-\frac{\frac{-t}{z}}{z}\right) + 3.13060547623, x\right)\\ \mathbf{if}\;z \leq -28:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-18}:\\ \;\;\;\;\mathsf{fma}\left(y, \mathsf{fma}\left(\mathsf{fma}\left(1.6453555072203998, a, -32.324150453290734 \cdot b\right), z, 1.6453555072203998 \cdot b\right), x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma y (+ (- (/ (/ (- t) z) z)) 3.13060547623) x)))
   (if (<= z -28.0)
     t_1
     (if (<= z 1.4e-18)
       (fma
        y
        (fma
         (fma 1.6453555072203998 a (* -32.324150453290734 b))
         z
         (* 1.6453555072203998 b))
        x)
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(y, (-((-t / z) / z) + 3.13060547623), x);
	double tmp;
	if (z <= -28.0) {
		tmp = t_1;
	} else if (z <= 1.4e-18) {
		tmp = fma(y, fma(fma(1.6453555072203998, a, (-32.324150453290734 * b)), z, (1.6453555072203998 * b)), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(y, Float64(Float64(-Float64(Float64(Float64(-t) / z) / z)) + 3.13060547623), x)
	tmp = 0.0
	if (z <= -28.0)
		tmp = t_1;
	elseif (z <= 1.4e-18)
		tmp = fma(y, fma(fma(1.6453555072203998, a, Float64(-32.324150453290734 * b)), z, Float64(1.6453555072203998 * b)), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[((-N[(N[((-t) / z), $MachinePrecision] / z), $MachinePrecision]) + 3.13060547623), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[z, -28.0], t$95$1, If[LessEqual[z, 1.4e-18], N[(y * N[(N[(1.6453555072203998 * a + N[(-32.324150453290734 * b), $MachinePrecision]), $MachinePrecision] * z + N[(1.6453555072203998 * b), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -28 or 1.40000000000000006e-18 < z

   1. Initial program 18.7%

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

   2. Taylor expanded in a around 0

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

   4. Applied rewrites 21.1%

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

   5. Taylor expanded in z around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower-+.f64 92.2

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

   7. Applied rewrites 92.2%

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

   8. Taylor expanded in t around inf

      \[\leadsto \mathsf{fma}\left(y, \left(-\frac{-1 \cdot \frac{t}{z}}{z}\right) + \frac{313060547623}{100000000000}, x\right) \]
   9. Step-by-step derivation

      1. associate-*r/ N/A

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

      2. mul-1-neg N/A

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

      3. lower-/.f64 N/A

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

      4. lower-neg.f64 92.1

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

   10. Applied rewrites 92.1%

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

   if -28 < z < 1.40000000000000006e-18

   1. Initial program 99.7%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 81.3%

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

   6. Applied rewrites 81.3%

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

   7. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

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

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

      5. lower-fma.f64 N/A

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

      6. metadata-eval N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 93.8

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

   9. Applied rewrites 93.8%

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

Alternative 7: 92.9% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y, \left(-\frac{\frac{-t}{z}}{z}\right) + 3.13060547623, x\right)\\ \mathbf{if}\;z \leq -28:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 0.84:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{\mathsf{fma}\left(a, z, b\right)}{0.607771387771}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma y (+ (- (/ (/ (- t) z) z)) 3.13060547623) x)))
   (if (<= z -28.0)
     t_1
     (if (<= z 0.84) (fma y (/ (fma a z b) 0.607771387771) x) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(y, (-((-t / z) / z) + 3.13060547623), x);
	double tmp;
	if (z <= -28.0) {
		tmp = t_1;
	} else if (z <= 0.84) {
		tmp = fma(y, (fma(a, z, b) / 0.607771387771), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(y, Float64(Float64(-Float64(Float64(Float64(-t) / z) / z)) + 3.13060547623), x)
	tmp = 0.0
	if (z <= -28.0)
		tmp = t_1;
	elseif (z <= 0.84)
		tmp = fma(y, Float64(fma(a, z, b) / 0.607771387771), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[((-N[(N[((-t) / z), $MachinePrecision] / z), $MachinePrecision]) + 3.13060547623), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[z, -28.0], t$95$1, If[LessEqual[z, 0.84], N[(y * N[(N[(a * z + b), $MachinePrecision] / 0.607771387771), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -28 or 0.839999999999999969 < z

   1. Initial program 16.5%

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

   2. Taylor expanded in a around 0

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

   4. Applied rewrites 19.5%

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

   5. Taylor expanded in z around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower-+.f64 93.4

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

   7. Applied rewrites 93.4%

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

   8. Taylor expanded in t around inf

      \[\leadsto \mathsf{fma}\left(y, \left(-\frac{-1 \cdot \frac{t}{z}}{z}\right) + \frac{313060547623}{100000000000}, x\right) \]
   9. Step-by-step derivation

      1. associate-*r/ N/A

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

      2. mul-1-neg N/A

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

      3. lower-/.f64 N/A

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

      4. lower-neg.f64 93.3

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

   10. Applied rewrites 93.3%

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

   if -28 < z < 0.839999999999999969

   1. Initial program 99.7%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 98.6%

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

   5. Taylor expanded in z around 0

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

   7. Applied rewrites 93.0%

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

   9. Applied rewrites 93.0%

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

Alternative 8: 92.9% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y, \frac{t}{z \cdot z} + 3.13060547623, x\right)\\ \mathbf{if}\;z \leq -28:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 0.84:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{\mathsf{fma}\left(a, z, b\right)}{0.607771387771}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (fma y (+ (/ t (* z z)) 3.13060547623) x)))
   (if (<= z -28.0)
     t_1
     (if (<= z 0.84) (fma y (/ (fma a z b) 0.607771387771) x) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(y, ((t / (z * z)) + 3.13060547623), x);
	double tmp;
	if (z <= -28.0) {
		tmp = t_1;
	} else if (z <= 0.84) {
		tmp = fma(y, (fma(a, z, b) / 0.607771387771), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(y, Float64(Float64(t / Float64(z * z)) + 3.13060547623), x)
	tmp = 0.0
	if (z <= -28.0)
		tmp = t_1;
	elseif (z <= 0.84)
		tmp = fma(y, Float64(fma(a, z, b) / 0.607771387771), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(N[(t / N[(z * z), $MachinePrecision]), $MachinePrecision] + 3.13060547623), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[z, -28.0], t$95$1, If[LessEqual[z, 0.84], N[(y * N[(N[(a * z + b), $MachinePrecision] / 0.607771387771), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -28 or 0.839999999999999969 < z

   1. Initial program 16.5%

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

   2. Taylor expanded in a around 0

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

   4. Applied rewrites 19.5%

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

   5. Taylor expanded in z around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower-+.f64 93.4

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

   7. Applied rewrites 93.4%

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

   8. Taylor expanded in t around inf

      \[\leadsto \mathsf{fma}\left(y, \frac{t}{{z}^{2}} + \frac{313060547623}{100000000000}, x\right) \]
   9. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \frac{t}{{z}^{2}} + \frac{313060547623}{100000000000}, x\right) \]

      2. pow2 N/A

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

      3. lift-*.f64 93.3

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

   10. Applied rewrites 93.3%

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

   if -28 < z < 0.839999999999999969

   1. Initial program 99.7%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 98.6%

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

   5. Taylor expanded in z around 0

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

   7. Applied rewrites 93.0%

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

   9. Applied rewrites 93.0%

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

Alternative 9: 87.4% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 92.9%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 85.3%

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

   5. Taylor expanded in z around 0

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

   7. Applied rewrites 81.5%

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

   9. Applied rewrites 81.5%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-fma.f64 97.0

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

   4. Applied rewrites 97.0%

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

Alternative 10: 83.8% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+61}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \mathbf{elif}\;z \leq -0.43:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{t}{z \cdot z}, x\right)\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-18}:\\ \;\;\;\;\mathsf{fma}\left(y, \mathsf{fma}\left(-32.324150453290734, z, 1.6453555072203998\right) \cdot b, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -4.6e+61)
   (fma 3.13060547623 y x)
   (if (<= z -0.43)
     (fma y (/ t (* z z)) x)
     (if (<= z 1.4e-18)
       (fma y (* (fma -32.324150453290734 z 1.6453555072203998) b) x)
       (fma 3.13060547623 y x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -4.6e+61) {
		tmp = fma(3.13060547623, y, x);
	} else if (z <= -0.43) {
		tmp = fma(y, (t / (z * z)), x);
	} else if (z <= 1.4e-18) {
		tmp = fma(y, (fma(-32.324150453290734, z, 1.6453555072203998) * b), x);
	} else {
		tmp = fma(3.13060547623, y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -4.6e+61)
		tmp = fma(3.13060547623, y, x);
	elseif (z <= -0.43)
		tmp = fma(y, Float64(t / Float64(z * z)), x);
	elseif (z <= 1.4e-18)
		tmp = fma(y, Float64(fma(-32.324150453290734, z, 1.6453555072203998) * b), x);
	else
		tmp = fma(3.13060547623, y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -4.6e+61], N[(3.13060547623 * y + x), $MachinePrecision], If[LessEqual[z, -0.43], N[(y * N[(t / N[(z * z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[z, 1.4e-18], N[(y * N[(N[(-32.324150453290734 * z + 1.6453555072203998), $MachinePrecision] * b), $MachinePrecision] + x), $MachinePrecision], N[(3.13060547623 * y + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.5999999999999999e61 or 1.40000000000000006e-18 < z

   1. Initial program 13.0%

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

   2. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-fma.f64 88.5

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

   4. Applied rewrites 88.5%

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

   if -4.5999999999999999e61 < z < -0.429999999999999993

   1. Initial program 72.3%

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

   2. Taylor expanded in a around 0

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

   4. Applied rewrites 79.8%

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

   5. Taylor expanded in z around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower-+.f64 72.7

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

   7. Applied rewrites 72.7%

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

   8. Taylor expanded in t around inf

      \[\leadsto \mathsf{fma}\left(y, \frac{t}{{z}^{\color{blue}{2}}}, x\right) \]
   9. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \frac{t}{{z}^{2}}, x\right) \]

      2. pow2 N/A

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

      3. lift-*.f64 61.2

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

   10. Applied rewrites 61.2%

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

   if -0.429999999999999993 < z < 1.40000000000000006e-18

   1. Initial program 99.7%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 81.4%

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

   6. Applied rewrites 81.4%

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

   7. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

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

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

      5. lower-fma.f64 N/A

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

      6. metadata-eval N/A

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

      7. lower-*.f64 N/A

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

      8. lower-*.f64 93.9

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

   9. Applied rewrites 93.9%

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

   10. Taylor expanded in b around inf

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

       1. *-commutative N/A

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

       2. lower-*.f64 N/A

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

       3. +-commutative N/A

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

       4. lower-fma.f64 81.4

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

   12. Applied rewrites 81.4%

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

Alternative 11: 83.7% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+61}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \mathbf{elif}\;z \leq -17:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{t}{z \cdot z}, x\right)\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+43}:\\ \;\;\;\;\mathsf{fma}\left(y, 1.6453555072203998 \cdot b, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -4.6e+61)
   (fma 3.13060547623 y x)
   (if (<= z -17.0)
     (fma y (/ t (* z z)) x)
     (if (<= z 6.5e+43)
       (fma y (* 1.6453555072203998 b) x)
       (fma 3.13060547623 y x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -4.6e+61) {
		tmp = fma(3.13060547623, y, x);
	} else if (z <= -17.0) {
		tmp = fma(y, (t / (z * z)), x);
	} else if (z <= 6.5e+43) {
		tmp = fma(y, (1.6453555072203998 * b), x);
	} else {
		tmp = fma(3.13060547623, y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -4.6e+61)
		tmp = fma(3.13060547623, y, x);
	elseif (z <= -17.0)
		tmp = fma(y, Float64(t / Float64(z * z)), x);
	elseif (z <= 6.5e+43)
		tmp = fma(y, Float64(1.6453555072203998 * b), x);
	else
		tmp = fma(3.13060547623, y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -4.6e+61], N[(3.13060547623 * y + x), $MachinePrecision], If[LessEqual[z, -17.0], N[(y * N[(t / N[(z * z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[z, 6.5e+43], N[(y * N[(1.6453555072203998 * b), $MachinePrecision] + x), $MachinePrecision], N[(3.13060547623 * y + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.5999999999999999e61 or 6.4999999999999998e43 < z

   1. Initial program 4.5%

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

   2. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-fma.f64 94.0

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

   4. Applied rewrites 94.0%

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

   if -4.5999999999999999e61 < z < -17

   1. Initial program 71.7%

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

   2. Taylor expanded in a around 0

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

   4. Applied rewrites 79.9%

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

   5. Taylor expanded in z around -inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower-+.f64 73.5

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

   7. Applied rewrites 73.5%

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

   8. Taylor expanded in t around inf

      \[\leadsto \mathsf{fma}\left(y, \frac{t}{{z}^{\color{blue}{2}}}, x\right) \]
   9. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \frac{t}{{z}^{2}}, x\right) \]

      2. pow2 N/A

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

      3. lift-*.f64 61.8

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

   10. Applied rewrites 61.8%

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

   if -17 < z < 6.4999999999999998e43

   1. Initial program 98.6%

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

   2. Taylor expanded in a around 0

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

   4. Applied rewrites 85.8%

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

   5. Taylor expanded in z around 0

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

      1. lower-*.f64 77.7

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

   7. Applied rewrites 77.7%

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

Alternative 12: 83.3% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -105000000:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+43}:\\ \;\;\;\;\mathsf{fma}\left(y, 1.6453555072203998 \cdot b, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -105000000.0)
   (fma 3.13060547623 y x)
   (if (<= z 6.5e+43)
     (fma y (* 1.6453555072203998 b) x)
     (fma 3.13060547623 y x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -105000000.0) {
		tmp = fma(3.13060547623, y, x);
	} else if (z <= 6.5e+43) {
		tmp = fma(y, (1.6453555072203998 * b), x);
	} else {
		tmp = fma(3.13060547623, y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -105000000.0)
		tmp = fma(3.13060547623, y, x);
	elseif (z <= 6.5e+43)
		tmp = fma(y, Float64(1.6453555072203998 * b), x);
	else
		tmp = fma(3.13060547623, y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -105000000.0], N[(3.13060547623 * y + x), $MachinePrecision], If[LessEqual[z, 6.5e+43], N[(y * N[(1.6453555072203998 * b), $MachinePrecision] + x), $MachinePrecision], N[(3.13060547623 * y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.05e8 or 6.4999999999999998e43 < z

   1. Initial program 10.7%

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

   2. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-fma.f64 90.0

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

   4. Applied rewrites 90.0%

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

   if -1.05e8 < z < 6.4999999999999998e43

   1. Initial program 98.5%

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

   2. Taylor expanded in a around 0

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

   4. Applied rewrites 85.7%

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

   5. Taylor expanded in z around 0

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

      1. lower-*.f64 77.3

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

   7. Applied rewrites 77.3%

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

Alternative 13: 81.5% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 92.9%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 73.6%

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

   6. Applied rewrites 74.0%

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

   7. Taylor expanded in z around 0

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

   9. Applied rewrites 71.9%

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

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

   1. Initial program 0.0%

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

   2. 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 97.0

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

   4. Applied rewrites 97.0%

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

Alternative 14: 63.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \leq 2 \cdot 10^{+139}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<=
      (/
       (*
        y
        (+
         (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z)
         b))
       (+
        (*
         (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721)
         z)
        0.607771387771))
      2e+139)
   x
   (fma 3.13060547623 y x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((y * ((((((((z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b)) / (((((((z + 15.234687407) * z) + 31.4690115749) * z) + 11.9400905721) * z) + 0.607771387771)) <= 2e+139) {
		tmp = x;
	} else {
		tmp = fma(3.13060547623, y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(Float64(y * Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b)) / Float64(Float64(Float64(Float64(Float64(Float64(Float64(z + 15.234687407) * z) + 31.4690115749) * z) + 11.9400905721) * z) + 0.607771387771)) <= 2e+139)
		tmp = x;
	else
		tmp = fma(3.13060547623, y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(N[(y * N[(N[(N[(N[(N[(N[(N[(N[(z * 3.13060547623), $MachinePrecision] + 11.1667541262), $MachinePrecision] * z), $MachinePrecision] + t), $MachinePrecision] * z), $MachinePrecision] + a), $MachinePrecision] * z), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(N[(N[(N[(N[(z + 15.234687407), $MachinePrecision] * z), $MachinePrecision] + 31.4690115749), $MachinePrecision] * z), $MachinePrecision] + 11.9400905721), $MachinePrecision] * z), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision], 2e+139], x, N[(3.13060547623 * y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z #s(literal 313060547623/100000000000 binary64)) #s(literal 55833770631/5000000000 binary64)) z) t) z) a) z) b)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z #s(literal 15234687407/1000000000 binary64)) z) #s(literal 314690115749/10000000000 binary64)) z) #s(literal 119400905721/10000000000 binary64)) z) #s(literal 607771387771/1000000000000 binary64))) < 2.00000000000000007e139

   1. Initial program 95.3%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 50.6%

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

   if 2.00000000000000007e139 < (/.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 21.4%

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

   2. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-fma.f64 76.4

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

   4. Applied rewrites 76.4%

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

Alternative 15: 45.5% accurate, 52.6× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := x

Derivation

1. Initial program 57.5%

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

2. Taylor expanded in x around inf

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

4. Applied rewrites 45.5%

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

Reproduce

herbie shell --seed 2025114 
(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))))