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

Percentage Accurate: 58.7% → 97.0%

Time: 17.4s

Alternatives: 15

Speedup: 11.3×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 58.7% 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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771} \leq \infty:\\ \;\;\;\;x + \frac{y}{\frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right)}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{0.31942702700572795 + \frac{\frac{\mathsf{fma}\left(\frac{t}{z}, -1.1905002162048226, \mathsf{fma}\left(-0.10203362558171805, \frac{a}{z}, \mathsf{fma}\left(3.5669630718360112, \frac{\mathsf{fma}\left(t, 0.10203362558171805, 3.241970391368047\right)}{z}, \frac{3.8139876336250245}{z}\right)\right)\right) - \mathsf{fma}\left(t, 0.10203362558171805, 3.241970391368047\right)}{z} - -3.7269864963038164}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<=
      (/
       (*
        y
        (+
         (* z (+ (* z (+ (* z (+ (* z 3.13060547623) 11.1667541262)) t)) a))
         b))
       (+
        (*
         z
         (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721))
        0.607771387771))
      INFINITY)
   (+
    x
    (/
     y
     (/
      (fma
       z
       (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721)
       0.607771387771)
      (fma z (fma z (fma z (fma z 3.13060547623 11.1667541262) t) a) b))))
   (+
    x
    (/
     y
     (+
      0.31942702700572795
      (/
       (-
        (/
         (-
          (fma
           (/ t z)
           -1.1905002162048226
           (fma
            -0.10203362558171805
            (/ a z)
            (fma
             3.5669630718360112
             (/ (fma t 0.10203362558171805 3.241970391368047) z)
             (/ 3.8139876336250245 z))))
          (fma t 0.10203362558171805 3.241970391368047))
         z)
        -3.7269864963038164)
       z))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)) <= ((double) INFINITY)) {
		tmp = x + (y / (fma(z, fma(z, fma(z, (z + 15.234687407), 31.4690115749), 11.9400905721), 0.607771387771) / fma(z, fma(z, fma(z, fma(z, 3.13060547623, 11.1667541262), t), a), b)));
	} else {
		tmp = x + (y / (0.31942702700572795 + ((((fma((t / z), -1.1905002162048226, fma(-0.10203362558171805, (a / z), fma(3.5669630718360112, (fma(t, 0.10203362558171805, 3.241970391368047) / z), (3.8139876336250245 / z)))) - fma(t, 0.10203362558171805, 3.241970391368047)) / z) - -3.7269864963038164) / z)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(Float64(y * Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)) <= Inf)
		tmp = Float64(x + Float64(y / Float64(fma(z, fma(z, fma(z, Float64(z + 15.234687407), 31.4690115749), 11.9400905721), 0.607771387771) / fma(z, fma(z, fma(z, fma(z, 3.13060547623, 11.1667541262), t), a), b))));
	else
		tmp = Float64(x + Float64(y / Float64(0.31942702700572795 + Float64(Float64(Float64(Float64(fma(Float64(t / z), -1.1905002162048226, fma(-0.10203362558171805, Float64(a / z), fma(3.5669630718360112, Float64(fma(t, 0.10203362558171805, 3.241970391368047) / z), Float64(3.8139876336250245 / z)))) - fma(t, 0.10203362558171805, 3.241970391368047)) / z) - -3.7269864963038164) / z))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(N[(y * N[(N[(z * N[(N[(z * N[(N[(z * N[(N[(z * 3.13060547623), $MachinePrecision] + 11.1667541262), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(N[(z * N[(N[(z * N[(N[(z * N[(z + 15.234687407), $MachinePrecision]), $MachinePrecision] + 31.4690115749), $MachinePrecision]), $MachinePrecision] + 11.9400905721), $MachinePrecision]), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision], Infinity], N[(x + N[(y / N[(N[(z * N[(z * N[(z * N[(z + 15.234687407), $MachinePrecision] + 31.4690115749), $MachinePrecision] + 11.9400905721), $MachinePrecision] + 0.607771387771), $MachinePrecision] / N[(z * N[(z * N[(z * N[(z * 3.13060547623 + 11.1667541262), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(0.31942702700572795 + N[(N[(N[(N[(N[(N[(t / z), $MachinePrecision] * -1.1905002162048226 + N[(-0.10203362558171805 * N[(a / z), $MachinePrecision] + N[(3.5669630718360112 * N[(N[(t * 0.10203362558171805 + 3.241970391368047), $MachinePrecision] / z), $MachinePrecision] + N[(3.8139876336250245 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * 0.10203362558171805 + 3.241970391368047), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] - -3.7269864963038164), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 92.5%

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

      1. associate-/l* N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

      4. /-lowering-/.f64 N/A

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

      5. /-lowering-/.f64 N/A

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

   4. Applied egg-rr 96.6%

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

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

   1. Initial program 0.0%

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

      1. associate-/l* N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

      4. /-lowering-/.f64 N/A

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

      5. /-lowering-/.f64 N/A

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

   4. Applied egg-rr 0.0%

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

   5. Taylor expanded in z around -inf

      \[\leadsto x + \frac{y}{\color{blue}{\frac{100000000000}{313060547623} + -1 \cdot \frac{-1 \cdot \frac{\left(\frac{-36527041698806418835610000000000000}{30682095812842786715169336002493367} \cdot \frac{t}{z} + \left(\frac{-10000000000000000000000}{98006906478012650950129} \cdot \frac{a}{z} + \left(\frac{1116675412620}{313060547623} \cdot \frac{\frac{99470446170353844637769068629165790}{30682095812842786715169336002493367} + \frac{10000000000000000000000}{98006906478012650950129} \cdot t}{z} + \frac{1194009057210}{313060547623} \cdot \frac{1}{z}\right)\right)\right) - \left(\frac{99470446170353844637769068629165790}{30682095812842786715169336002493367} + \frac{10000000000000000000000}{98006906478012650950129} \cdot t\right)}{z} - \frac{365270416988064188356100}{98006906478012650950129}}{z}}} \]

   7. Simplified 99.9%

      \[\leadsto x + \frac{y}{\color{blue}{0.31942702700572795 - \frac{\frac{\mathsf{fma}\left(\frac{t}{z}, -1.1905002162048226, \mathsf{fma}\left(-0.10203362558171805, \frac{a}{z}, \mathsf{fma}\left(3.5669630718360112, \frac{\mathsf{fma}\left(t, 0.10203362558171805, 3.241970391368047\right)}{z}, \frac{3.8139876336250245}{z}\right)\right)\right) - \mathsf{fma}\left(t, 0.10203362558171805, 3.241970391368047\right)}{-z} + -3.7269864963038164}{z}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 97.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771} \leq \infty:\\ \;\;\;\;x + \frac{y}{\frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right)}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{0.31942702700572795 + \frac{\frac{\mathsf{fma}\left(\frac{t}{z}, -1.1905002162048226, \mathsf{fma}\left(-0.10203362558171805, \frac{a}{z}, \mathsf{fma}\left(3.5669630718360112, \frac{\mathsf{fma}\left(t, 0.10203362558171805, 3.241970391368047\right)}{z}, \frac{3.8139876336250245}{z}\right)\right)\right) - \mathsf{fma}\left(t, 0.10203362558171805, 3.241970391368047\right)}{z} - -3.7269864963038164}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 97.9% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(N[(y * N[(N[(z * N[(N[(z * N[(N[(z * N[(N[(z * 3.13060547623), $MachinePrecision] + 11.1667541262), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(N[(z * N[(N[(z * N[(N[(z * N[(z + 15.234687407), $MachinePrecision]), $MachinePrecision] + 31.4690115749), $MachinePrecision]), $MachinePrecision] + 11.9400905721), $MachinePrecision]), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision], Infinity], N[(x + N[(y / N[(N[(z * N[(z * N[(z * N[(z + 15.234687407), $MachinePrecision] + 31.4690115749), $MachinePrecision] + 11.9400905721), $MachinePrecision] + 0.607771387771), $MachinePrecision] / N[(z * N[(z * N[(z * N[(z * 3.13060547623 + 11.1667541262), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(3.13060547623 - N[(N[(36.52704169880642 / z), $MachinePrecision] - N[(N[(t + 457.9610022158428), $MachinePrecision] / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 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))) < +inf.0

   1. Initial program 92.5%

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

      1. associate-/l* N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

      4. /-lowering-/.f64 N/A

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

      5. /-lowering-/.f64 N/A

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

   4. Applied egg-rr 96.6%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{x + \left(-1 \cdot \frac{\left(\frac{-55833770631}{5000000000} \cdot y + -1 \cdot \frac{t \cdot y - \left(\frac{-15234687407}{1000000000} \cdot \left(\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y\right) + \frac{98517059967927196814627}{1000000000000000000000} \cdot y\right)}{z}\right) - \frac{-4769379582500641883561}{100000000000000000000} \cdot y}{z} + \frac{313060547623}{100000000000} \cdot y\right)} \]

   5. Simplified 87.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, 3.13060547623, x\right) - \frac{\frac{\mathsf{fma}\left(y, t, \mathsf{fma}\left(y, -98.5170599679272, y \cdot 556.47806218377\right)\right)}{-z} + y \cdot 36.52704169880642}{z}} \]

   6. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. --lowering--.f64 N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

      6. unsub-neg N/A

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

      7. --lowering--.f64 N/A

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

      8. associate-*r/ N/A

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

      9. metadata-eval N/A

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

      10. /-lowering-/.f64 N/A

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

      11. /-lowering-/.f64 N/A

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

      12. +-lowering-+.f64 N/A

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

      13. unpow2 N/A

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

      14. *-lowering-*.f64 99.8

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

   8. Simplified 99.8%

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

4. Final simplification 97.8%

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

Alternative 3: 97.5% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(N[(y * N[(N[(z * N[(N[(z * N[(N[(z * N[(N[(z * 3.13060547623), $MachinePrecision] + 11.1667541262), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(N[(z * N[(N[(z * N[(N[(z * N[(z + 15.234687407), $MachinePrecision]), $MachinePrecision] + 31.4690115749), $MachinePrecision]), $MachinePrecision] + 11.9400905721), $MachinePrecision]), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(z * N[(z * N[(z * N[(z * 3.13060547623 + 11.1667541262), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision] + b), $MachinePrecision] * N[(y / N[(z * N[(z * N[(z * N[(z + 15.234687407), $MachinePrecision] + 31.4690115749), $MachinePrecision] + 11.9400905721), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(y * N[(3.13060547623 - N[(N[(36.52704169880642 / z), $MachinePrecision] - N[(N[(t + 457.9610022158428), $MachinePrecision] / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 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))) < +inf.0

   1. Initial program 92.5%

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. accelerator-lowering-fma.f64 N/A

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

   4. Applied egg-rr 96.0%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{x + \left(-1 \cdot \frac{\left(\frac{-55833770631}{5000000000} \cdot y + -1 \cdot \frac{t \cdot y - \left(\frac{-15234687407}{1000000000} \cdot \left(\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y\right) + \frac{98517059967927196814627}{1000000000000000000000} \cdot y\right)}{z}\right) - \frac{-4769379582500641883561}{100000000000000000000} \cdot y}{z} + \frac{313060547623}{100000000000} \cdot y\right)} \]

   5. Simplified 87.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, 3.13060547623, x\right) - \frac{\frac{\mathsf{fma}\left(y, t, \mathsf{fma}\left(y, -98.5170599679272, y \cdot 556.47806218377\right)\right)}{-z} + y \cdot 36.52704169880642}{z}} \]

   6. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. --lowering--.f64 N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

      6. unsub-neg N/A

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

      7. --lowering--.f64 N/A

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

      8. associate-*r/ N/A

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

      9. metadata-eval N/A

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

      10. /-lowering-/.f64 N/A

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

      11. /-lowering-/.f64 N/A

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

      12. +-lowering-+.f64 N/A

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

      13. unpow2 N/A

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

      14. *-lowering-*.f64 99.8

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

   8. Simplified 99.8%

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

4. Final simplification 97.5%

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

Alternative 4: 97.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y, 3.13060547623 - \left(\frac{36.52704169880642}{z} - \frac{t + 457.9610022158428}{z \cdot z}\right), x\right)\\ \mathbf{if}\;z \leq -8.8 \cdot 10^{+24}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 32500000000:\\ \;\;\;\;x + \frac{y \cdot \mathsf{fma}\left(z, \mathsf{fma}\left(z, t, a\right), b\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (fma
          y
          (-
           3.13060547623
           (- (/ 36.52704169880642 z) (/ (+ t 457.9610022158428) (* z z))))
          x)))
   (if (<= z -8.8e+24)
     t_1
     (if (<= z 32500000000.0)
       (+
        x
        (/
         (* y (fma z (fma z t a) b))
         (+
          (*
           z
           (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721))
          0.607771387771)))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(y, (3.13060547623 - ((36.52704169880642 / z) - ((t + 457.9610022158428) / (z * z)))), x);
	double tmp;
	if (z <= -8.8e+24) {
		tmp = t_1;
	} else if (z <= 32500000000.0) {
		tmp = x + ((y * fma(z, fma(z, t, a), b)) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(y, Float64(3.13060547623 - Float64(Float64(36.52704169880642 / z) - Float64(Float64(t + 457.9610022158428) / Float64(z * z)))), x)
	tmp = 0.0
	if (z <= -8.8e+24)
		tmp = t_1;
	elseif (z <= 32500000000.0)
		tmp = Float64(x + Float64(Float64(y * fma(z, fma(z, t, a), b)) / Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(3.13060547623 - N[(N[(36.52704169880642 / z), $MachinePrecision] - N[(N[(t + 457.9610022158428), $MachinePrecision] / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[z, -8.8e+24], t$95$1, If[LessEqual[z, 32500000000.0], N[(x + N[(N[(y * N[(z * N[(z * t + a), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(N[(z * N[(N[(z * N[(N[(z * N[(z + 15.234687407), $MachinePrecision]), $MachinePrecision] + 31.4690115749), $MachinePrecision]), $MachinePrecision] + 11.9400905721), $MachinePrecision]), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -8.80000000000000007e24 or 3.25e10 < z

   1. Initial program 11.7%

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

   3. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{x + \left(-1 \cdot \frac{\left(\frac{-55833770631}{5000000000} \cdot y + -1 \cdot \frac{t \cdot y - \left(\frac{-15234687407}{1000000000} \cdot \left(\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y\right) + \frac{98517059967927196814627}{1000000000000000000000} \cdot y\right)}{z}\right) - \frac{-4769379582500641883561}{100000000000000000000} \cdot y}{z} + \frac{313060547623}{100000000000} \cdot y\right)} \]

   5. Simplified 86.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, 3.13060547623, x\right) - \frac{\frac{\mathsf{fma}\left(y, t, \mathsf{fma}\left(y, -98.5170599679272, y \cdot 556.47806218377\right)\right)}{-z} + y \cdot 36.52704169880642}{z}} \]

   6. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. --lowering--.f64 N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

      6. unsub-neg N/A

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

      7. --lowering--.f64 N/A

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

      8. associate-*r/ N/A

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

      9. metadata-eval N/A

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

      10. /-lowering-/.f64 N/A

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

      11. /-lowering-/.f64 N/A

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

      12. +-lowering-+.f64 N/A

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

      13. unpow2 N/A

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

      14. *-lowering-*.f64 96.3

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

   8. Simplified 96.3%

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

   if -8.80000000000000007e24 < z < 3.25e10

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. accelerator-lowering-fma.f64 99.3

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

   5. Simplified 99.3%

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

4. Final simplification 97.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{+24}:\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623 - \left(\frac{36.52704169880642}{z} - \frac{t + 457.9610022158428}{z \cdot z}\right), x\right)\\ \mathbf{elif}\;z \leq 32500000000:\\ \;\;\;\;x + \frac{y \cdot \mathsf{fma}\left(z, \mathsf{fma}\left(z, t, a\right), b\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623 - \left(\frac{36.52704169880642}{z} - \frac{t + 457.9610022158428}{z \cdot z}\right), x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 96.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y, 3.13060547623 - \left(\frac{36.52704169880642}{z} - \frac{t + 457.9610022158428}{z \cdot z}\right), x\right)\\ \mathbf{if}\;z \leq -3.9 \cdot 10^{+23}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4000000:\\ \;\;\;\;x + \frac{y}{\frac{0.607771387771}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right)}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (fma
          y
          (-
           3.13060547623
           (- (/ 36.52704169880642 z) (/ (+ t 457.9610022158428) (* z z))))
          x)))
   (if (<= z -3.9e+23)
     t_1
     (if (<= z 4000000.0)
       (+
        x
        (/
         y
         (/
          0.607771387771
          (fma z (fma z (fma z (fma z 3.13060547623 11.1667541262) t) a) b))))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(y, (3.13060547623 - ((36.52704169880642 / z) - ((t + 457.9610022158428) / (z * z)))), x);
	double tmp;
	if (z <= -3.9e+23) {
		tmp = t_1;
	} else if (z <= 4000000.0) {
		tmp = x + (y / (0.607771387771 / fma(z, fma(z, fma(z, fma(z, 3.13060547623, 11.1667541262), t), a), b)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(y, Float64(3.13060547623 - Float64(Float64(36.52704169880642 / z) - Float64(Float64(t + 457.9610022158428) / Float64(z * z)))), x)
	tmp = 0.0
	if (z <= -3.9e+23)
		tmp = t_1;
	elseif (z <= 4000000.0)
		tmp = Float64(x + Float64(y / Float64(0.607771387771 / fma(z, fma(z, fma(z, fma(z, 3.13060547623, 11.1667541262), t), a), b))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(3.13060547623 - N[(N[(36.52704169880642 / z), $MachinePrecision] - N[(N[(t + 457.9610022158428), $MachinePrecision] / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[z, -3.9e+23], t$95$1, If[LessEqual[z, 4000000.0], N[(x + N[(y / N[(0.607771387771 / N[(z * N[(z * N[(z * N[(z * 3.13060547623 + 11.1667541262), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.9e23 or 4e6 < z

   1. Initial program 11.7%

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

   3. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{x + \left(-1 \cdot \frac{\left(\frac{-55833770631}{5000000000} \cdot y + -1 \cdot \frac{t \cdot y - \left(\frac{-15234687407}{1000000000} \cdot \left(\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y\right) + \frac{98517059967927196814627}{1000000000000000000000} \cdot y\right)}{z}\right) - \frac{-4769379582500641883561}{100000000000000000000} \cdot y}{z} + \frac{313060547623}{100000000000} \cdot y\right)} \]

   5. Simplified 86.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, 3.13060547623, x\right) - \frac{\frac{\mathsf{fma}\left(y, t, \mathsf{fma}\left(y, -98.5170599679272, y \cdot 556.47806218377\right)\right)}{-z} + y \cdot 36.52704169880642}{z}} \]

   6. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. --lowering--.f64 N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

      6. unsub-neg N/A

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

      7. --lowering--.f64 N/A

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

      8. associate-*r/ N/A

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

      9. metadata-eval N/A

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

      10. /-lowering-/.f64 N/A

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

      11. /-lowering-/.f64 N/A

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

      12. +-lowering-+.f64 N/A

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

      13. unpow2 N/A

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

      14. *-lowering-*.f64 96.3

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

   8. Simplified 96.3%

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

   if -3.9e23 < z < 4e6

   1. Initial program 99.7%

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

      1. associate-/l* N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

      4. /-lowering-/.f64 N/A

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

      5. /-lowering-/.f64 N/A

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

   4. Applied egg-rr 99.6%

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

   5. Taylor expanded in z around 0

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

   7. Simplified 96.5%

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

4. Final simplification 96.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{+23}:\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623 - \left(\frac{36.52704169880642}{z} - \frac{t + 457.9610022158428}{z \cdot z}\right), x\right)\\ \mathbf{elif}\;z \leq 4000000:\\ \;\;\;\;x + \frac{y}{\frac{0.607771387771}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right)}}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623 - \left(\frac{36.52704169880642}{z} - \frac{t + 457.9610022158428}{z \cdot z}\right), x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 91.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+24}:\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623, x\right)\\ \mathbf{elif}\;z \leq 118:\\ \;\;\;\;x + \frac{y \cdot \mathsf{fma}\left(z, a, b\right)}{0.607771387771}\\ \mathbf{elif}\;z \leq 10^{+71}:\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623, x\right) + \frac{\frac{y \cdot t}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.45e+24)
   (fma y 3.13060547623 x)
   (if (<= z 118.0)
     (+ x (/ (* y (fma z a b)) 0.607771387771))
     (if (<= z 1e+71)
       (+ (fma y 3.13060547623 x) (/ (/ (* y t) z) z))
       (fma y 3.13060547623 x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.45e+24) {
		tmp = fma(y, 3.13060547623, x);
	} else if (z <= 118.0) {
		tmp = x + ((y * fma(z, a, b)) / 0.607771387771);
	} else if (z <= 1e+71) {
		tmp = fma(y, 3.13060547623, x) + (((y * t) / z) / z);
	} else {
		tmp = fma(y, 3.13060547623, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.45e+24)
		tmp = fma(y, 3.13060547623, x);
	elseif (z <= 118.0)
		tmp = Float64(x + Float64(Float64(y * fma(z, a, b)) / 0.607771387771));
	elseif (z <= 1e+71)
		tmp = Float64(fma(y, 3.13060547623, x) + Float64(Float64(Float64(y * t) / z) / z));
	else
		tmp = fma(y, 3.13060547623, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.45e+24], N[(y * 3.13060547623 + x), $MachinePrecision], If[LessEqual[z, 118.0], N[(x + N[(N[(y * N[(z * a + b), $MachinePrecision]), $MachinePrecision] / 0.607771387771), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1e+71], N[(N[(y * 3.13060547623 + x), $MachinePrecision] + N[(N[(N[(y * t), $MachinePrecision] / z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(y * 3.13060547623 + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.4499999999999999e24 or 1e71 < z

   1. Initial program 8.2%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. accelerator-lowering-fma.f64 97.6

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

   5. Simplified 97.6%

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

   if -1.4499999999999999e24 < z < 118

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. accelerator-lowering-fma.f64 93.2

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

   5. Simplified 93.2%

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

   6. Taylor expanded in z around 0

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

   8. Simplified 92.1%

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

   if 118 < z < 1e71

   1. Initial program 49.1%

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

   3. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{x + \left(-1 \cdot \frac{\left(\frac{-55833770631}{5000000000} \cdot y + -1 \cdot \frac{t \cdot y - \left(\frac{-15234687407}{1000000000} \cdot \left(\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y\right) + \frac{98517059967927196814627}{1000000000000000000000} \cdot y\right)}{z}\right) - \frac{-4769379582500641883561}{100000000000000000000} \cdot y}{z} + \frac{313060547623}{100000000000} \cdot y\right)} \]

   5. Simplified 67.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, 3.13060547623, x\right) - \frac{\frac{\mathsf{fma}\left(y, t, \mathsf{fma}\left(y, -98.5170599679272, y \cdot 556.47806218377\right)\right)}{-z} + y \cdot 36.52704169880642}{z}} \]

   6. Taylor expanded in t around inf

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. neg-mul-1 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 N/A

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

      7. neg-mul-1 N/A

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

      8. neg-lowering-neg.f64 65.5

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

   8. Simplified 65.5%

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

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+24}:\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623, x\right)\\ \mathbf{elif}\;z \leq 118:\\ \;\;\;\;x + \frac{y \cdot \mathsf{fma}\left(z, a, b\right)}{0.607771387771}\\ \mathbf{elif}\;z \leq 10^{+71}:\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623, x\right) + \frac{\frac{y \cdot t}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 93.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y, 3.13060547623 - \left(\frac{36.52704169880642}{z} - \frac{t + 457.9610022158428}{z \cdot z}\right), x\right)\\ \mathbf{if}\;z \leq -4 \cdot 10^{+23}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 118:\\ \;\;\;\;x + \frac{y \cdot \mathsf{fma}\left(z, a, b\right)}{0.607771387771}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (fma
          y
          (-
           3.13060547623
           (- (/ 36.52704169880642 z) (/ (+ t 457.9610022158428) (* z z))))
          x)))
   (if (<= z -4e+23)
     t_1
     (if (<= z 118.0) (+ x (/ (* y (fma z a b)) 0.607771387771)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(y, (3.13060547623 - ((36.52704169880642 / z) - ((t + 457.9610022158428) / (z * z)))), x);
	double tmp;
	if (z <= -4e+23) {
		tmp = t_1;
	} else if (z <= 118.0) {
		tmp = x + ((y * fma(z, a, b)) / 0.607771387771);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(y, Float64(3.13060547623 - Float64(Float64(36.52704169880642 / z) - Float64(Float64(t + 457.9610022158428) / Float64(z * z)))), x)
	tmp = 0.0
	if (z <= -4e+23)
		tmp = t_1;
	elseif (z <= 118.0)
		tmp = Float64(x + Float64(Float64(y * fma(z, a, b)) / 0.607771387771));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(3.13060547623 - N[(N[(36.52704169880642 / z), $MachinePrecision] - N[(N[(t + 457.9610022158428), $MachinePrecision] / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[z, -4e+23], t$95$1, If[LessEqual[z, 118.0], N[(x + N[(N[(y * N[(z * a + b), $MachinePrecision]), $MachinePrecision] / 0.607771387771), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.9999999999999997e23 or 118 < 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. Add Preprocessing

   3. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{x + \left(-1 \cdot \frac{\left(\frac{-55833770631}{5000000000} \cdot y + -1 \cdot \frac{t \cdot y - \left(\frac{-15234687407}{1000000000} \cdot \left(\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y\right) + \frac{98517059967927196814627}{1000000000000000000000} \cdot y\right)}{z}\right) - \frac{-4769379582500641883561}{100000000000000000000} \cdot y}{z} + \frac{313060547623}{100000000000} \cdot y\right)} \]

   5. Simplified 85.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, 3.13060547623, x\right) - \frac{\frac{\mathsf{fma}\left(y, t, \mathsf{fma}\left(y, -98.5170599679272, y \cdot 556.47806218377\right)\right)}{-z} + y \cdot 36.52704169880642}{z}} \]

   6. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. --lowering--.f64 N/A

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

      4. +-commutative N/A

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

      5. mul-1-neg N/A

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

      6. unsub-neg N/A

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

      7. --lowering--.f64 N/A

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

      8. associate-*r/ N/A

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

      9. metadata-eval N/A

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

      10. /-lowering-/.f64 N/A

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

      11. /-lowering-/.f64 N/A

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

      12. +-lowering-+.f64 N/A

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

      13. unpow2 N/A

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

      14. *-lowering-*.f64 95.6

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

   8. Simplified 95.6%

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

   if -3.9999999999999997e23 < z < 118

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. accelerator-lowering-fma.f64 93.2

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

   5. Simplified 93.2%

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

   6. Taylor expanded in z around 0

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

   8. Simplified 92.1%

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

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+23}:\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623 - \left(\frac{36.52704169880642}{z} - \frac{t + 457.9610022158428}{z \cdot z}\right), x\right)\\ \mathbf{elif}\;z \leq 118:\\ \;\;\;\;x + \frac{y \cdot \mathsf{fma}\left(z, a, b\right)}{0.607771387771}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623 - \left(\frac{36.52704169880642}{z} - \frac{t + 457.9610022158428}{z \cdot z}\right), x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 90.3% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+24}:\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623, x\right)\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+36}:\\ \;\;\;\;x + \frac{y \cdot \mathsf{fma}\left(z, a, b\right)}{0.607771387771}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -3e+24)
   (fma y 3.13060547623 x)
   (if (<= z 2.8e+36)
     (+ x (/ (* y (fma z a b)) 0.607771387771))
     (fma y 3.13060547623 x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -3e+24) {
		tmp = fma(y, 3.13060547623, x);
	} else if (z <= 2.8e+36) {
		tmp = x + ((y * fma(z, a, b)) / 0.607771387771);
	} else {
		tmp = fma(y, 3.13060547623, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -3e+24)
		tmp = fma(y, 3.13060547623, x);
	elseif (z <= 2.8e+36)
		tmp = Float64(x + Float64(Float64(y * fma(z, a, b)) / 0.607771387771));
	else
		tmp = fma(y, 3.13060547623, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -3e+24], N[(y * 3.13060547623 + x), $MachinePrecision], If[LessEqual[z, 2.8e+36], N[(x + N[(N[(y * N[(z * a + b), $MachinePrecision]), $MachinePrecision] / 0.607771387771), $MachinePrecision]), $MachinePrecision], N[(y * 3.13060547623 + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.99999999999999995e24 or 2.8000000000000001e36 < z

   1. Initial program 10.4%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. accelerator-lowering-fma.f64 96.1

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

   5. Simplified 96.1%

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

   if -2.99999999999999995e24 < z < 2.8000000000000001e36

   1. Initial program 96.3%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. accelerator-lowering-fma.f64 88.8

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

   5. Simplified 88.8%

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

   6. Taylor expanded in z around 0

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

   8. Simplified 87.2%

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

Alternative 9: 83.6% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+35}:\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623, x\right)\\ \mathbf{elif}\;z \leq 0.034:\\ \;\;\;\;\mathsf{fma}\left(b, y \cdot \mathsf{fma}\left(z, -32.324150453290734, 1.6453555072203998\right), x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{z}, -36.52704169880642, \mathsf{fma}\left(y, 3.13060547623, x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -7e+35)
   (fma y 3.13060547623 x)
   (if (<= z 0.034)
     (fma b (* y (fma z -32.324150453290734 1.6453555072203998)) x)
     (fma (/ y z) -36.52704169880642 (fma y 3.13060547623 x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -7e+35) {
		tmp = fma(y, 3.13060547623, x);
	} else if (z <= 0.034) {
		tmp = fma(b, (y * fma(z, -32.324150453290734, 1.6453555072203998)), x);
	} else {
		tmp = fma((y / z), -36.52704169880642, fma(y, 3.13060547623, x));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -7e+35)
		tmp = fma(y, 3.13060547623, x);
	elseif (z <= 0.034)
		tmp = fma(b, Float64(y * fma(z, -32.324150453290734, 1.6453555072203998)), x);
	else
		tmp = fma(Float64(y / z), -36.52704169880642, fma(y, 3.13060547623, x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -7e+35], N[(y * 3.13060547623 + x), $MachinePrecision], If[LessEqual[z, 0.034], N[(b * N[(y * N[(z * -32.324150453290734 + 1.6453555072203998), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(N[(y / z), $MachinePrecision] * -36.52704169880642 + N[(y * 3.13060547623 + x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.0000000000000001e35

   1. Initial program 9.6%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. accelerator-lowering-fma.f64 97.3

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

   5. Simplified 97.3%

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

   if -7.0000000000000001e35 < z < 0.034000000000000002

   1. Initial program 99.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. accelerator-lowering-fma.f64 92.6

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

   5. Simplified 92.6%

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

   6. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. accelerator-lowering-fma.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. +-commutative N/A

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

      6. accelerator-lowering-fma.f64 N/A

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

      7. +-commutative N/A

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

      8. accelerator-lowering-fma.f64 N/A

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

      9. +-commutative N/A

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

      10. accelerator-lowering-fma.f64 N/A

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

      11. +-commutative N/A

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

      12. +-lowering-+.f64 73.0

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

   8. Simplified 73.0%

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

   9. Taylor expanded in z around 0

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

       1. +-commutative N/A

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

       2. *-commutative N/A

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

       3. associate-*r* N/A

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

       4. *-commutative N/A

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

       5. associate-*r* N/A

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

       6. distribute-rgt-out N/A

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

       7. accelerator-lowering-fma.f64 N/A

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

       8. *-commutative N/A

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

       9. associate-*l* N/A

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

       10. *-commutative N/A

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

       11. distribute-lft-out N/A

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

       12. *-lowering-*.f64 N/A

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

       13. accelerator-lowering-fma.f64 73.1

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

   11. Simplified 73.1%

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

   if 0.034000000000000002 < z

   1. Initial program 15.4%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. +-commutative N/A

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

      3. associate--l+ N/A

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

      4. +-commutative N/A

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

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

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

      6. metadata-eval N/A

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

      7. metadata-eval N/A

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

      8. metadata-eval N/A

         \[\leadsto \left(\frac{y}{z} \cdot \frac{\color{blue}{\frac{-55833770631}{5000000000} - \frac{-4769379582500641883561}{100000000000000000000}}}{-1} + \frac{313060547623}{100000000000} \cdot y\right) + x \]

      9. times-frac N/A

         \[\leadsto \left(\color{blue}{\frac{y \cdot \left(\frac{-55833770631}{5000000000} - \frac{-4769379582500641883561}{100000000000000000000}\right)}{z \cdot -1}} + \frac{313060547623}{100000000000} \cdot y\right) + x \]

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

          \[\leadsto \left(\frac{\color{blue}{\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y}}{z \cdot -1} + \frac{313060547623}{100000000000} \cdot y\right) + x \]

      11. *-commutative N/A

          \[\leadsto \left(\frac{\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y}{\color{blue}{-1 \cdot z}} + \frac{313060547623}{100000000000} \cdot y\right) + x \]

      12. mul-1-neg N/A

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

      13. distribute-neg-frac2 N/A

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

      14. mul-1-neg N/A

          \[\leadsto \left(\color{blue}{-1 \cdot \frac{\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y}{z}} + \frac{313060547623}{100000000000} \cdot y\right) + x \]

      15. associate-+l+ N/A

          \[\leadsto \color{blue}{-1 \cdot \frac{\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y}{z} + \left(\frac{313060547623}{100000000000} \cdot y + x\right)} \]

   5. Simplified 82.7%

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

Alternative 10: 83.6% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+34}:\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623, x\right)\\ \mathbf{elif}\;z \leq 0.034:\\ \;\;\;\;\mathsf{fma}\left(b, y \cdot \mathsf{fma}\left(z, -32.324150453290734, 1.6453555072203998\right), x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623 + \frac{-36.52704169880642}{z}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.85e+34)
   (fma y 3.13060547623 x)
   (if (<= z 0.034)
     (fma b (* y (fma z -32.324150453290734 1.6453555072203998)) x)
     (fma y (+ 3.13060547623 (/ -36.52704169880642 z)) x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.85e+34) {
		tmp = fma(y, 3.13060547623, x);
	} else if (z <= 0.034) {
		tmp = fma(b, (y * fma(z, -32.324150453290734, 1.6453555072203998)), x);
	} else {
		tmp = fma(y, (3.13060547623 + (-36.52704169880642 / z)), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.85e+34)
		tmp = fma(y, 3.13060547623, x);
	elseif (z <= 0.034)
		tmp = fma(b, Float64(y * fma(z, -32.324150453290734, 1.6453555072203998)), x);
	else
		tmp = fma(y, Float64(3.13060547623 + Float64(-36.52704169880642 / z)), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.85e+34], N[(y * 3.13060547623 + x), $MachinePrecision], If[LessEqual[z, 0.034], N[(b * N[(y * N[(z * -32.324150453290734 + 1.6453555072203998), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(y * N[(3.13060547623 + N[(-36.52704169880642 / z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.85000000000000004e34

   1. Initial program 9.6%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. accelerator-lowering-fma.f64 97.3

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

   5. Simplified 97.3%

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

   if -1.85000000000000004e34 < z < 0.034000000000000002

   1. Initial program 99.0%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. accelerator-lowering-fma.f64 92.6

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

   5. Simplified 92.6%

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

   6. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. accelerator-lowering-fma.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. +-commutative N/A

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

      6. accelerator-lowering-fma.f64 N/A

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

      7. +-commutative N/A

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

      8. accelerator-lowering-fma.f64 N/A

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

      9. +-commutative N/A

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

      10. accelerator-lowering-fma.f64 N/A

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

      11. +-commutative N/A

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

      12. +-lowering-+.f64 73.0

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

   8. Simplified 73.0%

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

   9. Taylor expanded in z around 0

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

       1. +-commutative N/A

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

       2. *-commutative N/A

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

       3. associate-*r* N/A

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

       4. *-commutative N/A

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

       5. associate-*r* N/A

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

       6. distribute-rgt-out N/A

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

       7. accelerator-lowering-fma.f64 N/A

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

       8. *-commutative N/A

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

       9. associate-*l* N/A

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

       10. *-commutative N/A

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

       11. distribute-lft-out N/A

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

       12. *-lowering-*.f64 N/A

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

       13. accelerator-lowering-fma.f64 73.1

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

   11. Simplified 73.1%

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

   if 0.034000000000000002 < z

   1. Initial program 15.4%

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

      1. associate-/l* N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

      4. /-lowering-/.f64 N/A

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

      5. /-lowering-/.f64 N/A

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

   4. Applied egg-rr 21.4%

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

   5. Taylor expanded in z around inf

      \[\leadsto x + \frac{y}{\color{blue}{\frac{100000000000}{313060547623} + \frac{365270416988064188356100}{98006906478012650950129} \cdot \frac{1}{z}}} \]
   6. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto x + \frac{y}{\color{blue}{\frac{100000000000}{313060547623} + \frac{365270416988064188356100}{98006906478012650950129} \cdot \frac{1}{z}}} \]

      2. associate-*r/ N/A

         \[\leadsto x + \frac{y}{\frac{100000000000}{313060547623} + \color{blue}{\frac{\frac{365270416988064188356100}{98006906478012650950129} \cdot 1}{z}}} \]

      3. metadata-eval N/A

         \[\leadsto x + \frac{y}{\frac{100000000000}{313060547623} + \frac{\color{blue}{\frac{365270416988064188356100}{98006906478012650950129}}}{z}} \]

      4. /-lowering-/.f64 82.6

         \[\leadsto x + \frac{y}{0.31942702700572795 + \color{blue}{\frac{3.7269864963038164}{z}}} \]

   7. Simplified 82.6%

      \[\leadsto x + \frac{y}{\color{blue}{0.31942702700572795 + \frac{3.7269864963038164}{z}}} \]
   8. Step-by-step derivation

      1. clear-num N/A

         \[\leadsto x + \color{blue}{\frac{1}{\frac{\frac{100000000000}{313060547623} + \frac{\frac{365270416988064188356100}{98006906478012650950129}}{z}}{y}}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto x + \color{blue}{\frac{1}{\frac{\frac{100000000000}{313060547623} + \frac{\frac{365270416988064188356100}{98006906478012650950129}}{z}}{y}}} \]

      3. /-lowering-/.f64 N/A

         \[\leadsto x + \frac{1}{\color{blue}{\frac{\frac{100000000000}{313060547623} + \frac{\frac{365270416988064188356100}{98006906478012650950129}}{z}}{y}}} \]

      4. +-lowering-+.f64 N/A

         \[\leadsto x + \frac{1}{\frac{\color{blue}{\frac{100000000000}{313060547623} + \frac{\frac{365270416988064188356100}{98006906478012650950129}}{z}}}{y}} \]

      5. /-lowering-/.f64 82.4

         \[\leadsto x + \frac{1}{\frac{0.31942702700572795 + \color{blue}{\frac{3.7269864963038164}{z}}}{y}} \]

   9. Applied egg-rr 82.4%

      \[\leadsto x + \color{blue}{\frac{1}{\frac{0.31942702700572795 + \frac{3.7269864963038164}{z}}{y}}} \]

   10. Taylor expanded in z around inf

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

       1. +-commutative N/A

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

       2. +-commutative N/A

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

       3. *-commutative N/A

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

       4. associate-*r/ N/A

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

       5. *-commutative N/A

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

       6. associate-/l* N/A

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

       7. distribute-lft-out N/A

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

       8. accelerator-lowering-fma.f64 N/A

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

       9. +-lowering-+.f64 N/A

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

       10. /-lowering-/.f64 82.6

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

   12. Simplified 82.6%

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

Alternative 11: 83.6% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{+24}:\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623, x\right)\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+27}:\\ \;\;\;\;x + 1.6453555072203998 \cdot \left(y \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -2.15e+24)
   (fma y 3.13060547623 x)
   (if (<= z 6.2e+27)
     (+ x (* 1.6453555072203998 (* y b)))
     (fma y 3.13060547623 x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.15e+24) {
		tmp = fma(y, 3.13060547623, x);
	} else if (z <= 6.2e+27) {
		tmp = x + (1.6453555072203998 * (y * b));
	} else {
		tmp = fma(y, 3.13060547623, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -2.15e+24)
		tmp = fma(y, 3.13060547623, x);
	elseif (z <= 6.2e+27)
		tmp = Float64(x + Float64(1.6453555072203998 * Float64(y * b)));
	else
		tmp = fma(y, 3.13060547623, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -2.15e+24], N[(y * 3.13060547623 + x), $MachinePrecision], If[LessEqual[z, 6.2e+27], N[(x + N[(1.6453555072203998 * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * 3.13060547623 + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.14999999999999994e24 or 6.19999999999999992e27 < z

   1. Initial program 10.4%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. accelerator-lowering-fma.f64 94.5

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

   5. Simplified 94.5%

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

   if -2.14999999999999994e24 < z < 6.19999999999999992e27

   1. Initial program 97.6%

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

   3. Taylor expanded in z around 0

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

      1. *-lowering-*.f64 N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 69.7

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

   5. Simplified 69.7%

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

Alternative 12: 83.6% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+24}:\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623, x\right)\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+28}:\\ \;\;\;\;\mathsf{fma}\left(1.6453555072203998, y \cdot b, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -2e+24)
   (fma y 3.13060547623 x)
   (if (<= z 3.1e+28)
     (fma 1.6453555072203998 (* y b) x)
     (fma y 3.13060547623 x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2e+24) {
		tmp = fma(y, 3.13060547623, x);
	} else if (z <= 3.1e+28) {
		tmp = fma(1.6453555072203998, (y * b), x);
	} else {
		tmp = fma(y, 3.13060547623, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -2e+24)
		tmp = fma(y, 3.13060547623, x);
	elseif (z <= 3.1e+28)
		tmp = fma(1.6453555072203998, Float64(y * b), x);
	else
		tmp = fma(y, 3.13060547623, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -2e+24], N[(y * 3.13060547623 + x), $MachinePrecision], If[LessEqual[z, 3.1e+28], N[(1.6453555072203998 * N[(y * b), $MachinePrecision] + x), $MachinePrecision], N[(y * 3.13060547623 + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -2e24 or 3.1000000000000001e28 < z

   1. Initial program 10.4%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. accelerator-lowering-fma.f64 94.5

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

   5. Simplified 94.5%

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

   if -2e24 < z < 3.1000000000000001e28

   1. Initial program 97.6%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. accelerator-lowering-fma.f64 90.0

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

   5. Simplified 90.0%

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

   6. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 69.7

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

   8. Simplified 69.7%

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

Alternative 13: 50.6% accurate, 4.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+75}:\\ \;\;\;\;y \cdot 3.13060547623\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+52}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot 3.13060547623\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -3.1e+75)
   (* y 3.13060547623)
   (if (<= y 1.1e+52) x (* y 3.13060547623))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -3.1e+75) {
		tmp = y * 3.13060547623;
	} else if (y <= 1.1e+52) {
		tmp = x;
	} else {
		tmp = y * 3.13060547623;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-3.1d+75)) then
        tmp = y * 3.13060547623d0
    else if (y <= 1.1d+52) then
        tmp = x
    else
        tmp = y * 3.13060547623d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -3.1e+75) {
		tmp = y * 3.13060547623;
	} else if (y <= 1.1e+52) {
		tmp = x;
	} else {
		tmp = y * 3.13060547623;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -3.1e+75:
		tmp = y * 3.13060547623
	elif y <= 1.1e+52:
		tmp = x
	else:
		tmp = y * 3.13060547623
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -3.1e+75)
		tmp = Float64(y * 3.13060547623);
	elseif (y <= 1.1e+52)
		tmp = x;
	else
		tmp = Float64(y * 3.13060547623);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -3.1e+75)
		tmp = y * 3.13060547623;
	elseif (y <= 1.1e+52)
		tmp = x;
	else
		tmp = y * 3.13060547623;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -3.1e+75], N[(y * 3.13060547623), $MachinePrecision], If[LessEqual[y, 1.1e+52], x, N[(y * 3.13060547623), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.1000000000000001e75 or 1.1e52 < y

   1. Initial program 51.6%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. accelerator-lowering-fma.f64 48.5

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

   5. Simplified 48.5%

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

   6. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 38.9

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

   8. Simplified 38.9%

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

   if -3.1000000000000001e75 < y < 1.1e52

   1. Initial program 59.9%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 62.8%

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

Alternative 14: 62.1% accurate, 11.3× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 56.7%

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

3. Taylor expanded in z around inf

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

   1. +-commutative N/A

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

   2. *-commutative N/A

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

   3. accelerator-lowering-fma.f64 61.9

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

5. Simplified 61.9%

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

Alternative 15: 45.0% accurate, 79.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 56.7%

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

3. Taylor expanded in x around inf

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

5. Simplified 43.4%

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

Developer Target 1: 98.3% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024199 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, D"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< z -649934499625263200000000000000000000000000000000000000) (+ x (* (+ (- 313060547623/100000000000 (/ 18263520849403207/500000000000000 z)) (/ t (* z z))) (/ y 1))) (if (< z 706696543691428700000000000000000000000000000000000000000000) (+ x (/ y (/ (+ (* (+ (* (+ (* (+ z 15234687407/1000000000) z) 314690115749/10000000000) z) 119400905721/10000000000) z) 607771387771/1000000000000) (+ (* (+ (* (+ (* (+ (* z 313060547623/100000000000) 55833770631/5000000000) z) t) z) a) z) b)))) (+ x (* (+ (- 313060547623/100000000000 (/ 18263520849403207/500000000000000 z)) (/ t (* z z))) (/ y 1))))))

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