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

Percentage Accurate: 58.1% → 97.1%

Time: 20.0s

Alternatives: 14

Speedup: 7.4×

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: 58.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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: 97.1% accurate, 0.0× speedup

Math

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

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
       (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721)
       z
       0.607771387771)
      (fma (fma (fma (fma z 3.13060547623 11.1667541262) z t) z a) z b))))
   (+
    x
    (/
     y
     (+
      (/ 3.7269864963038164 z)
      (-
       0.31942702700572795
       (/ (+ 3.241970391368047 (* t 0.10203362558171805)) (* z 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(fma(fma((z + 15.234687407), z, 31.4690115749), z, 11.9400905721), z, 0.607771387771) / fma(fma(fma(fma(z, 3.13060547623, 11.1667541262), z, t), z, a), z, b)));
	} else {
		tmp = x + (y / ((3.7269864963038164 / z) + (0.31942702700572795 - ((3.241970391368047 + (t * 0.10203362558171805)) / (z * 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(fma(fma(Float64(z + 15.234687407), z, 31.4690115749), z, 11.9400905721), z, 0.607771387771) / fma(fma(fma(fma(z, 3.13060547623, 11.1667541262), z, t), z, a), z, b))));
	else
		tmp = Float64(x + Float64(y / Float64(Float64(3.7269864963038164 / z) + Float64(0.31942702700572795 - Float64(Float64(3.241970391368047 + Float64(t * 0.10203362558171805)) / Float64(z * 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[(N[(N[(N[(z + 15.234687407), $MachinePrecision] * z + 31.4690115749), $MachinePrecision] * z + 11.9400905721), $MachinePrecision] * z + 0.607771387771), $MachinePrecision] / N[(N[(N[(N[(z * 3.13060547623 + 11.1667541262), $MachinePrecision] * z + t), $MachinePrecision] * z + a), $MachinePrecision] * z + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(N[(3.7269864963038164 / z), $MachinePrecision] + N[(0.31942702700572795 - N[(N[(3.241970391368047 + N[(t * 0.10203362558171805), $MachinePrecision]), $MachinePrecision] / N[(z * z), $MachinePrecision]), $MachinePrecision]), $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 313060547623/100000000000) 55833770631/5000000000) z) t) z) a) z) b)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z 15234687407/1000000000) z) 314690115749/10000000000) z) 119400905721/10000000000) z) 607771387771/1000000000000)) < +inf.0

   1. Initial program 93.4%

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

      1. associate-/l* 95.1%

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

      2. fma-def 95.1%

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

      3. fma-def 95.1%

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

      4. fma-def 95.1%

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

      5. fma-def 95.1%

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

      6. fma-def 95.1%

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

      7. fma-def 95.1%

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

      8. fma-def 95.1%

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

   3. Simplified 95.1%

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

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

   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. Step-by-step derivation

      1. associate-/l* 0.0%

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

      2. fma-def 0.0%

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

      3. fma-def 0.0%

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

      4. fma-def 0.0%

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

      5. fma-def 0.0%

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

      6. fma-def 0.0%

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

      7. fma-def 0.0%

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

      8. fma-def 0.0%

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

   3. Simplified 0.0%

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

   4. Taylor expanded in z around inf 98.4%

      \[\leadsto x + \frac{y}{\color{blue}{3.7269864963038164 \cdot \frac{1}{z} + \left(0.31942702700572795 + -1 \cdot \frac{3.241970391368047 + 0.10203362558171805 \cdot t}{{z}^{2}}\right)}} \]
   5. Step-by-step derivation

      1. associate-*r/ 98.4%

         \[\leadsto x + \frac{y}{\color{blue}{\frac{3.7269864963038164 \cdot 1}{z}} + \left(0.31942702700572795 + -1 \cdot \frac{3.241970391368047 + 0.10203362558171805 \cdot t}{{z}^{2}}\right)} \]

      2. metadata-eval 98.4%

         \[\leadsto x + \frac{y}{\frac{\color{blue}{3.7269864963038164}}{z} + \left(0.31942702700572795 + -1 \cdot \frac{3.241970391368047 + 0.10203362558171805 \cdot t}{{z}^{2}}\right)} \]

      3. mul-1-neg 98.4%

         \[\leadsto x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 + \color{blue}{\left(-\frac{3.241970391368047 + 0.10203362558171805 \cdot t}{{z}^{2}}\right)}\right)} \]

      4. *-commutative 98.4%

         \[\leadsto x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 + \left(-\frac{3.241970391368047 + \color{blue}{t \cdot 0.10203362558171805}}{{z}^{2}}\right)\right)} \]

      5. unpow2 98.4%

         \[\leadsto x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 + \left(-\frac{3.241970391368047 + t \cdot 0.10203362558171805}{\color{blue}{z \cdot z}}\right)\right)} \]

   6. Simplified 98.4%

      \[\leadsto x + \frac{y}{\color{blue}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 + \left(-\frac{3.241970391368047 + t \cdot 0.10203362558171805}{z \cdot z}\right)\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 96.2%

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

Alternative 2: 96.7% accurate, 0.0× speedup

Math

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

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)))
   (+
    x
    (/
     y
     (+
      (/ 3.7269864963038164 z)
      (-
       0.31942702700572795
       (/ (+ 3.241970391368047 (* t 0.10203362558171805)) (* z 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 / ((3.7269864963038164 / z) + (0.31942702700572795 - ((3.241970391368047 + (t * 0.10203362558171805)) / (z * 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(Float64(y / 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(Float64(3.7269864963038164 / z) + Float64(0.31942702700572795 - Float64(Float64(3.241970391368047 + Float64(t * 0.10203362558171805)) / Float64(z * 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[(N[(y / N[(z * N[(z * N[(z * N[(z + 15.234687407), $MachinePrecision] + 31.4690115749), $MachinePrecision] + 11.9400905721), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision] * N[(z * N[(z * N[(z * N[(z * 3.13060547623 + 11.1667541262), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(N[(3.7269864963038164 / z), $MachinePrecision] + N[(0.31942702700572795 - N[(N[(3.241970391368047 + N[(t * 0.10203362558171805), $MachinePrecision]), $MachinePrecision] / N[(z * z), $MachinePrecision]), $MachinePrecision]), $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 313060547623/100000000000) 55833770631/5000000000) z) t) z) a) z) b)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z 15234687407/1000000000) z) 314690115749/10000000000) z) 119400905721/10000000000) z) 607771387771/1000000000000)) < +inf.0

   1. Initial program 93.4%

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

      1. associate-*l/ 94.5%

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

      2. *-commutative 94.5%

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

      3. fma-def 94.5%

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

      4. *-commutative 94.5%

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

      5. fma-def 94.5%

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

      6. *-commutative 94.5%

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

      7. fma-def 94.5%

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

      8. *-commutative 94.5%

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

      9. fma-def 94.5%

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

   3. Simplified 94.5%

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

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

   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. Step-by-step derivation

      1. associate-/l* 0.0%

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

      2. fma-def 0.0%

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

      3. fma-def 0.0%

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

      4. fma-def 0.0%

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

      5. fma-def 0.0%

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

      6. fma-def 0.0%

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

      7. fma-def 0.0%

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

      8. fma-def 0.0%

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

   3. Simplified 0.0%

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

   4. Taylor expanded in z around inf 98.4%

      \[\leadsto x + \frac{y}{\color{blue}{3.7269864963038164 \cdot \frac{1}{z} + \left(0.31942702700572795 + -1 \cdot \frac{3.241970391368047 + 0.10203362558171805 \cdot t}{{z}^{2}}\right)}} \]
   5. Step-by-step derivation

      1. associate-*r/ 98.4%

         \[\leadsto x + \frac{y}{\color{blue}{\frac{3.7269864963038164 \cdot 1}{z}} + \left(0.31942702700572795 + -1 \cdot \frac{3.241970391368047 + 0.10203362558171805 \cdot t}{{z}^{2}}\right)} \]

      2. metadata-eval 98.4%

         \[\leadsto x + \frac{y}{\frac{\color{blue}{3.7269864963038164}}{z} + \left(0.31942702700572795 + -1 \cdot \frac{3.241970391368047 + 0.10203362558171805 \cdot t}{{z}^{2}}\right)} \]

      3. mul-1-neg 98.4%

         \[\leadsto x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 + \color{blue}{\left(-\frac{3.241970391368047 + 0.10203362558171805 \cdot t}{{z}^{2}}\right)}\right)} \]

      4. *-commutative 98.4%

         \[\leadsto x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 + \left(-\frac{3.241970391368047 + \color{blue}{t \cdot 0.10203362558171805}}{{z}^{2}}\right)\right)} \]

      5. unpow2 98.4%

         \[\leadsto x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 + \left(-\frac{3.241970391368047 + t \cdot 0.10203362558171805}{\color{blue}{z \cdot z}}\right)\right)} \]

   6. Simplified 98.4%

      \[\leadsto x + \frac{y}{\color{blue}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 + \left(-\frac{3.241970391368047 + t \cdot 0.10203362558171805}{z \cdot z}\right)\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 95.8%

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

Alternative 3: 94.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\\ \mathbf{if}\;t_1 \leq \infty:\\ \;\;\;\;t_1 + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 - \frac{3.241970391368047 + t \cdot 0.10203362558171805}{z \cdot z}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (/
          (*
           y
           (+
            (* z (+ (* z (+ (* z (+ (* z 3.13060547623) 11.1667541262)) t)) a))
            b))
          (+
           (*
            z
            (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721))
           0.607771387771))))
   (if (<= t_1 INFINITY)
     (+ t_1 x)
     (+
      x
      (/
       y
       (+
        (/ 3.7269864963038164 z)
        (-
         0.31942702700572795
         (/ (+ 3.241970391368047 (* t 0.10203362558171805)) (* z z)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (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 tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1 + x;
	} else {
		tmp = x + (y / ((3.7269864963038164 / z) + (0.31942702700572795 - ((3.241970391368047 + (t * 0.10203362558171805)) / (z * z)))));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (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 tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1 + x;
	} else {
		tmp = x + (y / ((3.7269864963038164 / z) + (0.31942702700572795 - ((3.241970391368047 + (t * 0.10203362558171805)) / (z * z)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1 + x
	else:
		tmp = x + (y / ((3.7269864963038164 / z) + (0.31942702700572795 - ((3.241970391368047 + (t * 0.10203362558171805)) / (z * z)))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = 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))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = Float64(t_1 + x);
	else
		tmp = Float64(x + Float64(y / Float64(Float64(3.7269864963038164 / z) + Float64(0.31942702700572795 - Float64(Float64(3.241970391368047 + Float64(t * 0.10203362558171805)) / Float64(z * z))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771);
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1 + x;
	else
		tmp = x + (y / ((3.7269864963038164 / z) + (0.31942702700572795 - ((3.241970391368047 + (t * 0.10203362558171805)) / (z * z)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = 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]}, If[LessEqual[t$95$1, Infinity], N[(t$95$1 + x), $MachinePrecision], N[(x + N[(y / N[(N[(3.7269864963038164 / z), $MachinePrecision] + N[(0.31942702700572795 - N[(N[(3.241970391368047 + N[(t * 0.10203362558171805), $MachinePrecision]), $MachinePrecision] / N[(z * z), $MachinePrecision]), $MachinePrecision]), $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 313060547623/100000000000) 55833770631/5000000000) z) t) z) a) z) b)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z 15234687407/1000000000) z) 314690115749/10000000000) z) 119400905721/10000000000) z) 607771387771/1000000000000)) < +inf.0

   1. Initial program 93.4%

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

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

   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. Step-by-step derivation

      1. associate-/l* 0.0%

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

      2. fma-def 0.0%

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

      3. fma-def 0.0%

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

      4. fma-def 0.0%

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

      5. fma-def 0.0%

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

      6. fma-def 0.0%

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

      7. fma-def 0.0%

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

      8. fma-def 0.0%

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

   3. Simplified 0.0%

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

   4. Taylor expanded in z around inf 98.4%

      \[\leadsto x + \frac{y}{\color{blue}{3.7269864963038164 \cdot \frac{1}{z} + \left(0.31942702700572795 + -1 \cdot \frac{3.241970391368047 + 0.10203362558171805 \cdot t}{{z}^{2}}\right)}} \]
   5. Step-by-step derivation

      1. associate-*r/ 98.4%

         \[\leadsto x + \frac{y}{\color{blue}{\frac{3.7269864963038164 \cdot 1}{z}} + \left(0.31942702700572795 + -1 \cdot \frac{3.241970391368047 + 0.10203362558171805 \cdot t}{{z}^{2}}\right)} \]

      2. metadata-eval 98.4%

         \[\leadsto x + \frac{y}{\frac{\color{blue}{3.7269864963038164}}{z} + \left(0.31942702700572795 + -1 \cdot \frac{3.241970391368047 + 0.10203362558171805 \cdot t}{{z}^{2}}\right)} \]

      3. mul-1-neg 98.4%

         \[\leadsto x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 + \color{blue}{\left(-\frac{3.241970391368047 + 0.10203362558171805 \cdot t}{{z}^{2}}\right)}\right)} \]

      4. *-commutative 98.4%

         \[\leadsto x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 + \left(-\frac{3.241970391368047 + \color{blue}{t \cdot 0.10203362558171805}}{{z}^{2}}\right)\right)} \]

      5. unpow2 98.4%

         \[\leadsto x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 + \left(-\frac{3.241970391368047 + t \cdot 0.10203362558171805}{\color{blue}{z \cdot z}}\right)\right)} \]

   6. Simplified 98.4%

      \[\leadsto x + \frac{y}{\color{blue}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 + \left(-\frac{3.241970391368047 + t \cdot 0.10203362558171805}{z \cdot z}\right)\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 95.1%

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

Alternative 4: 95.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{+41}:\\ \;\;\;\;x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 - \frac{3.241970391368047 + t \cdot 0.10203362558171805}{z \cdot z}\right)}\\ \mathbf{elif}\;z \leq 1.16 \cdot 10^{+30}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot 11.1667541262\right)\right)\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{0.31942702700572795}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -5.6e+41)
   (+
    x
    (/
     y
     (+
      (/ 3.7269864963038164 z)
      (-
       0.31942702700572795
       (/ (+ 3.241970391368047 (* t 0.10203362558171805)) (* z z))))))
   (if (<= z 1.16e+30)
     (+
      x
      (/
       (* y (+ b (* z (+ a (* z (+ t (* z 11.1667541262)))))))
       (+
        (*
         z
         (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721))
        0.607771387771)))
     (+ x (/ y 0.31942702700572795)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -5.6e+41) {
		tmp = x + (y / ((3.7269864963038164 / z) + (0.31942702700572795 - ((3.241970391368047 + (t * 0.10203362558171805)) / (z * z)))));
	} else if (z <= 1.16e+30) {
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771));
	} else {
		tmp = x + (y / 0.31942702700572795);
	}
	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 (z <= (-5.6d+41)) then
        tmp = x + (y / ((3.7269864963038164d0 / z) + (0.31942702700572795d0 - ((3.241970391368047d0 + (t * 0.10203362558171805d0)) / (z * z)))))
    else if (z <= 1.16d+30) then
        tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262d0))))))) / ((z * ((z * ((z * (z + 15.234687407d0)) + 31.4690115749d0)) + 11.9400905721d0)) + 0.607771387771d0))
    else
        tmp = x + (y / 0.31942702700572795d0)
    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 (z <= -5.6e+41) {
		tmp = x + (y / ((3.7269864963038164 / z) + (0.31942702700572795 - ((3.241970391368047 + (t * 0.10203362558171805)) / (z * z)))));
	} else if (z <= 1.16e+30) {
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771));
	} else {
		tmp = x + (y / 0.31942702700572795);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -5.6e+41:
		tmp = x + (y / ((3.7269864963038164 / z) + (0.31942702700572795 - ((3.241970391368047 + (t * 0.10203362558171805)) / (z * z)))))
	elif z <= 1.16e+30:
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771))
	else:
		tmp = x + (y / 0.31942702700572795)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -5.6e+41)
		tmp = Float64(x + Float64(y / Float64(Float64(3.7269864963038164 / z) + Float64(0.31942702700572795 - Float64(Float64(3.241970391368047 + Float64(t * 0.10203362558171805)) / Float64(z * z))))));
	elseif (z <= 1.16e+30)
		tmp = Float64(x + Float64(Float64(y * Float64(b + Float64(z * Float64(a + Float64(z * Float64(t + Float64(z * 11.1667541262))))))) / Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)));
	else
		tmp = Float64(x + Float64(y / 0.31942702700572795));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -5.6e+41)
		tmp = x + (y / ((3.7269864963038164 / z) + (0.31942702700572795 - ((3.241970391368047 + (t * 0.10203362558171805)) / (z * z)))));
	elseif (z <= 1.16e+30)
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771));
	else
		tmp = x + (y / 0.31942702700572795);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -5.6e+41], N[(x + N[(y / N[(N[(3.7269864963038164 / z), $MachinePrecision] + N[(0.31942702700572795 - N[(N[(3.241970391368047 + N[(t * 0.10203362558171805), $MachinePrecision]), $MachinePrecision] / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.16e+30], N[(x + N[(N[(y * N[(b + N[(z * N[(a + N[(z * N[(t + N[(z * 11.1667541262), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $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], N[(x + N[(y / 0.31942702700572795), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.5999999999999999e41

   1. Initial program 0.5%

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

      1. associate-/l* 0.5%

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

      2. fma-def 0.5%

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

      3. fma-def 0.5%

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

      4. fma-def 0.5%

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

      5. fma-def 0.5%

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

      6. fma-def 0.5%

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

      7. fma-def 0.5%

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

      8. fma-def 0.5%

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

   3. Simplified 0.5%

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

   4. Taylor expanded in z around inf 95.6%

      \[\leadsto x + \frac{y}{\color{blue}{3.7269864963038164 \cdot \frac{1}{z} + \left(0.31942702700572795 + -1 \cdot \frac{3.241970391368047 + 0.10203362558171805 \cdot t}{{z}^{2}}\right)}} \]
   5. Step-by-step derivation

      1. associate-*r/ 95.6%

         \[\leadsto x + \frac{y}{\color{blue}{\frac{3.7269864963038164 \cdot 1}{z}} + \left(0.31942702700572795 + -1 \cdot \frac{3.241970391368047 + 0.10203362558171805 \cdot t}{{z}^{2}}\right)} \]

      2. metadata-eval 95.6%

         \[\leadsto x + \frac{y}{\frac{\color{blue}{3.7269864963038164}}{z} + \left(0.31942702700572795 + -1 \cdot \frac{3.241970391368047 + 0.10203362558171805 \cdot t}{{z}^{2}}\right)} \]

      3. mul-1-neg 95.6%

         \[\leadsto x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 + \color{blue}{\left(-\frac{3.241970391368047 + 0.10203362558171805 \cdot t}{{z}^{2}}\right)}\right)} \]

      4. *-commutative 95.6%

         \[\leadsto x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 + \left(-\frac{3.241970391368047 + \color{blue}{t \cdot 0.10203362558171805}}{{z}^{2}}\right)\right)} \]

      5. unpow2 95.6%

         \[\leadsto x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 + \left(-\frac{3.241970391368047 + t \cdot 0.10203362558171805}{\color{blue}{z \cdot z}}\right)\right)} \]

   6. Simplified 95.6%

      \[\leadsto x + \frac{y}{\color{blue}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 + \left(-\frac{3.241970391368047 + t \cdot 0.10203362558171805}{z \cdot z}\right)\right)}} \]

   if -5.5999999999999999e41 < z < 1.16e30

   1. Initial program 99.0%

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

   2. Taylor expanded in z around 0 99.0%

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

      1. *-commutative 99.0%

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

   4. Simplified 99.0%

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

   if 1.16e30 < 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. Step-by-step derivation

      1. associate-/l* 13.7%

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

      2. fma-def 13.7%

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

      3. fma-def 13.7%

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

      4. fma-def 13.7%

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

      5. fma-def 13.7%

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

      6. fma-def 13.7%

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

      7. fma-def 13.7%

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

      8. fma-def 13.7%

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

   3. Simplified 13.7%

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

   4. Taylor expanded in z around inf 89.5%

      \[\leadsto x + \frac{y}{\color{blue}{0.31942702700572795}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 96.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{+41}:\\ \;\;\;\;x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 - \frac{3.241970391368047 + t \cdot 0.10203362558171805}{z \cdot z}\right)}\\ \mathbf{elif}\;z \leq 1.16 \cdot 10^{+30}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot 11.1667541262\right)\right)\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{0.31942702700572795}\\ \end{array} \]

Alternative 5: 94.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.7 \cdot 10^{+38}:\\ \;\;\;\;x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 - \frac{3.241970391368047 + t \cdot 0.10203362558171805}{z \cdot z}\right)}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+31}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot 11.1667541262\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot z\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{0.31942702700572795}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -6.7e+38)
   (+
    x
    (/
     y
     (+
      (/ 3.7269864963038164 z)
      (-
       0.31942702700572795
       (/ (+ 3.241970391368047 (* t 0.10203362558171805)) (* z z))))))
   (if (<= z 4e+31)
     (+
      x
      (/
       (* y (+ b (* z (+ a (* z (+ t (* z 11.1667541262)))))))
       (+
        0.607771387771
        (* z (+ 11.9400905721 (* z (+ 31.4690115749 (* z z))))))))
     (+ x (/ y 0.31942702700572795)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -6.7e+38) {
		tmp = x + (y / ((3.7269864963038164 / z) + (0.31942702700572795 - ((3.241970391368047 + (t * 0.10203362558171805)) / (z * z)))));
	} else if (z <= 4e+31) {
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))) / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * z)))))));
	} else {
		tmp = x + (y / 0.31942702700572795);
	}
	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 (z <= (-6.7d+38)) then
        tmp = x + (y / ((3.7269864963038164d0 / z) + (0.31942702700572795d0 - ((3.241970391368047d0 + (t * 0.10203362558171805d0)) / (z * z)))))
    else if (z <= 4d+31) then
        tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262d0))))))) / (0.607771387771d0 + (z * (11.9400905721d0 + (z * (31.4690115749d0 + (z * z)))))))
    else
        tmp = x + (y / 0.31942702700572795d0)
    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 (z <= -6.7e+38) {
		tmp = x + (y / ((3.7269864963038164 / z) + (0.31942702700572795 - ((3.241970391368047 + (t * 0.10203362558171805)) / (z * z)))));
	} else if (z <= 4e+31) {
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))) / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * z)))))));
	} else {
		tmp = x + (y / 0.31942702700572795);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -6.7e+38:
		tmp = x + (y / ((3.7269864963038164 / z) + (0.31942702700572795 - ((3.241970391368047 + (t * 0.10203362558171805)) / (z * z)))))
	elif z <= 4e+31:
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))) / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * z)))))))
	else:
		tmp = x + (y / 0.31942702700572795)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -6.7e+38)
		tmp = Float64(x + Float64(y / Float64(Float64(3.7269864963038164 / z) + Float64(0.31942702700572795 - Float64(Float64(3.241970391368047 + Float64(t * 0.10203362558171805)) / Float64(z * z))))));
	elseif (z <= 4e+31)
		tmp = Float64(x + Float64(Float64(y * Float64(b + Float64(z * Float64(a + Float64(z * Float64(t + Float64(z * 11.1667541262))))))) / Float64(0.607771387771 + Float64(z * Float64(11.9400905721 + Float64(z * Float64(31.4690115749 + Float64(z * z))))))));
	else
		tmp = Float64(x + Float64(y / 0.31942702700572795));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -6.7e+38)
		tmp = x + (y / ((3.7269864963038164 / z) + (0.31942702700572795 - ((3.241970391368047 + (t * 0.10203362558171805)) / (z * z)))));
	elseif (z <= 4e+31)
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))) / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * z)))))));
	else
		tmp = x + (y / 0.31942702700572795);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -6.7e+38], N[(x + N[(y / N[(N[(3.7269864963038164 / z), $MachinePrecision] + N[(0.31942702700572795 - N[(N[(3.241970391368047 + N[(t * 0.10203362558171805), $MachinePrecision]), $MachinePrecision] / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4e+31], N[(x + N[(N[(y * N[(b + N[(z * N[(a + N[(z * N[(t + N[(z * 11.1667541262), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(0.607771387771 + N[(z * N[(11.9400905721 + N[(z * N[(31.4690115749 + N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / 0.31942702700572795), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.70000000000000025e38

   1. Initial program 0.5%

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

      1. associate-/l* 0.5%

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

      2. fma-def 0.5%

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

      3. fma-def 0.5%

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

      4. fma-def 0.5%

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

      5. fma-def 0.5%

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

      6. fma-def 0.5%

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

      7. fma-def 0.5%

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

      8. fma-def 0.5%

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

   3. Simplified 0.5%

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

   4. Taylor expanded in z around inf 95.6%

      \[\leadsto x + \frac{y}{\color{blue}{3.7269864963038164 \cdot \frac{1}{z} + \left(0.31942702700572795 + -1 \cdot \frac{3.241970391368047 + 0.10203362558171805 \cdot t}{{z}^{2}}\right)}} \]
   5. Step-by-step derivation

      1. associate-*r/ 95.6%

         \[\leadsto x + \frac{y}{\color{blue}{\frac{3.7269864963038164 \cdot 1}{z}} + \left(0.31942702700572795 + -1 \cdot \frac{3.241970391368047 + 0.10203362558171805 \cdot t}{{z}^{2}}\right)} \]

      2. metadata-eval 95.6%

         \[\leadsto x + \frac{y}{\frac{\color{blue}{3.7269864963038164}}{z} + \left(0.31942702700572795 + -1 \cdot \frac{3.241970391368047 + 0.10203362558171805 \cdot t}{{z}^{2}}\right)} \]

      3. mul-1-neg 95.6%

         \[\leadsto x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 + \color{blue}{\left(-\frac{3.241970391368047 + 0.10203362558171805 \cdot t}{{z}^{2}}\right)}\right)} \]

      4. *-commutative 95.6%

         \[\leadsto x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 + \left(-\frac{3.241970391368047 + \color{blue}{t \cdot 0.10203362558171805}}{{z}^{2}}\right)\right)} \]

      5. unpow2 95.6%

         \[\leadsto x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 + \left(-\frac{3.241970391368047 + t \cdot 0.10203362558171805}{\color{blue}{z \cdot z}}\right)\right)} \]

   6. Simplified 95.6%

      \[\leadsto x + \frac{y}{\color{blue}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 + \left(-\frac{3.241970391368047 + t \cdot 0.10203362558171805}{z \cdot z}\right)\right)}} \]

   if -6.70000000000000025e38 < z < 3.9999999999999999e31

   1. Initial program 99.0%

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

   2. Taylor expanded in z around 0 99.0%

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

      1. *-commutative 99.0%

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

   4. Simplified 99.0%

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

   5. Taylor expanded in z around inf 98.6%

      \[\leadsto x + \frac{y \cdot \left(\left(\left(z \cdot 11.1667541262 + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\color{blue}{{z}^{2}} + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   6. Step-by-step derivation

      1. unpow2 88.7%

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

   7. Simplified 98.6%

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

   if 3.9999999999999999e31 < 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. Step-by-step derivation

      1. associate-/l* 13.7%

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

      2. fma-def 13.7%

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

      3. fma-def 13.7%

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

      4. fma-def 13.7%

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

      5. fma-def 13.7%

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

      6. fma-def 13.7%

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

      7. fma-def 13.7%

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

      8. fma-def 13.7%

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

   3. Simplified 13.7%

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

   4. Taylor expanded in z around inf 89.5%

      \[\leadsto x + \frac{y}{\color{blue}{0.31942702700572795}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 95.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.7 \cdot 10^{+38}:\\ \;\;\;\;x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 - \frac{3.241970391368047 + t \cdot 0.10203362558171805}{z \cdot z}\right)}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+31}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot 11.1667541262\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot z\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{0.31942702700572795}\\ \end{array} \]

Alternative 6: 91.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+48}:\\ \;\;\;\;x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 - \frac{3.241970391368047 + t \cdot 0.10203362558171805}{z \cdot z}\right)}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+31}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot a\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{0.31942702700572795}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.05e+48)
   (+
    x
    (/
     y
     (+
      (/ 3.7269864963038164 z)
      (-
       0.31942702700572795
       (/ (+ 3.241970391368047 (* t 0.10203362558171805)) (* z z))))))
   (if (<= z 7.2e+31)
     (+
      x
      (/
       (* y (+ b (* z a)))
       (+
        (*
         z
         (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721))
        0.607771387771)))
     (+ x (/ y 0.31942702700572795)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.05e+48) {
		tmp = x + (y / ((3.7269864963038164 / z) + (0.31942702700572795 - ((3.241970391368047 + (t * 0.10203362558171805)) / (z * z)))));
	} else if (z <= 7.2e+31) {
		tmp = x + ((y * (b + (z * a))) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771));
	} else {
		tmp = x + (y / 0.31942702700572795);
	}
	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 (z <= (-1.05d+48)) then
        tmp = x + (y / ((3.7269864963038164d0 / z) + (0.31942702700572795d0 - ((3.241970391368047d0 + (t * 0.10203362558171805d0)) / (z * z)))))
    else if (z <= 7.2d+31) then
        tmp = x + ((y * (b + (z * a))) / ((z * ((z * ((z * (z + 15.234687407d0)) + 31.4690115749d0)) + 11.9400905721d0)) + 0.607771387771d0))
    else
        tmp = x + (y / 0.31942702700572795d0)
    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 (z <= -1.05e+48) {
		tmp = x + (y / ((3.7269864963038164 / z) + (0.31942702700572795 - ((3.241970391368047 + (t * 0.10203362558171805)) / (z * z)))));
	} else if (z <= 7.2e+31) {
		tmp = x + ((y * (b + (z * a))) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771));
	} else {
		tmp = x + (y / 0.31942702700572795);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.05e+48:
		tmp = x + (y / ((3.7269864963038164 / z) + (0.31942702700572795 - ((3.241970391368047 + (t * 0.10203362558171805)) / (z * z)))))
	elif z <= 7.2e+31:
		tmp = x + ((y * (b + (z * a))) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771))
	else:
		tmp = x + (y / 0.31942702700572795)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.05e+48)
		tmp = Float64(x + Float64(y / Float64(Float64(3.7269864963038164 / z) + Float64(0.31942702700572795 - Float64(Float64(3.241970391368047 + Float64(t * 0.10203362558171805)) / Float64(z * z))))));
	elseif (z <= 7.2e+31)
		tmp = Float64(x + Float64(Float64(y * Float64(b + Float64(z * a))) / Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)));
	else
		tmp = Float64(x + Float64(y / 0.31942702700572795));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1.05e+48)
		tmp = x + (y / ((3.7269864963038164 / z) + (0.31942702700572795 - ((3.241970391368047 + (t * 0.10203362558171805)) / (z * z)))));
	elseif (z <= 7.2e+31)
		tmp = x + ((y * (b + (z * a))) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771));
	else
		tmp = x + (y / 0.31942702700572795);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.05e+48], N[(x + N[(y / N[(N[(3.7269864963038164 / z), $MachinePrecision] + N[(0.31942702700572795 - N[(N[(3.241970391368047 + N[(t * 0.10203362558171805), $MachinePrecision]), $MachinePrecision] / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.2e+31], N[(x + N[(N[(y * N[(b + N[(z * a), $MachinePrecision]), $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], N[(x + N[(y / 0.31942702700572795), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.0499999999999999e48

   1. Initial program 0.4%

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

      1. associate-/l* 0.4%

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

      2. fma-def 0.4%

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

      3. fma-def 0.4%

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

      4. fma-def 0.4%

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

      5. fma-def 0.4%

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

      6. fma-def 0.4%

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

      7. fma-def 0.4%

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

      8. fma-def 0.4%

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

   3. Simplified 0.4%

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

   4. Taylor expanded in z around inf 95.5%

      \[\leadsto x + \frac{y}{\color{blue}{3.7269864963038164 \cdot \frac{1}{z} + \left(0.31942702700572795 + -1 \cdot \frac{3.241970391368047 + 0.10203362558171805 \cdot t}{{z}^{2}}\right)}} \]
   5. Step-by-step derivation

      1. associate-*r/ 95.5%

         \[\leadsto x + \frac{y}{\color{blue}{\frac{3.7269864963038164 \cdot 1}{z}} + \left(0.31942702700572795 + -1 \cdot \frac{3.241970391368047 + 0.10203362558171805 \cdot t}{{z}^{2}}\right)} \]

      2. metadata-eval 95.5%

         \[\leadsto x + \frac{y}{\frac{\color{blue}{3.7269864963038164}}{z} + \left(0.31942702700572795 + -1 \cdot \frac{3.241970391368047 + 0.10203362558171805 \cdot t}{{z}^{2}}\right)} \]

      3. mul-1-neg 95.5%

         \[\leadsto x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 + \color{blue}{\left(-\frac{3.241970391368047 + 0.10203362558171805 \cdot t}{{z}^{2}}\right)}\right)} \]

      4. *-commutative 95.5%

         \[\leadsto x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 + \left(-\frac{3.241970391368047 + \color{blue}{t \cdot 0.10203362558171805}}{{z}^{2}}\right)\right)} \]

      5. unpow2 95.5%

         \[\leadsto x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 + \left(-\frac{3.241970391368047 + t \cdot 0.10203362558171805}{\color{blue}{z \cdot z}}\right)\right)} \]

   6. Simplified 95.5%

      \[\leadsto x + \frac{y}{\color{blue}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 + \left(-\frac{3.241970391368047 + t \cdot 0.10203362558171805}{z \cdot z}\right)\right)}} \]

   if -1.0499999999999999e48 < z < 7.19999999999999992e31

   1. Initial program 98.4%

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

   2. Taylor expanded in z around 0 89.2%

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

      1. +-commutative 89.2%

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

      2. associate-*r* 83.9%

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

      3. *-commutative 83.9%

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

      4. associate-*r* 89.6%

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

      5. distribute-lft-out 90.9%

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

      6. *-commutative 90.9%

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

   4. Simplified 90.9%

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

   if 7.19999999999999992e31 < 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. Step-by-step derivation

      1. associate-/l* 13.7%

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

      2. fma-def 13.7%

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

      3. fma-def 13.7%

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

      4. fma-def 13.7%

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

      5. fma-def 13.7%

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

      6. fma-def 13.7%

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

      7. fma-def 13.7%

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

      8. fma-def 13.7%

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

   3. Simplified 13.7%

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

   4. Taylor expanded in z around inf 89.5%

      \[\leadsto x + \frac{y}{\color{blue}{0.31942702700572795}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+48}:\\ \;\;\;\;x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 - \frac{3.241970391368047 + t \cdot 0.10203362558171805}{z \cdot z}\right)}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+31}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot a\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{0.31942702700572795}\\ \end{array} \]

Alternative 7: 90.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+70}:\\ \;\;\;\;x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 - \frac{3.241970391368047 + t \cdot 0.10203362558171805}{z \cdot z}\right)}\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+29}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot a\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot z\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{0.31942702700572795}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -6.6e+70)
   (+
    x
    (/
     y
     (+
      (/ 3.7269864963038164 z)
      (-
       0.31942702700572795
       (/ (+ 3.241970391368047 (* t 0.10203362558171805)) (* z z))))))
   (if (<= z 5.4e+29)
     (+
      x
      (/
       (* y (+ b (* z a)))
       (+
        0.607771387771
        (* z (+ 11.9400905721 (* z (+ 31.4690115749 (* z z))))))))
     (+ x (/ y 0.31942702700572795)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -6.6e+70) {
		tmp = x + (y / ((3.7269864963038164 / z) + (0.31942702700572795 - ((3.241970391368047 + (t * 0.10203362558171805)) / (z * z)))));
	} else if (z <= 5.4e+29) {
		tmp = x + ((y * (b + (z * a))) / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * z)))))));
	} else {
		tmp = x + (y / 0.31942702700572795);
	}
	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 (z <= (-6.6d+70)) then
        tmp = x + (y / ((3.7269864963038164d0 / z) + (0.31942702700572795d0 - ((3.241970391368047d0 + (t * 0.10203362558171805d0)) / (z * z)))))
    else if (z <= 5.4d+29) then
        tmp = x + ((y * (b + (z * a))) / (0.607771387771d0 + (z * (11.9400905721d0 + (z * (31.4690115749d0 + (z * z)))))))
    else
        tmp = x + (y / 0.31942702700572795d0)
    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 (z <= -6.6e+70) {
		tmp = x + (y / ((3.7269864963038164 / z) + (0.31942702700572795 - ((3.241970391368047 + (t * 0.10203362558171805)) / (z * z)))));
	} else if (z <= 5.4e+29) {
		tmp = x + ((y * (b + (z * a))) / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * z)))))));
	} else {
		tmp = x + (y / 0.31942702700572795);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -6.6e+70:
		tmp = x + (y / ((3.7269864963038164 / z) + (0.31942702700572795 - ((3.241970391368047 + (t * 0.10203362558171805)) / (z * z)))))
	elif z <= 5.4e+29:
		tmp = x + ((y * (b + (z * a))) / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * z)))))))
	else:
		tmp = x + (y / 0.31942702700572795)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -6.6e+70)
		tmp = Float64(x + Float64(y / Float64(Float64(3.7269864963038164 / z) + Float64(0.31942702700572795 - Float64(Float64(3.241970391368047 + Float64(t * 0.10203362558171805)) / Float64(z * z))))));
	elseif (z <= 5.4e+29)
		tmp = Float64(x + Float64(Float64(y * Float64(b + Float64(z * a))) / Float64(0.607771387771 + Float64(z * Float64(11.9400905721 + Float64(z * Float64(31.4690115749 + Float64(z * z))))))));
	else
		tmp = Float64(x + Float64(y / 0.31942702700572795));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -6.6e+70)
		tmp = x + (y / ((3.7269864963038164 / z) + (0.31942702700572795 - ((3.241970391368047 + (t * 0.10203362558171805)) / (z * z)))));
	elseif (z <= 5.4e+29)
		tmp = x + ((y * (b + (z * a))) / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * z)))))));
	else
		tmp = x + (y / 0.31942702700572795);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -6.6e+70], N[(x + N[(y / N[(N[(3.7269864963038164 / z), $MachinePrecision] + N[(0.31942702700572795 - N[(N[(3.241970391368047 + N[(t * 0.10203362558171805), $MachinePrecision]), $MachinePrecision] / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.4e+29], N[(x + N[(N[(y * N[(b + N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(0.607771387771 + N[(z * N[(11.9400905721 + N[(z * N[(31.4690115749 + N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / 0.31942702700572795), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.60000000000000033e70

   1. Initial program 0.1%

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

      1. associate-/l* 0.1%

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

      2. fma-def 0.1%

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

      3. fma-def 0.1%

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

      4. fma-def 0.1%

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

      5. fma-def 0.1%

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

      6. fma-def 0.1%

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

      7. fma-def 0.1%

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

      8. fma-def 0.1%

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

   3. Simplified 0.1%

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

   4. Taylor expanded in z around inf 97.6%

      \[\leadsto x + \frac{y}{\color{blue}{3.7269864963038164 \cdot \frac{1}{z} + \left(0.31942702700572795 + -1 \cdot \frac{3.241970391368047 + 0.10203362558171805 \cdot t}{{z}^{2}}\right)}} \]
   5. Step-by-step derivation

      1. associate-*r/ 97.6%

         \[\leadsto x + \frac{y}{\color{blue}{\frac{3.7269864963038164 \cdot 1}{z}} + \left(0.31942702700572795 + -1 \cdot \frac{3.241970391368047 + 0.10203362558171805 \cdot t}{{z}^{2}}\right)} \]

      2. metadata-eval 97.6%

         \[\leadsto x + \frac{y}{\frac{\color{blue}{3.7269864963038164}}{z} + \left(0.31942702700572795 + -1 \cdot \frac{3.241970391368047 + 0.10203362558171805 \cdot t}{{z}^{2}}\right)} \]

      3. mul-1-neg 97.6%

         \[\leadsto x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 + \color{blue}{\left(-\frac{3.241970391368047 + 0.10203362558171805 \cdot t}{{z}^{2}}\right)}\right)} \]

      4. *-commutative 97.6%

         \[\leadsto x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 + \left(-\frac{3.241970391368047 + \color{blue}{t \cdot 0.10203362558171805}}{{z}^{2}}\right)\right)} \]

      5. unpow2 97.6%

         \[\leadsto x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 + \left(-\frac{3.241970391368047 + t \cdot 0.10203362558171805}{\color{blue}{z \cdot z}}\right)\right)} \]

   6. Simplified 97.6%

      \[\leadsto x + \frac{y}{\color{blue}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 + \left(-\frac{3.241970391368047 + t \cdot 0.10203362558171805}{z \cdot z}\right)\right)}} \]

   if -6.60000000000000033e70 < z < 5.4e29

   1. Initial program 97.2%

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

   2. Taylor expanded in z around 0 88.7%

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

   3. Taylor expanded in z around inf 88.3%

      \[\leadsto x + \frac{y \cdot b + a \cdot \left(y \cdot z\right)}{\left(\left(\color{blue}{{z}^{2}} + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   4. Step-by-step derivation

      1. unpow2 88.3%

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

   5. Simplified 88.3%

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

   6. Taylor expanded in y around 0 89.9%

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

   if 5.4e29 < 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. Step-by-step derivation

      1. associate-/l* 13.7%

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

      2. fma-def 13.7%

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

      3. fma-def 13.7%

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

      4. fma-def 13.7%

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

      5. fma-def 13.7%

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

      6. fma-def 13.7%

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

      7. fma-def 13.7%

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

      8. fma-def 13.7%

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

   3. Simplified 13.7%

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

   4. Taylor expanded in z around inf 89.5%

      \[\leadsto x + \frac{y}{\color{blue}{0.31942702700572795}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+70}:\\ \;\;\;\;x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 - \frac{3.241970391368047 + t \cdot 0.10203362558171805}{z \cdot z}\right)}\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+29}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot a\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot z\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{0.31942702700572795}\\ \end{array} \]

Alternative 8: 89.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+45} \lor \neg \left(z \leq 51000\right):\\ \;\;\;\;x + \frac{y}{0.31942702700572795}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(z \cdot \left(a \cdot 1.6453555072203998 - b \cdot 32.324150453290734\right) + b \cdot 1.6453555072203998\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -8.5e+45) (not (<= z 51000.0)))
   (+ x (/ y 0.31942702700572795))
   (+
    x
    (*
     y
     (+
      (* z (- (* a 1.6453555072203998) (* b 32.324150453290734)))
      (* b 1.6453555072203998))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -8.5e+45) || !(z <= 51000.0)) {
		tmp = x + (y / 0.31942702700572795);
	} else {
		tmp = x + (y * ((z * ((a * 1.6453555072203998) - (b * 32.324150453290734))) + (b * 1.6453555072203998)));
	}
	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 ((z <= (-8.5d+45)) .or. (.not. (z <= 51000.0d0))) then
        tmp = x + (y / 0.31942702700572795d0)
    else
        tmp = x + (y * ((z * ((a * 1.6453555072203998d0) - (b * 32.324150453290734d0))) + (b * 1.6453555072203998d0)))
    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 ((z <= -8.5e+45) || !(z <= 51000.0)) {
		tmp = x + (y / 0.31942702700572795);
	} else {
		tmp = x + (y * ((z * ((a * 1.6453555072203998) - (b * 32.324150453290734))) + (b * 1.6453555072203998)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -8.5e+45) or not (z <= 51000.0):
		tmp = x + (y / 0.31942702700572795)
	else:
		tmp = x + (y * ((z * ((a * 1.6453555072203998) - (b * 32.324150453290734))) + (b * 1.6453555072203998)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -8.5e+45) || !(z <= 51000.0))
		tmp = Float64(x + Float64(y / 0.31942702700572795));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(z * Float64(Float64(a * 1.6453555072203998) - Float64(b * 32.324150453290734))) + Float64(b * 1.6453555072203998))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -8.5e+45) || ~((z <= 51000.0)))
		tmp = x + (y / 0.31942702700572795);
	else
		tmp = x + (y * ((z * ((a * 1.6453555072203998) - (b * 32.324150453290734))) + (b * 1.6453555072203998)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -8.5e+45], N[Not[LessEqual[z, 51000.0]], $MachinePrecision]], N[(x + N[(y / 0.31942702700572795), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(z * N[(N[(a * 1.6453555072203998), $MachinePrecision] - N[(b * 32.324150453290734), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * 1.6453555072203998), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.4999999999999996e45 or 51000 < z

   1. Initial program 11.3%

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

      1. associate-/l* 13.0%

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

      2. fma-def 13.0%

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

      3. fma-def 13.0%

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

      4. fma-def 13.0%

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

      5. fma-def 13.0%

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

      6. fma-def 13.0%

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

      7. fma-def 13.0%

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

      8. fma-def 13.0%

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

   3. Simplified 13.0%

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

   4. Taylor expanded in z around inf 89.9%

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

   if -8.4999999999999996e45 < z < 51000

   1. Initial program 98.3%

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

      1. associate-*l/ 98.9%

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

      2. *-commutative 98.9%

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

      3. fma-def 98.9%

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

      4. *-commutative 98.9%

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

      5. fma-def 98.9%

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

      6. *-commutative 98.9%

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

      7. fma-def 98.9%

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

      8. *-commutative 98.9%

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

      9. fma-def 98.9%

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

   3. Simplified 98.9%

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

   4. Taylor expanded in z around 0 77.7%

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

   5. Taylor expanded in y around 0 89.8%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+45} \lor \neg \left(z \leq 51000\right):\\ \;\;\;\;x + \frac{y}{0.31942702700572795}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(z \cdot \left(a \cdot 1.6453555072203998 - b \cdot 32.324150453290734\right) + b \cdot 1.6453555072203998\right)\\ \end{array} \]

Alternative 9: 89.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{+43}:\\ \;\;\;\;x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 - \frac{3.241970391368047 + t \cdot 0.10203362558171805}{z \cdot z}\right)}\\ \mathbf{elif}\;z \leq 29000:\\ \;\;\;\;x + y \cdot \left(z \cdot \left(a \cdot 1.6453555072203998 - b \cdot 32.324150453290734\right) + b \cdot 1.6453555072203998\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{0.31942702700572795}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -7.6e+43)
   (+
    x
    (/
     y
     (+
      (/ 3.7269864963038164 z)
      (-
       0.31942702700572795
       (/ (+ 3.241970391368047 (* t 0.10203362558171805)) (* z z))))))
   (if (<= z 29000.0)
     (+
      x
      (*
       y
       (+
        (* z (- (* a 1.6453555072203998) (* b 32.324150453290734)))
        (* b 1.6453555072203998))))
     (+ x (/ y 0.31942702700572795)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -7.6e+43) {
		tmp = x + (y / ((3.7269864963038164 / z) + (0.31942702700572795 - ((3.241970391368047 + (t * 0.10203362558171805)) / (z * z)))));
	} else if (z <= 29000.0) {
		tmp = x + (y * ((z * ((a * 1.6453555072203998) - (b * 32.324150453290734))) + (b * 1.6453555072203998)));
	} else {
		tmp = x + (y / 0.31942702700572795);
	}
	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 (z <= (-7.6d+43)) then
        tmp = x + (y / ((3.7269864963038164d0 / z) + (0.31942702700572795d0 - ((3.241970391368047d0 + (t * 0.10203362558171805d0)) / (z * z)))))
    else if (z <= 29000.0d0) then
        tmp = x + (y * ((z * ((a * 1.6453555072203998d0) - (b * 32.324150453290734d0))) + (b * 1.6453555072203998d0)))
    else
        tmp = x + (y / 0.31942702700572795d0)
    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 (z <= -7.6e+43) {
		tmp = x + (y / ((3.7269864963038164 / z) + (0.31942702700572795 - ((3.241970391368047 + (t * 0.10203362558171805)) / (z * z)))));
	} else if (z <= 29000.0) {
		tmp = x + (y * ((z * ((a * 1.6453555072203998) - (b * 32.324150453290734))) + (b * 1.6453555072203998)));
	} else {
		tmp = x + (y / 0.31942702700572795);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -7.6e+43:
		tmp = x + (y / ((3.7269864963038164 / z) + (0.31942702700572795 - ((3.241970391368047 + (t * 0.10203362558171805)) / (z * z)))))
	elif z <= 29000.0:
		tmp = x + (y * ((z * ((a * 1.6453555072203998) - (b * 32.324150453290734))) + (b * 1.6453555072203998)))
	else:
		tmp = x + (y / 0.31942702700572795)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -7.6e+43)
		tmp = Float64(x + Float64(y / Float64(Float64(3.7269864963038164 / z) + Float64(0.31942702700572795 - Float64(Float64(3.241970391368047 + Float64(t * 0.10203362558171805)) / Float64(z * z))))));
	elseif (z <= 29000.0)
		tmp = Float64(x + Float64(y * Float64(Float64(z * Float64(Float64(a * 1.6453555072203998) - Float64(b * 32.324150453290734))) + Float64(b * 1.6453555072203998))));
	else
		tmp = Float64(x + Float64(y / 0.31942702700572795));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -7.6e+43)
		tmp = x + (y / ((3.7269864963038164 / z) + (0.31942702700572795 - ((3.241970391368047 + (t * 0.10203362558171805)) / (z * z)))));
	elseif (z <= 29000.0)
		tmp = x + (y * ((z * ((a * 1.6453555072203998) - (b * 32.324150453290734))) + (b * 1.6453555072203998)));
	else
		tmp = x + (y / 0.31942702700572795);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -7.6e+43], N[(x + N[(y / N[(N[(3.7269864963038164 / z), $MachinePrecision] + N[(0.31942702700572795 - N[(N[(3.241970391368047 + N[(t * 0.10203362558171805), $MachinePrecision]), $MachinePrecision] / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 29000.0], N[(x + N[(y * N[(N[(z * N[(N[(a * 1.6453555072203998), $MachinePrecision] - N[(b * 32.324150453290734), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * 1.6453555072203998), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / 0.31942702700572795), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.60000000000000016e43

   1. Initial program 0.4%

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

      1. associate-/l* 0.4%

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

      2. fma-def 0.4%

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

      3. fma-def 0.4%

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

      4. fma-def 0.4%

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

      5. fma-def 0.4%

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

      6. fma-def 0.4%

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

      7. fma-def 0.4%

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

      8. fma-def 0.4%

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

   3. Simplified 0.4%

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

   4. Taylor expanded in z around inf 95.5%

      \[\leadsto x + \frac{y}{\color{blue}{3.7269864963038164 \cdot \frac{1}{z} + \left(0.31942702700572795 + -1 \cdot \frac{3.241970391368047 + 0.10203362558171805 \cdot t}{{z}^{2}}\right)}} \]
   5. Step-by-step derivation

      1. associate-*r/ 95.5%

         \[\leadsto x + \frac{y}{\color{blue}{\frac{3.7269864963038164 \cdot 1}{z}} + \left(0.31942702700572795 + -1 \cdot \frac{3.241970391368047 + 0.10203362558171805 \cdot t}{{z}^{2}}\right)} \]

      2. metadata-eval 95.5%

         \[\leadsto x + \frac{y}{\frac{\color{blue}{3.7269864963038164}}{z} + \left(0.31942702700572795 + -1 \cdot \frac{3.241970391368047 + 0.10203362558171805 \cdot t}{{z}^{2}}\right)} \]

      3. mul-1-neg 95.5%

         \[\leadsto x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 + \color{blue}{\left(-\frac{3.241970391368047 + 0.10203362558171805 \cdot t}{{z}^{2}}\right)}\right)} \]

      4. *-commutative 95.5%

         \[\leadsto x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 + \left(-\frac{3.241970391368047 + \color{blue}{t \cdot 0.10203362558171805}}{{z}^{2}}\right)\right)} \]

      5. unpow2 95.5%

         \[\leadsto x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 + \left(-\frac{3.241970391368047 + t \cdot 0.10203362558171805}{\color{blue}{z \cdot z}}\right)\right)} \]

   6. Simplified 95.5%

      \[\leadsto x + \frac{y}{\color{blue}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 + \left(-\frac{3.241970391368047 + t \cdot 0.10203362558171805}{z \cdot z}\right)\right)}} \]

   if -7.60000000000000016e43 < z < 29000

   1. Initial program 98.3%

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

      1. associate-*l/ 98.9%

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

      2. *-commutative 98.9%

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

      3. fma-def 98.9%

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

      4. *-commutative 98.9%

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

      5. fma-def 98.9%

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

      6. *-commutative 98.9%

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

      7. fma-def 98.9%

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

      8. *-commutative 98.9%

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

      9. fma-def 98.9%

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

   3. Simplified 98.9%

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

   4. Taylor expanded in z around 0 77.7%

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

   5. Taylor expanded in y around 0 89.8%

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

   if 29000 < z

   1. Initial program 18.5%

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

      1. associate-/l* 21.5%

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

      2. fma-def 21.5%

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

      3. fma-def 21.5%

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

      4. fma-def 21.5%

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

      5. fma-def 21.5%

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

      6. fma-def 21.5%

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

      7. fma-def 21.5%

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

      8. fma-def 21.5%

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

   3. Simplified 21.5%

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

   4. Taylor expanded in z around inf 86.1%

      \[\leadsto x + \frac{y}{\color{blue}{0.31942702700572795}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{+43}:\\ \;\;\;\;x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 - \frac{3.241970391368047 + t \cdot 0.10203362558171805}{z \cdot z}\right)}\\ \mathbf{elif}\;z \leq 29000:\\ \;\;\;\;x + y \cdot \left(z \cdot \left(a \cdot 1.6453555072203998 - b \cdot 32.324150453290734\right) + b \cdot 1.6453555072203998\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{0.31942702700572795}\\ \end{array} \]

Alternative 10: 86.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{+43} \lor \neg \left(z \leq 6.6 \cdot 10^{+27}\right):\\ \;\;\;\;x + \frac{y}{0.31942702700572795}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z \cdot \left(a \cdot \left(y \cdot 1.6453555072203998\right)\right) + 1.6453555072203998 \cdot \left(y \cdot b\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -7.6e+43) (not (<= z 6.6e+27)))
   (+ x (/ y 0.31942702700572795))
   (+
    x
    (+ (* z (* a (* y 1.6453555072203998))) (* 1.6453555072203998 (* y b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -7.6e+43) || !(z <= 6.6e+27)) {
		tmp = x + (y / 0.31942702700572795);
	} else {
		tmp = x + ((z * (a * (y * 1.6453555072203998))) + (1.6453555072203998 * (y * b)));
	}
	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 ((z <= (-7.6d+43)) .or. (.not. (z <= 6.6d+27))) then
        tmp = x + (y / 0.31942702700572795d0)
    else
        tmp = x + ((z * (a * (y * 1.6453555072203998d0))) + (1.6453555072203998d0 * (y * b)))
    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 ((z <= -7.6e+43) || !(z <= 6.6e+27)) {
		tmp = x + (y / 0.31942702700572795);
	} else {
		tmp = x + ((z * (a * (y * 1.6453555072203998))) + (1.6453555072203998 * (y * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -7.6e+43) or not (z <= 6.6e+27):
		tmp = x + (y / 0.31942702700572795)
	else:
		tmp = x + ((z * (a * (y * 1.6453555072203998))) + (1.6453555072203998 * (y * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -7.6e+43) || !(z <= 6.6e+27))
		tmp = Float64(x + Float64(y / 0.31942702700572795));
	else
		tmp = Float64(x + Float64(Float64(z * Float64(a * Float64(y * 1.6453555072203998))) + Float64(1.6453555072203998 * Float64(y * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -7.6e+43) || ~((z <= 6.6e+27)))
		tmp = x + (y / 0.31942702700572795);
	else
		tmp = x + ((z * (a * (y * 1.6453555072203998))) + (1.6453555072203998 * (y * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -7.6e+43], N[Not[LessEqual[z, 6.6e+27]], $MachinePrecision]], N[(x + N[(y / 0.31942702700572795), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z * N[(a * N[(y * 1.6453555072203998), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(1.6453555072203998 * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.60000000000000016e43 or 6.5999999999999996e27 < z

   1. Initial program 6.2%

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

      1. associate-/l* 8.1%

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

      2. fma-def 8.1%

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

      3. fma-def 8.1%

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

      4. fma-def 8.1%

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

      5. fma-def 8.1%

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

      6. fma-def 8.1%

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

      7. fma-def 8.1%

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

      8. fma-def 8.1%

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

   3. Simplified 8.1%

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

   4. Taylor expanded in z around inf 92.1%

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

   if -7.60000000000000016e43 < z < 6.5999999999999996e27

   1. Initial program 98.4%

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

      1. associate-*l/ 98.9%

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

      2. *-commutative 98.9%

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

      3. fma-def 98.9%

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

      4. *-commutative 98.9%

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

      5. fma-def 98.9%

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

      6. *-commutative 98.9%

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

      7. fma-def 98.9%

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

      8. *-commutative 98.9%

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

      9. fma-def 98.9%

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

   3. Simplified 98.9%

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

   4. Taylor expanded in z around 0 76.7%

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

   5. Taylor expanded in a around inf 81.0%

      \[\leadsto x + \left(\color{blue}{\left(1.6453555072203998 \cdot \left(a \cdot y\right)\right)} \cdot z + 1.6453555072203998 \cdot \left(y \cdot b\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative 81.0%

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

      2. associate-*r* 81.0%

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

   7. Simplified 81.0%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{+43} \lor \neg \left(z \leq 6.6 \cdot 10^{+27}\right):\\ \;\;\;\;x + \frac{y}{0.31942702700572795}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z \cdot \left(a \cdot \left(y \cdot 1.6453555072203998\right)\right) + 1.6453555072203998 \cdot \left(y \cdot b\right)\right)\\ \end{array} \]

Alternative 11: 83.3% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{+43} \lor \neg \left(z \leq 0.15\right):\\ \;\;\;\;x + \frac{y}{0.31942702700572795}\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(-32.324150453290734 \cdot \left(y \cdot z\right) + y \cdot 1.6453555072203998\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -7.6e+43) (not (<= z 0.15)))
   (+ x (/ y 0.31942702700572795))
   (+ x (* b (+ (* -32.324150453290734 (* y z)) (* y 1.6453555072203998))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -7.6e+43) || !(z <= 0.15)) {
		tmp = x + (y / 0.31942702700572795);
	} else {
		tmp = x + (b * ((-32.324150453290734 * (y * z)) + (y * 1.6453555072203998)));
	}
	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 ((z <= (-7.6d+43)) .or. (.not. (z <= 0.15d0))) then
        tmp = x + (y / 0.31942702700572795d0)
    else
        tmp = x + (b * (((-32.324150453290734d0) * (y * z)) + (y * 1.6453555072203998d0)))
    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 ((z <= -7.6e+43) || !(z <= 0.15)) {
		tmp = x + (y / 0.31942702700572795);
	} else {
		tmp = x + (b * ((-32.324150453290734 * (y * z)) + (y * 1.6453555072203998)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -7.6e+43) or not (z <= 0.15):
		tmp = x + (y / 0.31942702700572795)
	else:
		tmp = x + (b * ((-32.324150453290734 * (y * z)) + (y * 1.6453555072203998)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -7.6e+43) || !(z <= 0.15))
		tmp = Float64(x + Float64(y / 0.31942702700572795));
	else
		tmp = Float64(x + Float64(b * Float64(Float64(-32.324150453290734 * Float64(y * z)) + Float64(y * 1.6453555072203998))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -7.6e+43) || ~((z <= 0.15)))
		tmp = x + (y / 0.31942702700572795);
	else
		tmp = x + (b * ((-32.324150453290734 * (y * z)) + (y * 1.6453555072203998)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -7.6e+43], N[Not[LessEqual[z, 0.15]], $MachinePrecision]], N[(x + N[(y / 0.31942702700572795), $MachinePrecision]), $MachinePrecision], N[(x + N[(b * N[(N[(-32.324150453290734 * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(y * 1.6453555072203998), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.60000000000000016e43 or 0.149999999999999994 < z

   1. Initial program 12.9%

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

      1. associate-/l* 14.6%

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

      2. fma-def 14.6%

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

      3. fma-def 14.6%

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

      4. fma-def 14.6%

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

      5. fma-def 14.6%

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

      6. fma-def 14.6%

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

      7. fma-def 14.6%

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

      8. fma-def 14.6%

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

   3. Simplified 14.6%

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

   4. Taylor expanded in z around inf 89.2%

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

   if -7.60000000000000016e43 < z < 0.149999999999999994

   1. Initial program 98.3%

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

      1. associate-*l/ 98.9%

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

      2. *-commutative 98.9%

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

      3. fma-def 98.9%

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

      4. *-commutative 98.9%

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

      5. fma-def 98.9%

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

      6. *-commutative 98.9%

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

      7. fma-def 98.9%

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

      8. *-commutative 98.9%

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

      9. fma-def 98.9%

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

   3. Simplified 98.9%

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

   4. Taylor expanded in z around 0 77.4%

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

   5. Taylor expanded in b around inf 77.7%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{+43} \lor \neg \left(z \leq 0.15\right):\\ \;\;\;\;x + \frac{y}{0.31942702700572795}\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(-32.324150453290734 \cdot \left(y \cdot z\right) + y \cdot 1.6453555072203998\right)\\ \end{array} \]

Alternative 12: 83.3% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{+43} \lor \neg \left(z \leq 1.65 \cdot 10^{+17}\right):\\ \;\;\;\;x + \frac{y}{0.31942702700572795}\\ \mathbf{else}:\\ \;\;\;\;x + 1.6453555072203998 \cdot \left(y \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -7.6e+43) (not (<= z 1.65e+17)))
   (+ x (/ y 0.31942702700572795))
   (+ x (* 1.6453555072203998 (* y b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -7.6e+43) || !(z <= 1.65e+17)) {
		tmp = x + (y / 0.31942702700572795);
	} else {
		tmp = x + (1.6453555072203998 * (y * b));
	}
	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 ((z <= (-7.6d+43)) .or. (.not. (z <= 1.65d+17))) then
        tmp = x + (y / 0.31942702700572795d0)
    else
        tmp = x + (1.6453555072203998d0 * (y * b))
    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 ((z <= -7.6e+43) || !(z <= 1.65e+17)) {
		tmp = x + (y / 0.31942702700572795);
	} else {
		tmp = x + (1.6453555072203998 * (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -7.6e+43) or not (z <= 1.65e+17):
		tmp = x + (y / 0.31942702700572795)
	else:
		tmp = x + (1.6453555072203998 * (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -7.6e+43) || !(z <= 1.65e+17))
		tmp = Float64(x + Float64(y / 0.31942702700572795));
	else
		tmp = Float64(x + Float64(1.6453555072203998 * Float64(y * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -7.6e+43) || ~((z <= 1.65e+17)))
		tmp = x + (y / 0.31942702700572795);
	else
		tmp = x + (1.6453555072203998 * (y * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -7.6e+43], N[Not[LessEqual[z, 1.65e+17]], $MachinePrecision]], N[(x + N[(y / 0.31942702700572795), $MachinePrecision]), $MachinePrecision], N[(x + N[(1.6453555072203998 * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.60000000000000016e43 or 1.65e17 < z

   1. Initial program 7.1%

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

      1. associate-/l* 8.9%

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

      2. fma-def 8.9%

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

      3. fma-def 8.9%

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

      4. fma-def 8.9%

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

      5. fma-def 8.9%

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

      6. fma-def 8.9%

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

      7. fma-def 8.9%

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

      8. fma-def 8.9%

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

   3. Simplified 8.9%

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

   4. Taylor expanded in z around inf 91.2%

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

   if -7.60000000000000016e43 < z < 1.65e17

   1. Initial program 98.4%

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

      1. associate-*l/ 98.9%

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

      2. *-commutative 98.9%

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

      3. fma-def 98.9%

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

      4. *-commutative 98.9%

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

      5. fma-def 98.9%

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

      6. *-commutative 98.9%

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

      7. fma-def 98.9%

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

      8. *-commutative 98.9%

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

      9. fma-def 98.9%

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

   3. Simplified 98.9%

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

   4. Taylor expanded in z around 0 76.5%

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

4. Final simplification 82.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{+43} \lor \neg \left(z \leq 1.65 \cdot 10^{+17}\right):\\ \;\;\;\;x + \frac{y}{0.31942702700572795}\\ \mathbf{else}:\\ \;\;\;\;x + 1.6453555072203998 \cdot \left(y \cdot b\right)\\ \end{array} \]

Alternative 13: 62.5% accurate, 7.4× speedup

Math

\[\begin{array}{l} \\ x + \frac{y}{0.31942702700572795} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (+ x (/ y 0.31942702700572795)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return x + (y / 0.31942702700572795);
}

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 / 0.31942702700572795d0)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x + (y / 0.31942702700572795);
}

Python

def code(x, y, z, t, a, b):
	return x + (y / 0.31942702700572795)

Julia

function code(x, y, z, t, a, b)
	return Float64(x + Float64(y / 0.31942702700572795))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x + (y / 0.31942702700572795);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x + N[(y / 0.31942702700572795), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 60.9%

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

   1. associate-/l* 62.0%

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

   2. fma-def 62.0%

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

   3. fma-def 62.0%

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

   4. fma-def 62.0%

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

   5. fma-def 62.0%

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

   6. fma-def 62.0%

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

   7. fma-def 62.0%

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

   8. fma-def 62.0%

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

3. Simplified 62.0%

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

4. Taylor expanded in z around inf 56.7%

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

5. Final simplification 56.7%

   \[\leadsto x + \frac{y}{0.31942702700572795} \]

Alternative 14: 45.1% accurate, 37.0× 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 60.9%

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

   1. associate-/l* 62.0%

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

   2. fma-def 62.0%

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

   3. fma-def 62.0%

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

   4. fma-def 62.0%

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

   5. fma-def 62.0%

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

   6. fma-def 62.0%

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

   7. fma-def 62.0%

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

   8. fma-def 62.0%

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

3. Simplified 62.0%

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

4. Taylor expanded in z around inf 56.7%

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

5. Taylor expanded in x around inf 40.2%

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

6. Final simplification 40.2%

   \[\leadsto x \]

Developer target: 98.4% accurate, 0.9× 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 2023185 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, D"
  :precision binary64

  :herbie-target
  (if (< z -6.499344996252632e+53) (+ x (* (+ (- 3.13060547623 (/ 36.527041698806414 z)) (/ t (* z z))) (/ y 1.0))) (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)))) (+ x (* (+ (- 3.13060547623 (/ 36.527041698806414 z)) (/ t (* z z))) (/ y 1.0)))))

  (+ 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))))