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

Percentage Accurate: 59.2% → 98.3%

Time: 15.7s

Alternatives: 14

Speedup: 4.0×

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: 59.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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: 98.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.25 \cdot 10^{+35} \lor \neg \left(z \leq 4.5 \cdot 10^{+35}\right):\\ \;\;\;\;x + \left(\mathsf{fma}\left(-1, \frac{y \cdot 36.52704169880642}{z}, y \cdot 3.13060547623 + \frac{y}{\frac{z \cdot z}{t}}\right) - \mathsf{fma}\left(-15.234687407, \frac{y \cdot 36.52704169880642}{z \cdot z}, 98.5170599679272 \cdot \frac{y}{z \cdot z}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)} \cdot \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -3.25e+35) (not (<= z 4.5e+35)))
   (+
    x
    (-
     (fma
      -1.0
      (/ (* y 36.52704169880642) z)
      (+ (* y 3.13060547623) (/ y (/ (* z z) t))))
     (fma
      -15.234687407
      (/ (* y 36.52704169880642) (* z z))
      (* 98.5170599679272 (/ y (* z z))))))
   (+
    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)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3.25e+35) || !(z <= 4.5e+35)) {
		tmp = x + (fma(-1.0, ((y * 36.52704169880642) / z), ((y * 3.13060547623) + (y / ((z * z) / t)))) - fma(-15.234687407, ((y * 36.52704169880642) / (z * z)), (98.5170599679272 * (y / (z * z)))));
	} else {
		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));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -3.25e+35) || !(z <= 4.5e+35))
		tmp = Float64(x + Float64(fma(-1.0, Float64(Float64(y * 36.52704169880642) / z), Float64(Float64(y * 3.13060547623) + Float64(y / Float64(Float64(z * z) / t)))) - fma(-15.234687407, Float64(Float64(y * 36.52704169880642) / Float64(z * z)), Float64(98.5170599679272 * Float64(y / Float64(z * z))))));
	else
		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)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -3.25e+35], N[Not[LessEqual[z, 4.5e+35]], $MachinePrecision]], N[(x + N[(N[(-1.0 * N[(N[(y * 36.52704169880642), $MachinePrecision] / z), $MachinePrecision] + N[(N[(y * 3.13060547623), $MachinePrecision] + N[(y / N[(N[(z * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(-15.234687407 * N[(N[(y * 36.52704169880642), $MachinePrecision] / N[(z * z), $MachinePrecision]), $MachinePrecision] + N[(98.5170599679272 * N[(y / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 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]]

Derivation

1. Split input into 2 regimes

2. if z < -3.2500000000000002e35 or 4.4999999999999997e35 < z

   1. Initial program 7.3%

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

      1. associate-*l/ 6.4%

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

      2. *-commutative 6.4%

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

      3. fma-def 6.4%

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

      4. *-commutative 6.4%

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

      5. fma-def 6.4%

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

      6. *-commutative 6.4%

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

      7. fma-def 6.4%

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

      8. *-commutative 6.4%

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

      9. fma-def 6.4%

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

   3. Simplified 6.4%

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

   4. Taylor expanded in z around -inf 81.5%

      \[\leadsto x + \color{blue}{\left(\left(-1 \cdot \frac{-11.1667541262 \cdot y - -47.69379582500642 \cdot y}{z} + \left(\frac{y \cdot t}{{z}^{2}} + 3.13060547623 \cdot y\right)\right) - \left(-15.234687407 \cdot \frac{-11.1667541262 \cdot y - -47.69379582500642 \cdot y}{{z}^{2}} + 98.5170599679272 \cdot \frac{y}{{z}^{2}}\right)\right)} \]
   5. Step-by-step derivation

      1. fma-def 81.5%

         \[\leadsto x + \left(\color{blue}{\mathsf{fma}\left(-1, \frac{-11.1667541262 \cdot y - -47.69379582500642 \cdot y}{z}, \frac{y \cdot t}{{z}^{2}} + 3.13060547623 \cdot y\right)} - \left(-15.234687407 \cdot \frac{-11.1667541262 \cdot y - -47.69379582500642 \cdot y}{{z}^{2}} + 98.5170599679272 \cdot \frac{y}{{z}^{2}}\right)\right) \]

      2. distribute-rgt-out-- 81.5%

         \[\leadsto x + \left(\mathsf{fma}\left(-1, \frac{\color{blue}{y \cdot \left(-11.1667541262 - -47.69379582500642\right)}}{z}, \frac{y \cdot t}{{z}^{2}} + 3.13060547623 \cdot y\right) - \left(-15.234687407 \cdot \frac{-11.1667541262 \cdot y - -47.69379582500642 \cdot y}{{z}^{2}} + 98.5170599679272 \cdot \frac{y}{{z}^{2}}\right)\right) \]

      3. metadata-eval 81.5%

         \[\leadsto x + \left(\mathsf{fma}\left(-1, \frac{y \cdot \color{blue}{36.52704169880642}}{z}, \frac{y \cdot t}{{z}^{2}} + 3.13060547623 \cdot y\right) - \left(-15.234687407 \cdot \frac{-11.1667541262 \cdot y - -47.69379582500642 \cdot y}{{z}^{2}} + 98.5170599679272 \cdot \frac{y}{{z}^{2}}\right)\right) \]

      4. +-commutative 81.5%

         \[\leadsto x + \left(\mathsf{fma}\left(-1, \frac{y \cdot 36.52704169880642}{z}, \color{blue}{3.13060547623 \cdot y + \frac{y \cdot t}{{z}^{2}}}\right) - \left(-15.234687407 \cdot \frac{-11.1667541262 \cdot y - -47.69379582500642 \cdot y}{{z}^{2}} + 98.5170599679272 \cdot \frac{y}{{z}^{2}}\right)\right) \]

      5. *-commutative 81.5%

         \[\leadsto x + \left(\mathsf{fma}\left(-1, \frac{y \cdot 36.52704169880642}{z}, \color{blue}{y \cdot 3.13060547623} + \frac{y \cdot t}{{z}^{2}}\right) - \left(-15.234687407 \cdot \frac{-11.1667541262 \cdot y - -47.69379582500642 \cdot y}{{z}^{2}} + 98.5170599679272 \cdot \frac{y}{{z}^{2}}\right)\right) \]

      6. associate-/l* 98.9%

         \[\leadsto x + \left(\mathsf{fma}\left(-1, \frac{y \cdot 36.52704169880642}{z}, y \cdot 3.13060547623 + \color{blue}{\frac{y}{\frac{{z}^{2}}{t}}}\right) - \left(-15.234687407 \cdot \frac{-11.1667541262 \cdot y - -47.69379582500642 \cdot y}{{z}^{2}} + 98.5170599679272 \cdot \frac{y}{{z}^{2}}\right)\right) \]

      7. unpow2 98.9%

         \[\leadsto x + \left(\mathsf{fma}\left(-1, \frac{y \cdot 36.52704169880642}{z}, y \cdot 3.13060547623 + \frac{y}{\frac{\color{blue}{z \cdot z}}{t}}\right) - \left(-15.234687407 \cdot \frac{-11.1667541262 \cdot y - -47.69379582500642 \cdot y}{{z}^{2}} + 98.5170599679272 \cdot \frac{y}{{z}^{2}}\right)\right) \]

      8. fma-def 98.9%

         \[\leadsto x + \left(\mathsf{fma}\left(-1, \frac{y \cdot 36.52704169880642}{z}, y \cdot 3.13060547623 + \frac{y}{\frac{z \cdot z}{t}}\right) - \color{blue}{\mathsf{fma}\left(-15.234687407, \frac{-11.1667541262 \cdot y - -47.69379582500642 \cdot y}{{z}^{2}}, 98.5170599679272 \cdot \frac{y}{{z}^{2}}\right)}\right) \]

      9. distribute-rgt-out-- 98.9%

         \[\leadsto x + \left(\mathsf{fma}\left(-1, \frac{y \cdot 36.52704169880642}{z}, y \cdot 3.13060547623 + \frac{y}{\frac{z \cdot z}{t}}\right) - \mathsf{fma}\left(-15.234687407, \frac{\color{blue}{y \cdot \left(-11.1667541262 - -47.69379582500642\right)}}{{z}^{2}}, 98.5170599679272 \cdot \frac{y}{{z}^{2}}\right)\right) \]

      10. metadata-eval 98.9%

          \[\leadsto x + \left(\mathsf{fma}\left(-1, \frac{y \cdot 36.52704169880642}{z}, y \cdot 3.13060547623 + \frac{y}{\frac{z \cdot z}{t}}\right) - \mathsf{fma}\left(-15.234687407, \frac{y \cdot \color{blue}{36.52704169880642}}{{z}^{2}}, 98.5170599679272 \cdot \frac{y}{{z}^{2}}\right)\right) \]

      11. unpow2 98.9%

          \[\leadsto x + \left(\mathsf{fma}\left(-1, \frac{y \cdot 36.52704169880642}{z}, y \cdot 3.13060547623 + \frac{y}{\frac{z \cdot z}{t}}\right) - \mathsf{fma}\left(-15.234687407, \frac{y \cdot 36.52704169880642}{\color{blue}{z \cdot z}}, 98.5170599679272 \cdot \frac{y}{{z}^{2}}\right)\right) \]

      12. unpow2 98.9%

          \[\leadsto x + \left(\mathsf{fma}\left(-1, \frac{y \cdot 36.52704169880642}{z}, y \cdot 3.13060547623 + \frac{y}{\frac{z \cdot z}{t}}\right) - \mathsf{fma}\left(-15.234687407, \frac{y \cdot 36.52704169880642}{z \cdot z}, 98.5170599679272 \cdot \frac{y}{\color{blue}{z \cdot z}}\right)\right) \]

   6. Simplified 98.9%

      \[\leadsto x + \color{blue}{\left(\mathsf{fma}\left(-1, \frac{y \cdot 36.52704169880642}{z}, y \cdot 3.13060547623 + \frac{y}{\frac{z \cdot z}{t}}\right) - \mathsf{fma}\left(-15.234687407, \frac{y \cdot 36.52704169880642}{z \cdot z}, 98.5170599679272 \cdot \frac{y}{z \cdot z}\right)\right)} \]

   if -3.2500000000000002e35 < z < 4.4999999999999997e35

   1. Initial program 99.2%

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

      1. associate-*l/ 99.7%

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

      2. *-commutative 99.7%

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

      3. fma-def 99.7%

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

      4. *-commutative 99.7%

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

      5. fma-def 99.7%

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

      6. *-commutative 99.7%

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

      7. fma-def 99.7%

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

      8. *-commutative 99.7%

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

      9. fma-def 99.7%

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

   3. Simplified 99.7%

      \[\leadsto \color{blue}{x + \frac{y}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)} \cdot \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.25 \cdot 10^{+35} \lor \neg \left(z \leq 4.5 \cdot 10^{+35}\right):\\ \;\;\;\;x + \left(\mathsf{fma}\left(-1, \frac{y \cdot 36.52704169880642}{z}, y \cdot 3.13060547623 + \frac{y}{\frac{z \cdot z}{t}}\right) - \mathsf{fma}\left(-15.234687407, \frac{y \cdot 36.52704169880642}{z \cdot z}, 98.5170599679272 \cdot \frac{y}{z \cdot z}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)} \cdot \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right)\\ \end{array} \]

Alternative 2: 98.0% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\right)\right) + b\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771} \leq \infty:\\ \;\;\;\;x + \frac{y}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687407, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), z, t\right), z, a\right), z, b\right)}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\mathsf{fma}\left(-1, \frac{y \cdot 36.52704169880642}{z}, y \cdot 3.13060547623 + \frac{y}{\frac{z \cdot z}{t}}\right) - \mathsf{fma}\left(-15.234687407, \frac{y \cdot 36.52704169880642}{z \cdot z}, 98.5170599679272 \cdot \frac{y}{z \cdot z}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<=
      (/
       (*
        y
        (+
         (* z (+ a (* z (+ t (* z (+ 11.1667541262 (* z 3.13060547623)))))))
         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
    (-
     (fma
      -1.0
      (/ (* y 36.52704169880642) z)
      (+ (* y 3.13060547623) (/ y (/ (* z z) t))))
     (fma
      -15.234687407
      (/ (* y 36.52704169880642) (* z z))
      (* 98.5170599679272 (/ y (* z z))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((y * ((z * (a + (z * (t + (z * (11.1667541262 + (z * 3.13060547623))))))) + 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 + (fma(-1.0, ((y * 36.52704169880642) / z), ((y * 3.13060547623) + (y / ((z * z) / t)))) - fma(-15.234687407, ((y * 36.52704169880642) / (z * z)), (98.5170599679272 * (y / (z * z)))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(Float64(y * Float64(Float64(z * Float64(a + Float64(z * Float64(t + Float64(z * Float64(11.1667541262 + Float64(z * 3.13060547623))))))) + 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(fma(-1.0, Float64(Float64(y * 36.52704169880642) / z), Float64(Float64(y * 3.13060547623) + Float64(y / Float64(Float64(z * z) / t)))) - fma(-15.234687407, Float64(Float64(y * 36.52704169880642) / Float64(z * z)), Float64(98.5170599679272 * Float64(y / Float64(z * z))))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(N[(y * N[(N[(z * N[(a + N[(z * N[(t + N[(z * N[(11.1667541262 + N[(z * 3.13060547623), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $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[(N[(-1.0 * N[(N[(y * 36.52704169880642), $MachinePrecision] / z), $MachinePrecision] + N[(N[(y * 3.13060547623), $MachinePrecision] + N[(y / N[(N[(z * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(-15.234687407 * N[(N[(y * 36.52704169880642), $MachinePrecision] / N[(z * z), $MachinePrecision]), $MachinePrecision] + N[(98.5170599679272 * N[(y / 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 96.4%

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

      1. associate-/l* 97.0%

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

      2. fma-def 97.0%

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

      3. fma-def 97.0%

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

      4. fma-def 97.0%

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

      5. fma-def 97.0%

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

      6. fma-def 97.0%

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

      7. fma-def 97.0%

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

      8. fma-def 97.0%

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

   3. Simplified 97.0%

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

   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%

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

      2. *-commutative 0.0%

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

      3. fma-def 0.0%

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

      4. *-commutative 0.0%

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

      5. fma-def 0.0%

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

      6. *-commutative 0.0%

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

      7. fma-def 0.0%

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

      8. *-commutative 0.0%

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

      9. fma-def 0.0%

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

   3. Simplified 0.0%

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

   4. Taylor expanded in z around -inf 82.2%

      \[\leadsto x + \color{blue}{\left(\left(-1 \cdot \frac{-11.1667541262 \cdot y - -47.69379582500642 \cdot y}{z} + \left(\frac{y \cdot t}{{z}^{2}} + 3.13060547623 \cdot y\right)\right) - \left(-15.234687407 \cdot \frac{-11.1667541262 \cdot y - -47.69379582500642 \cdot y}{{z}^{2}} + 98.5170599679272 \cdot \frac{y}{{z}^{2}}\right)\right)} \]
   5. Step-by-step derivation

      1. fma-def 82.2%

         \[\leadsto x + \left(\color{blue}{\mathsf{fma}\left(-1, \frac{-11.1667541262 \cdot y - -47.69379582500642 \cdot y}{z}, \frac{y \cdot t}{{z}^{2}} + 3.13060547623 \cdot y\right)} - \left(-15.234687407 \cdot \frac{-11.1667541262 \cdot y - -47.69379582500642 \cdot y}{{z}^{2}} + 98.5170599679272 \cdot \frac{y}{{z}^{2}}\right)\right) \]

      2. distribute-rgt-out-- 82.2%

         \[\leadsto x + \left(\mathsf{fma}\left(-1, \frac{\color{blue}{y \cdot \left(-11.1667541262 - -47.69379582500642\right)}}{z}, \frac{y \cdot t}{{z}^{2}} + 3.13060547623 \cdot y\right) - \left(-15.234687407 \cdot \frac{-11.1667541262 \cdot y - -47.69379582500642 \cdot y}{{z}^{2}} + 98.5170599679272 \cdot \frac{y}{{z}^{2}}\right)\right) \]

      3. metadata-eval 82.2%

         \[\leadsto x + \left(\mathsf{fma}\left(-1, \frac{y \cdot \color{blue}{36.52704169880642}}{z}, \frac{y \cdot t}{{z}^{2}} + 3.13060547623 \cdot y\right) - \left(-15.234687407 \cdot \frac{-11.1667541262 \cdot y - -47.69379582500642 \cdot y}{{z}^{2}} + 98.5170599679272 \cdot \frac{y}{{z}^{2}}\right)\right) \]

      4. +-commutative 82.2%

         \[\leadsto x + \left(\mathsf{fma}\left(-1, \frac{y \cdot 36.52704169880642}{z}, \color{blue}{3.13060547623 \cdot y + \frac{y \cdot t}{{z}^{2}}}\right) - \left(-15.234687407 \cdot \frac{-11.1667541262 \cdot y - -47.69379582500642 \cdot y}{{z}^{2}} + 98.5170599679272 \cdot \frac{y}{{z}^{2}}\right)\right) \]

      5. *-commutative 82.2%

         \[\leadsto x + \left(\mathsf{fma}\left(-1, \frac{y \cdot 36.52704169880642}{z}, \color{blue}{y \cdot 3.13060547623} + \frac{y \cdot t}{{z}^{2}}\right) - \left(-15.234687407 \cdot \frac{-11.1667541262 \cdot y - -47.69379582500642 \cdot y}{{z}^{2}} + 98.5170599679272 \cdot \frac{y}{{z}^{2}}\right)\right) \]

      6. associate-/l* 99.9%

         \[\leadsto x + \left(\mathsf{fma}\left(-1, \frac{y \cdot 36.52704169880642}{z}, y \cdot 3.13060547623 + \color{blue}{\frac{y}{\frac{{z}^{2}}{t}}}\right) - \left(-15.234687407 \cdot \frac{-11.1667541262 \cdot y - -47.69379582500642 \cdot y}{{z}^{2}} + 98.5170599679272 \cdot \frac{y}{{z}^{2}}\right)\right) \]

      7. unpow2 99.9%

         \[\leadsto x + \left(\mathsf{fma}\left(-1, \frac{y \cdot 36.52704169880642}{z}, y \cdot 3.13060547623 + \frac{y}{\frac{\color{blue}{z \cdot z}}{t}}\right) - \left(-15.234687407 \cdot \frac{-11.1667541262 \cdot y - -47.69379582500642 \cdot y}{{z}^{2}} + 98.5170599679272 \cdot \frac{y}{{z}^{2}}\right)\right) \]

      8. fma-def 99.9%

         \[\leadsto x + \left(\mathsf{fma}\left(-1, \frac{y \cdot 36.52704169880642}{z}, y \cdot 3.13060547623 + \frac{y}{\frac{z \cdot z}{t}}\right) - \color{blue}{\mathsf{fma}\left(-15.234687407, \frac{-11.1667541262 \cdot y - -47.69379582500642 \cdot y}{{z}^{2}}, 98.5170599679272 \cdot \frac{y}{{z}^{2}}\right)}\right) \]

      9. distribute-rgt-out-- 99.9%

         \[\leadsto x + \left(\mathsf{fma}\left(-1, \frac{y \cdot 36.52704169880642}{z}, y \cdot 3.13060547623 + \frac{y}{\frac{z \cdot z}{t}}\right) - \mathsf{fma}\left(-15.234687407, \frac{\color{blue}{y \cdot \left(-11.1667541262 - -47.69379582500642\right)}}{{z}^{2}}, 98.5170599679272 \cdot \frac{y}{{z}^{2}}\right)\right) \]

      10. metadata-eval 99.9%

          \[\leadsto x + \left(\mathsf{fma}\left(-1, \frac{y \cdot 36.52704169880642}{z}, y \cdot 3.13060547623 + \frac{y}{\frac{z \cdot z}{t}}\right) - \mathsf{fma}\left(-15.234687407, \frac{y \cdot \color{blue}{36.52704169880642}}{{z}^{2}}, 98.5170599679272 \cdot \frac{y}{{z}^{2}}\right)\right) \]

      11. unpow2 99.9%

          \[\leadsto x + \left(\mathsf{fma}\left(-1, \frac{y \cdot 36.52704169880642}{z}, y \cdot 3.13060547623 + \frac{y}{\frac{z \cdot z}{t}}\right) - \mathsf{fma}\left(-15.234687407, \frac{y \cdot 36.52704169880642}{\color{blue}{z \cdot z}}, 98.5170599679272 \cdot \frac{y}{{z}^{2}}\right)\right) \]

      12. unpow2 99.9%

          \[\leadsto x + \left(\mathsf{fma}\left(-1, \frac{y \cdot 36.52704169880642}{z}, y \cdot 3.13060547623 + \frac{y}{\frac{z \cdot z}{t}}\right) - \mathsf{fma}\left(-15.234687407, \frac{y \cdot 36.52704169880642}{z \cdot z}, 98.5170599679272 \cdot \frac{y}{\color{blue}{z \cdot z}}\right)\right) \]

   6. Simplified 99.9%

      \[\leadsto x + \color{blue}{\left(\mathsf{fma}\left(-1, \frac{y \cdot 36.52704169880642}{z}, y \cdot 3.13060547623 + \frac{y}{\frac{z \cdot z}{t}}\right) - \mathsf{fma}\left(-15.234687407, \frac{y \cdot 36.52704169880642}{z \cdot z}, 98.5170599679272 \cdot \frac{y}{z \cdot z}\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\right)\right) + b\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771} \leq \infty:\\ \;\;\;\;x + \frac{y}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687407, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), z, t\right), z, a\right), z, b\right)}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\mathsf{fma}\left(-1, \frac{y \cdot 36.52704169880642}{z}, y \cdot 3.13060547623 + \frac{y}{\frac{z \cdot z}{t}}\right) - \mathsf{fma}\left(-15.234687407, \frac{y \cdot 36.52704169880642}{z \cdot z}, 98.5170599679272 \cdot \frac{y}{z \cdot z}\right)\right)\\ \end{array} \]

Alternative 3: 96.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\right)\right) + b\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\\ \mathbf{if}\;t_1 \leq \infty:\\ \;\;\;\;t_1 + x\\ \mathbf{else}:\\ \;\;\;\;x + \left(\mathsf{fma}\left(-1, \frac{y \cdot 36.52704169880642}{z}, y \cdot 3.13060547623 + \frac{y}{\frac{z \cdot z}{t}}\right) - \mathsf{fma}\left(-15.234687407, \frac{y \cdot 36.52704169880642}{z \cdot z}, 98.5170599679272 \cdot \frac{y}{z \cdot z}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (/
          (*
           y
           (+
            (* z (+ a (* z (+ t (* z (+ 11.1667541262 (* z 3.13060547623)))))))
            b))
          (+
           (*
            z
            (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721))
           0.607771387771))))
   (if (<= t_1 INFINITY)
     (+ t_1 x)
     (+
      x
      (-
       (fma
        -1.0
        (/ (* y 36.52704169880642) z)
        (+ (* y 3.13060547623) (/ y (/ (* z z) t))))
       (fma
        -15.234687407
        (/ (* y 36.52704169880642) (* z z))
        (* 98.5170599679272 (/ y (* z z)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * ((z * (a + (z * (t + (z * (11.1667541262 + (z * 3.13060547623))))))) + 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 + (fma(-1.0, ((y * 36.52704169880642) / z), ((y * 3.13060547623) + (y / ((z * z) / t)))) - fma(-15.234687407, ((y * 36.52704169880642) / (z * z)), (98.5170599679272 * (y / (z * z)))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y * Float64(Float64(z * Float64(a + Float64(z * Float64(t + Float64(z * Float64(11.1667541262 + Float64(z * 3.13060547623))))))) + 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(fma(-1.0, Float64(Float64(y * 36.52704169880642) / z), Float64(Float64(y * 3.13060547623) + Float64(y / Float64(Float64(z * z) / t)))) - fma(-15.234687407, Float64(Float64(y * 36.52704169880642) / Float64(z * z)), Float64(98.5170599679272 * Float64(y / Float64(z * z))))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y * N[(N[(z * N[(a + N[(z * N[(t + N[(z * N[(11.1667541262 + N[(z * 3.13060547623), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $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[(N[(-1.0 * N[(N[(y * 36.52704169880642), $MachinePrecision] / z), $MachinePrecision] + N[(N[(y * 3.13060547623), $MachinePrecision] + N[(y / N[(N[(z * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(-15.234687407 * N[(N[(y * 36.52704169880642), $MachinePrecision] / N[(z * z), $MachinePrecision]), $MachinePrecision] + N[(98.5170599679272 * N[(y / 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 96.4%

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

   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%

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

      2. *-commutative 0.0%

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

      3. fma-def 0.0%

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

      4. *-commutative 0.0%

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

      5. fma-def 0.0%

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

      6. *-commutative 0.0%

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

      7. fma-def 0.0%

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

      8. *-commutative 0.0%

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

      9. fma-def 0.0%

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

   3. Simplified 0.0%

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

   4. Taylor expanded in z around -inf 82.2%

      \[\leadsto x + \color{blue}{\left(\left(-1 \cdot \frac{-11.1667541262 \cdot y - -47.69379582500642 \cdot y}{z} + \left(\frac{y \cdot t}{{z}^{2}} + 3.13060547623 \cdot y\right)\right) - \left(-15.234687407 \cdot \frac{-11.1667541262 \cdot y - -47.69379582500642 \cdot y}{{z}^{2}} + 98.5170599679272 \cdot \frac{y}{{z}^{2}}\right)\right)} \]
   5. Step-by-step derivation

      1. fma-def 82.2%

         \[\leadsto x + \left(\color{blue}{\mathsf{fma}\left(-1, \frac{-11.1667541262 \cdot y - -47.69379582500642 \cdot y}{z}, \frac{y \cdot t}{{z}^{2}} + 3.13060547623 \cdot y\right)} - \left(-15.234687407 \cdot \frac{-11.1667541262 \cdot y - -47.69379582500642 \cdot y}{{z}^{2}} + 98.5170599679272 \cdot \frac{y}{{z}^{2}}\right)\right) \]

      2. distribute-rgt-out-- 82.2%

         \[\leadsto x + \left(\mathsf{fma}\left(-1, \frac{\color{blue}{y \cdot \left(-11.1667541262 - -47.69379582500642\right)}}{z}, \frac{y \cdot t}{{z}^{2}} + 3.13060547623 \cdot y\right) - \left(-15.234687407 \cdot \frac{-11.1667541262 \cdot y - -47.69379582500642 \cdot y}{{z}^{2}} + 98.5170599679272 \cdot \frac{y}{{z}^{2}}\right)\right) \]

      3. metadata-eval 82.2%

         \[\leadsto x + \left(\mathsf{fma}\left(-1, \frac{y \cdot \color{blue}{36.52704169880642}}{z}, \frac{y \cdot t}{{z}^{2}} + 3.13060547623 \cdot y\right) - \left(-15.234687407 \cdot \frac{-11.1667541262 \cdot y - -47.69379582500642 \cdot y}{{z}^{2}} + 98.5170599679272 \cdot \frac{y}{{z}^{2}}\right)\right) \]

      4. +-commutative 82.2%

         \[\leadsto x + \left(\mathsf{fma}\left(-1, \frac{y \cdot 36.52704169880642}{z}, \color{blue}{3.13060547623 \cdot y + \frac{y \cdot t}{{z}^{2}}}\right) - \left(-15.234687407 \cdot \frac{-11.1667541262 \cdot y - -47.69379582500642 \cdot y}{{z}^{2}} + 98.5170599679272 \cdot \frac{y}{{z}^{2}}\right)\right) \]

      5. *-commutative 82.2%

         \[\leadsto x + \left(\mathsf{fma}\left(-1, \frac{y \cdot 36.52704169880642}{z}, \color{blue}{y \cdot 3.13060547623} + \frac{y \cdot t}{{z}^{2}}\right) - \left(-15.234687407 \cdot \frac{-11.1667541262 \cdot y - -47.69379582500642 \cdot y}{{z}^{2}} + 98.5170599679272 \cdot \frac{y}{{z}^{2}}\right)\right) \]

      6. associate-/l* 99.9%

         \[\leadsto x + \left(\mathsf{fma}\left(-1, \frac{y \cdot 36.52704169880642}{z}, y \cdot 3.13060547623 + \color{blue}{\frac{y}{\frac{{z}^{2}}{t}}}\right) - \left(-15.234687407 \cdot \frac{-11.1667541262 \cdot y - -47.69379582500642 \cdot y}{{z}^{2}} + 98.5170599679272 \cdot \frac{y}{{z}^{2}}\right)\right) \]

      7. unpow2 99.9%

         \[\leadsto x + \left(\mathsf{fma}\left(-1, \frac{y \cdot 36.52704169880642}{z}, y \cdot 3.13060547623 + \frac{y}{\frac{\color{blue}{z \cdot z}}{t}}\right) - \left(-15.234687407 \cdot \frac{-11.1667541262 \cdot y - -47.69379582500642 \cdot y}{{z}^{2}} + 98.5170599679272 \cdot \frac{y}{{z}^{2}}\right)\right) \]

      8. fma-def 99.9%

         \[\leadsto x + \left(\mathsf{fma}\left(-1, \frac{y \cdot 36.52704169880642}{z}, y \cdot 3.13060547623 + \frac{y}{\frac{z \cdot z}{t}}\right) - \color{blue}{\mathsf{fma}\left(-15.234687407, \frac{-11.1667541262 \cdot y - -47.69379582500642 \cdot y}{{z}^{2}}, 98.5170599679272 \cdot \frac{y}{{z}^{2}}\right)}\right) \]

      9. distribute-rgt-out-- 99.9%

         \[\leadsto x + \left(\mathsf{fma}\left(-1, \frac{y \cdot 36.52704169880642}{z}, y \cdot 3.13060547623 + \frac{y}{\frac{z \cdot z}{t}}\right) - \mathsf{fma}\left(-15.234687407, \frac{\color{blue}{y \cdot \left(-11.1667541262 - -47.69379582500642\right)}}{{z}^{2}}, 98.5170599679272 \cdot \frac{y}{{z}^{2}}\right)\right) \]

      10. metadata-eval 99.9%

          \[\leadsto x + \left(\mathsf{fma}\left(-1, \frac{y \cdot 36.52704169880642}{z}, y \cdot 3.13060547623 + \frac{y}{\frac{z \cdot z}{t}}\right) - \mathsf{fma}\left(-15.234687407, \frac{y \cdot \color{blue}{36.52704169880642}}{{z}^{2}}, 98.5170599679272 \cdot \frac{y}{{z}^{2}}\right)\right) \]

      11. unpow2 99.9%

          \[\leadsto x + \left(\mathsf{fma}\left(-1, \frac{y \cdot 36.52704169880642}{z}, y \cdot 3.13060547623 + \frac{y}{\frac{z \cdot z}{t}}\right) - \mathsf{fma}\left(-15.234687407, \frac{y \cdot 36.52704169880642}{\color{blue}{z \cdot z}}, 98.5170599679272 \cdot \frac{y}{{z}^{2}}\right)\right) \]

      12. unpow2 99.9%

          \[\leadsto x + \left(\mathsf{fma}\left(-1, \frac{y \cdot 36.52704169880642}{z}, y \cdot 3.13060547623 + \frac{y}{\frac{z \cdot z}{t}}\right) - \mathsf{fma}\left(-15.234687407, \frac{y \cdot 36.52704169880642}{z \cdot z}, 98.5170599679272 \cdot \frac{y}{\color{blue}{z \cdot z}}\right)\right) \]

   6. Simplified 99.9%

      \[\leadsto x + \color{blue}{\left(\mathsf{fma}\left(-1, \frac{y \cdot 36.52704169880642}{z}, y \cdot 3.13060547623 + \frac{y}{\frac{z \cdot z}{t}}\right) - \mathsf{fma}\left(-15.234687407, \frac{y \cdot 36.52704169880642}{z \cdot z}, 98.5170599679272 \cdot \frac{y}{z \cdot z}\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 97.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\right)\right) + b\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771} \leq \infty:\\ \;\;\;\;\frac{y \cdot \left(z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\right)\right) + b\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771} + x\\ \mathbf{else}:\\ \;\;\;\;x + \left(\mathsf{fma}\left(-1, \frac{y \cdot 36.52704169880642}{z}, y \cdot 3.13060547623 + \frac{y}{\frac{z \cdot z}{t}}\right) - \mathsf{fma}\left(-15.234687407, \frac{y \cdot 36.52704169880642}{z \cdot z}, 98.5170599679272 \cdot \frac{y}{z \cdot z}\right)\right)\\ \end{array} \]

Alternative 4: 95.4% accurate, 0.5× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * ((z * (a + (z * (t + (z * (11.1667541262 + (z * 3.13060547623))))))) + 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 * 3.13060547623);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * ((z * (a + (z * (t + (z * (11.1667541262 + (z * 3.13060547623))))))) + 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 * 3.13060547623);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (y * ((z * (a + (z * (t + (z * (11.1667541262 + (z * 3.13060547623))))))) + 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 * 3.13060547623)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y * Float64(Float64(z * Float64(a + Float64(z * Float64(t + Float64(z * Float64(11.1667541262 + Float64(z * 3.13060547623))))))) + 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 * 3.13060547623));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (y * ((z * (a + (z * (t + (z * (11.1667541262 + (z * 3.13060547623))))))) + 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 * 3.13060547623);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y * N[(N[(z * N[(a + N[(z * N[(t + N[(z * N[(11.1667541262 + N[(z * 3.13060547623), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $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 * 3.13060547623), $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 96.4%

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

   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%

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

      2. *-commutative 0.0%

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

      3. fma-def 0.0%

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

      4. *-commutative 0.0%

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

      5. fma-def 0.0%

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

      6. *-commutative 0.0%

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

      7. fma-def 0.0%

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

      8. *-commutative 0.0%

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

      9. fma-def 0.0%

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

   3. Simplified 0.0%

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

   4. Taylor expanded in z around inf 96.6%

      \[\leadsto x + \color{blue}{3.13060547623 \cdot y} \]
   5. Step-by-step derivation

      1. *-commutative 96.6%

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

   6. Simplified 96.6%

      \[\leadsto x + \color{blue}{y \cdot 3.13060547623} \]
3. Recombined 2 regimes into one program.

4. Final simplification 96.5%

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

Alternative 5: 94.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\right)\right)\\ t_2 := x + y \cdot 3.13060547623\\ \mathbf{if}\;z \leq -1.04 \cdot 10^{+74}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -8.8 \cdot 10^{-7}:\\ \;\;\;\;x + \frac{y}{\frac{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}{t_1}}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+37}:\\ \;\;\;\;x + \frac{y \cdot \left(t_1 + b\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (* z (+ a (* z (+ t (* z (+ 11.1667541262 (* z 3.13060547623))))))))
        (t_2 (+ x (* y 3.13060547623))))
   (if (<= z -1.04e+74)
     t_2
     (if (<= z -8.8e-7)
       (+
        x
        (/
         y
         (/
          (+
           (*
            z
            (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721))
           0.607771387771)
          t_1)))
       (if (<= z 1.7e+37)
         (+ x (/ (* y (+ t_1 b)) (+ 0.607771387771 (* z 11.9400905721))))
         t_2)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (a + (z * (t + (z * (11.1667541262 + (z * 3.13060547623))))));
	double t_2 = x + (y * 3.13060547623);
	double tmp;
	if (z <= -1.04e+74) {
		tmp = t_2;
	} else if (z <= -8.8e-7) {
		tmp = x + (y / (((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771) / t_1));
	} else if (z <= 1.7e+37) {
		tmp = x + ((y * (t_1 + b)) / (0.607771387771 + (z * 11.9400905721)));
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = z * (a + (z * (t + (z * (11.1667541262d0 + (z * 3.13060547623d0))))))
    t_2 = x + (y * 3.13060547623d0)
    if (z <= (-1.04d+74)) then
        tmp = t_2
    else if (z <= (-8.8d-7)) then
        tmp = x + (y / (((z * ((z * ((z * (z + 15.234687407d0)) + 31.4690115749d0)) + 11.9400905721d0)) + 0.607771387771d0) / t_1))
    else if (z <= 1.7d+37) then
        tmp = x + ((y * (t_1 + b)) / (0.607771387771d0 + (z * 11.9400905721d0)))
    else
        tmp = t_2
    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 = z * (a + (z * (t + (z * (11.1667541262 + (z * 3.13060547623))))));
	double t_2 = x + (y * 3.13060547623);
	double tmp;
	if (z <= -1.04e+74) {
		tmp = t_2;
	} else if (z <= -8.8e-7) {
		tmp = x + (y / (((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771) / t_1));
	} else if (z <= 1.7e+37) {
		tmp = x + ((y * (t_1 + b)) / (0.607771387771 + (z * 11.9400905721)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (a + (z * (t + (z * (11.1667541262 + (z * 3.13060547623))))))
	t_2 = x + (y * 3.13060547623)
	tmp = 0
	if z <= -1.04e+74:
		tmp = t_2
	elif z <= -8.8e-7:
		tmp = x + (y / (((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771) / t_1))
	elif z <= 1.7e+37:
		tmp = x + ((y * (t_1 + b)) / (0.607771387771 + (z * 11.9400905721)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(a + Float64(z * Float64(t + Float64(z * Float64(11.1667541262 + Float64(z * 3.13060547623)))))))
	t_2 = Float64(x + Float64(y * 3.13060547623))
	tmp = 0.0
	if (z <= -1.04e+74)
		tmp = t_2;
	elseif (z <= -8.8e-7)
		tmp = Float64(x + Float64(y / Float64(Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771) / t_1)));
	elseif (z <= 1.7e+37)
		tmp = Float64(x + Float64(Float64(y * Float64(t_1 + b)) / Float64(0.607771387771 + Float64(z * 11.9400905721))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (a + (z * (t + (z * (11.1667541262 + (z * 3.13060547623))))));
	t_2 = x + (y * 3.13060547623);
	tmp = 0.0;
	if (z <= -1.04e+74)
		tmp = t_2;
	elseif (z <= -8.8e-7)
		tmp = x + (y / (((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771) / t_1));
	elseif (z <= 1.7e+37)
		tmp = x + ((y * (t_1 + b)) / (0.607771387771 + (z * 11.9400905721)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(a + N[(z * N[(t + N[(z * N[(11.1667541262 + N[(z * 3.13060547623), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.04e+74], t$95$2, If[LessEqual[z, -8.8e-7], N[(x + N[(y / N[(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] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.7e+37], N[(x + N[(N[(y * N[(t$95$1 + b), $MachinePrecision]), $MachinePrecision] / N[(0.607771387771 + N[(z * 11.9400905721), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.04e74 or 1.70000000000000003e37 < z

   1. Initial program 3.3%

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

      1. associate-*l/ 2.3%

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

      2. *-commutative 2.3%

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

      3. fma-def 2.3%

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

      4. *-commutative 2.3%

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

      5. fma-def 2.3%

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

      6. *-commutative 2.3%

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

      7. fma-def 2.3%

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

      8. *-commutative 2.3%

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

      9. fma-def 2.3%

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

   3. Simplified 2.3%

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

   4. Taylor expanded in z around inf 96.7%

      \[\leadsto x + \color{blue}{3.13060547623 \cdot y} \]
   5. Step-by-step derivation

      1. *-commutative 96.7%

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

   6. Simplified 96.7%

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

   if -1.04e74 < z < -8.8000000000000004e-7

   1. Initial program 72.2%

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

      1. associate-/l* 77.7%

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

      2. fma-def 77.7%

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

      3. fma-def 77.7%

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

      4. fma-def 77.8%

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

      5. fma-def 77.8%

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

      6. fma-def 77.8%

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

      7. fma-def 77.8%

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

      8. fma-def 77.8%

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

   3. Simplified 77.8%

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

   4. Taylor expanded in b around 0 71.9%

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

   if -8.8000000000000004e-7 < z < 1.70000000000000003e37

   1. Initial program 99.1%

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

   2. Taylor expanded in z around 0 96.9%

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

      1. *-commutative 91.1%

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

   4. Simplified 96.9%

      \[\leadsto x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\color{blue}{z \cdot 11.9400905721} + 0.607771387771} \]
3. Recombined 3 regimes into one program.

4. Final simplification 95.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.04 \cdot 10^{+74}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{elif}\;z \leq -8.8 \cdot 10^{-7}:\\ \;\;\;\;x + \frac{y}{\frac{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}{z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\right)\right)}}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+37}:\\ \;\;\;\;x + \frac{y \cdot \left(z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\right)\right) + b\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \]

Alternative 6: 93.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -13:\\ \;\;\;\;x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 - \frac{3.241970391368047 + t \cdot 0.10203362558171805}{z \cdot z}\right)}\\ \mathbf{elif}\;z \leq 7.9 \cdot 10^{+37}:\\ \;\;\;\;x + \frac{y \cdot \left(z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\right)\right) + b\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -13.0)
   (+
    x
    (/
     y
     (+
      (/ 3.7269864963038164 z)
      (-
       0.31942702700572795
       (/ (+ 3.241970391368047 (* t 0.10203362558171805)) (* z z))))))
   (if (<= z 7.9e+37)
     (+
      x
      (/
       (*
        y
        (+
         (* z (+ a (* z (+ t (* z (+ 11.1667541262 (* z 3.13060547623)))))))
         b))
       (+ 0.607771387771 (* z 11.9400905721))))
     (+ x (* y 3.13060547623)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -13.0) {
		tmp = x + (y / ((3.7269864963038164 / z) + (0.31942702700572795 - ((3.241970391368047 + (t * 0.10203362558171805)) / (z * z)))));
	} else if (z <= 7.9e+37) {
		tmp = x + ((y * ((z * (a + (z * (t + (z * (11.1667541262 + (z * 3.13060547623))))))) + b)) / (0.607771387771 + (z * 11.9400905721)));
	} else {
		tmp = x + (y * 3.13060547623);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-13.0d0)) then
        tmp = x + (y / ((3.7269864963038164d0 / z) + (0.31942702700572795d0 - ((3.241970391368047d0 + (t * 0.10203362558171805d0)) / (z * z)))))
    else if (z <= 7.9d+37) then
        tmp = x + ((y * ((z * (a + (z * (t + (z * (11.1667541262d0 + (z * 3.13060547623d0))))))) + b)) / (0.607771387771d0 + (z * 11.9400905721d0)))
    else
        tmp = x + (y * 3.13060547623d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -13.0) {
		tmp = x + (y / ((3.7269864963038164 / z) + (0.31942702700572795 - ((3.241970391368047 + (t * 0.10203362558171805)) / (z * z)))));
	} else if (z <= 7.9e+37) {
		tmp = x + ((y * ((z * (a + (z * (t + (z * (11.1667541262 + (z * 3.13060547623))))))) + b)) / (0.607771387771 + (z * 11.9400905721)));
	} else {
		tmp = x + (y * 3.13060547623);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -13.0:
		tmp = x + (y / ((3.7269864963038164 / z) + (0.31942702700572795 - ((3.241970391368047 + (t * 0.10203362558171805)) / (z * z)))))
	elif z <= 7.9e+37:
		tmp = x + ((y * ((z * (a + (z * (t + (z * (11.1667541262 + (z * 3.13060547623))))))) + b)) / (0.607771387771 + (z * 11.9400905721)))
	else:
		tmp = x + (y * 3.13060547623)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -13.0)
		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 <= 7.9e+37)
		tmp = Float64(x + Float64(Float64(y * Float64(Float64(z * Float64(a + Float64(z * Float64(t + Float64(z * Float64(11.1667541262 + Float64(z * 3.13060547623))))))) + b)) / Float64(0.607771387771 + Float64(z * 11.9400905721))));
	else
		tmp = Float64(x + Float64(y * 3.13060547623));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -13.0)
		tmp = x + (y / ((3.7269864963038164 / z) + (0.31942702700572795 - ((3.241970391368047 + (t * 0.10203362558171805)) / (z * z)))));
	elseif (z <= 7.9e+37)
		tmp = x + ((y * ((z * (a + (z * (t + (z * (11.1667541262 + (z * 3.13060547623))))))) + b)) / (0.607771387771 + (z * 11.9400905721)));
	else
		tmp = x + (y * 3.13060547623);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -13.0], 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, 7.9e+37], N[(x + N[(N[(y * N[(N[(z * N[(a + N[(z * N[(t + N[(z * N[(11.1667541262 + N[(z * 3.13060547623), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(0.607771387771 + N[(z * 11.9400905721), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -13

   1. Initial program 18.2%

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

      1. associate-/l* 19.7%

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

      2. fma-def 19.7%

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

      3. fma-def 19.7%

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

      4. fma-def 19.7%

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

      5. fma-def 19.7%

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

      6. fma-def 19.7%

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

      7. fma-def 19.7%

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

      8. fma-def 19.7%

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

   3. Simplified 19.7%

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

   4. Taylor expanded in z around inf 85.8%

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

      1. associate-*r/ 85.8%

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

      2. metadata-eval 85.8%

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

      3. mul-1-neg 85.8%

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

      4. *-commutative 85.8%

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

      5. unpow2 85.8%

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

   6. Simplified 85.8%

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

   if -13 < z < 7.9000000000000001e37

   1. Initial program 99.1%

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

   2. Taylor expanded in z around 0 96.4%

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

      1. *-commutative 90.5%

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

   4. Simplified 96.4%

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

   if 7.9000000000000001e37 < z

   1. Initial program 6.7%

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

      1. associate-*l/ 4.7%

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

      2. *-commutative 4.7%

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

      3. fma-def 4.7%

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

      4. *-commutative 4.7%

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

      5. fma-def 4.7%

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

      6. *-commutative 4.7%

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

      7. fma-def 4.7%

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

      8. *-commutative 4.7%

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

      9. fma-def 4.7%

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

   3. Simplified 4.7%

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

   4. Taylor expanded in z around inf 93.5%

      \[\leadsto x + \color{blue}{3.13060547623 \cdot y} \]
   5. Step-by-step derivation

      1. *-commutative 93.5%

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

   6. Simplified 93.5%

      \[\leadsto x + \color{blue}{y \cdot 3.13060547623} \]
3. Recombined 3 regimes into one program.

4. Final simplification 93.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -13:\\ \;\;\;\;x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 - \frac{3.241970391368047 + t \cdot 0.10203362558171805}{z \cdot z}\right)}\\ \mathbf{elif}\;z \leq 7.9 \cdot 10^{+37}:\\ \;\;\;\;x + \frac{y \cdot \left(z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\right)\right) + b\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \]

Alternative 7: 91.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.05 \cdot 10^{+68} \lor \neg \left(z \leq 1.52 \cdot 10^{+26}\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot a\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -4.05e+68) (not (<= z 1.52e+26)))
   (+ x (* y 3.13060547623))
   (+
    x
    (/
     (* y (+ b (* z a)))
     (+
      (* z (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721))
      0.607771387771)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -4.05e+68) || !(z <= 1.52e+26)) {
		tmp = x + (y * 3.13060547623);
	} else {
		tmp = x + ((y * (b + (z * a))) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771));
	}
	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 <= (-4.05d+68)) .or. (.not. (z <= 1.52d+26))) then
        tmp = x + (y * 3.13060547623d0)
    else
        tmp = x + ((y * (b + (z * a))) / ((z * ((z * ((z * (z + 15.234687407d0)) + 31.4690115749d0)) + 11.9400905721d0)) + 0.607771387771d0))
    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 <= -4.05e+68) || !(z <= 1.52e+26)) {
		tmp = x + (y * 3.13060547623);
	} else {
		tmp = x + ((y * (b + (z * a))) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -4.05e+68) or not (z <= 1.52e+26):
		tmp = x + (y * 3.13060547623)
	else:
		tmp = x + ((y * (b + (z * a))) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -4.05e+68) || !(z <= 1.52e+26))
		tmp = Float64(x + Float64(y * 3.13060547623));
	else
		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)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -4.05e+68) || ~((z <= 1.52e+26)))
		tmp = x + (y * 3.13060547623);
	else
		tmp = x + ((y * (b + (z * a))) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -4.05e+68], N[Not[LessEqual[z, 1.52e+26]], $MachinePrecision]], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision], 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]]

Derivation

1. Split input into 2 regimes

2. if z < -4.0500000000000001e68 or 1.52e26 < z

   1. Initial program 5.4%

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

      1. associate-*l/ 4.5%

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

      2. *-commutative 4.5%

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

      3. fma-def 4.5%

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

      4. *-commutative 4.5%

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

      5. fma-def 4.5%

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

      6. *-commutative 4.5%

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

      7. fma-def 4.5%

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

      8. *-commutative 4.5%

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

      9. fma-def 4.5%

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

   3. Simplified 4.5%

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

   4. Taylor expanded in z around inf 94.8%

      \[\leadsto x + \color{blue}{3.13060547623 \cdot y} \]
   5. Step-by-step derivation

      1. *-commutative 94.8%

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

   6. Simplified 94.8%

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

   if -4.0500000000000001e68 < z < 1.52e26

   1. Initial program 96.9%

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

   2. Taylor expanded in z around 0 88.3%

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

      1. associate-*r* 86.0%

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

      2. *-commutative 86.0%

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

      3. associate-*r* 89.4%

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

      4. distribute-lft-out 90.7%

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

      5. *-commutative 90.7%

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

   4. Simplified 90.7%

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

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.05 \cdot 10^{+68} \lor \neg \left(z \leq 1.52 \cdot 10^{+26}\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot a\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\\ \end{array} \]

Alternative 8: 89.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.66 \cdot 10^{-19}:\\ \;\;\;\;x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 - \frac{3.241970391368047 + t \cdot 0.10203362558171805}{z \cdot z}\right)}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+23}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot a\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.66e-19)
   (+
    x
    (/
     y
     (+
      (/ 3.7269864963038164 z)
      (-
       0.31942702700572795
       (/ (+ 3.241970391368047 (* t 0.10203362558171805)) (* z z))))))
   (if (<= z 1.5e+23)
     (+ x (/ (* y (+ b (* z a))) (+ 0.607771387771 (* z 11.9400905721))))
     (+ x (* y 3.13060547623)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.66e-19) {
		tmp = x + (y / ((3.7269864963038164 / z) + (0.31942702700572795 - ((3.241970391368047 + (t * 0.10203362558171805)) / (z * z)))));
	} else if (z <= 1.5e+23) {
		tmp = x + ((y * (b + (z * a))) / (0.607771387771 + (z * 11.9400905721)));
	} else {
		tmp = x + (y * 3.13060547623);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-1.66d-19)) then
        tmp = x + (y / ((3.7269864963038164d0 / z) + (0.31942702700572795d0 - ((3.241970391368047d0 + (t * 0.10203362558171805d0)) / (z * z)))))
    else if (z <= 1.5d+23) then
        tmp = x + ((y * (b + (z * a))) / (0.607771387771d0 + (z * 11.9400905721d0)))
    else
        tmp = x + (y * 3.13060547623d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.66e-19) {
		tmp = x + (y / ((3.7269864963038164 / z) + (0.31942702700572795 - ((3.241970391368047 + (t * 0.10203362558171805)) / (z * z)))));
	} else if (z <= 1.5e+23) {
		tmp = x + ((y * (b + (z * a))) / (0.607771387771 + (z * 11.9400905721)));
	} else {
		tmp = x + (y * 3.13060547623);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.66e-19:
		tmp = x + (y / ((3.7269864963038164 / z) + (0.31942702700572795 - ((3.241970391368047 + (t * 0.10203362558171805)) / (z * z)))))
	elif z <= 1.5e+23:
		tmp = x + ((y * (b + (z * a))) / (0.607771387771 + (z * 11.9400905721)))
	else:
		tmp = x + (y * 3.13060547623)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.66e-19)
		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 <= 1.5e+23)
		tmp = Float64(x + Float64(Float64(y * Float64(b + Float64(z * a))) / Float64(0.607771387771 + Float64(z * 11.9400905721))));
	else
		tmp = Float64(x + Float64(y * 3.13060547623));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1.66e-19)
		tmp = x + (y / ((3.7269864963038164 / z) + (0.31942702700572795 - ((3.241970391368047 + (t * 0.10203362558171805)) / (z * z)))));
	elseif (z <= 1.5e+23)
		tmp = x + ((y * (b + (z * a))) / (0.607771387771 + (z * 11.9400905721)));
	else
		tmp = x + (y * 3.13060547623);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.66e-19], 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, 1.5e+23], N[(x + N[(N[(y * N[(b + N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(0.607771387771 + N[(z * 11.9400905721), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.65999999999999998e-19

   1. Initial program 20.7%

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

      1. associate-/l* 22.2%

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

      2. fma-def 22.2%

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

      3. fma-def 22.2%

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

      4. fma-def 22.2%

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

      5. fma-def 22.2%

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

      6. fma-def 22.2%

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

      7. fma-def 22.2%

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

      8. fma-def 22.2%

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

   3. Simplified 22.2%

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

   4. Taylor expanded in z around inf 83.4%

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

      1. associate-*r/ 83.4%

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

      2. metadata-eval 83.4%

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

      3. mul-1-neg 83.4%

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

      4. *-commutative 83.4%

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

      5. unpow2 83.4%

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

   6. Simplified 83.4%

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

   if -1.65999999999999998e-19 < z < 1.5e23

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 92.4%

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

      1. associate-*r* 89.9%

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

      2. *-commutative 89.9%

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

      3. associate-*r* 93.7%

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

      4. distribute-lft-out 95.1%

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

      5. *-commutative 95.1%

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

   4. Simplified 95.1%

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

   5. Taylor expanded in z around 0 93.4%

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

      1. *-commutative 93.4%

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

   7. Simplified 93.4%

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

   if 1.5e23 < z

   1. Initial program 12.4%

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

      1. associate-*l/ 10.6%

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

      2. *-commutative 10.6%

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

      3. fma-def 10.6%

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

      4. *-commutative 10.6%

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

      5. fma-def 10.6%

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

      6. *-commutative 10.6%

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

      7. fma-def 10.6%

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

      8. *-commutative 10.6%

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

      9. fma-def 10.6%

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

   3. Simplified 10.6%

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

   4. Taylor expanded in z around inf 88.1%

      \[\leadsto x + \color{blue}{3.13060547623 \cdot y} \]
   5. Step-by-step derivation

      1. *-commutative 88.1%

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

   6. Simplified 88.1%

      \[\leadsto x + \color{blue}{y \cdot 3.13060547623} \]
3. Recombined 3 regimes into one program.

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.66 \cdot 10^{-19}:\\ \;\;\;\;x + \frac{y}{\frac{3.7269864963038164}{z} + \left(0.31942702700572795 - \frac{3.241970391368047 + t \cdot 0.10203362558171805}{z \cdot z}\right)}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+23}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot a\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \]

Alternative 9: 89.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+38} \lor \neg \left(z \leq 4.5 \cdot 10^{+22}\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot \left(b \cdot 1.6453555072203998\right) + y \cdot \left(\left(z \cdot a\right) \cdot 1.6453555072203998\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1e+38) (not (<= z 4.5e+22)))
   (+ x (* y 3.13060547623))
   (+
    x
    (+ (* y (* b 1.6453555072203998)) (* y (* (* z a) 1.6453555072203998))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1e+38) || !(z <= 4.5e+22)) {
		tmp = x + (y * 3.13060547623);
	} else {
		tmp = x + ((y * (b * 1.6453555072203998)) + (y * ((z * a) * 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 <= (-1d+38)) .or. (.not. (z <= 4.5d+22))) then
        tmp = x + (y * 3.13060547623d0)
    else
        tmp = x + ((y * (b * 1.6453555072203998d0)) + (y * ((z * a) * 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 <= -1e+38) || !(z <= 4.5e+22)) {
		tmp = x + (y * 3.13060547623);
	} else {
		tmp = x + ((y * (b * 1.6453555072203998)) + (y * ((z * a) * 1.6453555072203998)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1e+38) or not (z <= 4.5e+22):
		tmp = x + (y * 3.13060547623)
	else:
		tmp = x + ((y * (b * 1.6453555072203998)) + (y * ((z * a) * 1.6453555072203998)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1e+38) || !(z <= 4.5e+22))
		tmp = Float64(x + Float64(y * 3.13060547623));
	else
		tmp = Float64(x + Float64(Float64(y * Float64(b * 1.6453555072203998)) + Float64(y * Float64(Float64(z * a) * 1.6453555072203998))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1e+38) || ~((z <= 4.5e+22)))
		tmp = x + (y * 3.13060547623);
	else
		tmp = x + ((y * (b * 1.6453555072203998)) + (y * ((z * a) * 1.6453555072203998)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1e+38], N[Not[LessEqual[z, 4.5e+22]], $MachinePrecision]], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * N[(b * 1.6453555072203998), $MachinePrecision]), $MachinePrecision] + N[(y * N[(N[(z * a), $MachinePrecision] * 1.6453555072203998), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.99999999999999977e37 or 4.4999999999999998e22 < z

   1. Initial program 8.3%

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

      1. associate-*l/ 7.4%

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

      2. *-commutative 7.4%

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

      3. fma-def 7.4%

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

      4. *-commutative 7.4%

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

      5. fma-def 7.4%

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

      6. *-commutative 7.4%

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

      7. fma-def 7.4%

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

      8. *-commutative 7.4%

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

      9. fma-def 7.4%

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

   3. Simplified 7.4%

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

   4. Taylor expanded in z around inf 91.2%

      \[\leadsto x + \color{blue}{3.13060547623 \cdot y} \]
   5. Step-by-step derivation

      1. *-commutative 91.2%

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

   6. Simplified 91.2%

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

   if -9.99999999999999977e37 < z < 4.4999999999999998e22

   1. Initial program 98.5%

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

   2. Taylor expanded in z around 0 89.6%

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

      1. associate-*r* 87.3%

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

      2. *-commutative 87.3%

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

      3. associate-*r* 90.8%

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

      4. distribute-lft-out 92.1%

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

      5. *-commutative 92.1%

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

   4. Simplified 92.1%

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

   5. Taylor expanded in b around inf 90.8%

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

   6. Taylor expanded in z around 0 88.4%

      \[\leadsto x + \left(\frac{y \cdot b}{0.607771387771 + \left(11.9400905721 + z \cdot \left(31.4690115749 + \left(15.234687407 + z\right) \cdot z\right)\right) \cdot z} + \color{blue}{1.6453555072203998 \cdot \left(y \cdot \left(a \cdot z\right)\right)}\right) \]
   7. Step-by-step derivation

      1. *-commutative 88.4%

         \[\leadsto x + \left(\frac{y \cdot b}{0.607771387771 + \left(11.9400905721 + z \cdot \left(31.4690115749 + \left(15.234687407 + z\right) \cdot z\right)\right) \cdot z} + \color{blue}{\left(y \cdot \left(a \cdot z\right)\right) \cdot 1.6453555072203998}\right) \]

      2. associate-*l* 88.3%

         \[\leadsto x + \left(\frac{y \cdot b}{0.607771387771 + \left(11.9400905721 + z \cdot \left(31.4690115749 + \left(15.234687407 + z\right) \cdot z\right)\right) \cdot z} + \color{blue}{y \cdot \left(\left(a \cdot z\right) \cdot 1.6453555072203998\right)}\right) \]

   8. Simplified 88.3%

      \[\leadsto x + \left(\frac{y \cdot b}{0.607771387771 + \left(11.9400905721 + z \cdot \left(31.4690115749 + \left(15.234687407 + z\right) \cdot z\right)\right) \cdot z} + \color{blue}{y \cdot \left(\left(a \cdot z\right) \cdot 1.6453555072203998\right)}\right) \]

   9. Taylor expanded in z around 0 87.7%

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

       1. associate-*r* 87.7%

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

       2. *-commutative 87.7%

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

       3. associate-*l* 87.7%

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

   11. Simplified 87.7%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+38} \lor \neg \left(z \leq 4.5 \cdot 10^{+22}\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot \left(b \cdot 1.6453555072203998\right) + y \cdot \left(\left(z \cdot a\right) \cdot 1.6453555072203998\right)\right)\\ \end{array} \]

Alternative 10: 90.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.085:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 - \frac{y \cdot 36.52704169880642}{z}\right)\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+22}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot a\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -0.085)
   (+ x (- (* y 3.13060547623) (/ (* y 36.52704169880642) z)))
   (if (<= z 6e+22)
     (+ x (/ (* y (+ b (* z a))) (+ 0.607771387771 (* z 11.9400905721))))
     (+ x (* y 3.13060547623)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -0.085) {
		tmp = x + ((y * 3.13060547623) - ((y * 36.52704169880642) / z));
	} else if (z <= 6e+22) {
		tmp = x + ((y * (b + (z * a))) / (0.607771387771 + (z * 11.9400905721)));
	} else {
		tmp = x + (y * 3.13060547623);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-0.085d0)) then
        tmp = x + ((y * 3.13060547623d0) - ((y * 36.52704169880642d0) / z))
    else if (z <= 6d+22) then
        tmp = x + ((y * (b + (z * a))) / (0.607771387771d0 + (z * 11.9400905721d0)))
    else
        tmp = x + (y * 3.13060547623d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -0.085) {
		tmp = x + ((y * 3.13060547623) - ((y * 36.52704169880642) / z));
	} else if (z <= 6e+22) {
		tmp = x + ((y * (b + (z * a))) / (0.607771387771 + (z * 11.9400905721)));
	} else {
		tmp = x + (y * 3.13060547623);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -0.085:
		tmp = x + ((y * 3.13060547623) - ((y * 36.52704169880642) / z))
	elif z <= 6e+22:
		tmp = x + ((y * (b + (z * a))) / (0.607771387771 + (z * 11.9400905721)))
	else:
		tmp = x + (y * 3.13060547623)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -0.085)
		tmp = Float64(x + Float64(Float64(y * 3.13060547623) - Float64(Float64(y * 36.52704169880642) / z)));
	elseif (z <= 6e+22)
		tmp = Float64(x + Float64(Float64(y * Float64(b + Float64(z * a))) / Float64(0.607771387771 + Float64(z * 11.9400905721))));
	else
		tmp = Float64(x + Float64(y * 3.13060547623));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -0.085)
		tmp = x + ((y * 3.13060547623) - ((y * 36.52704169880642) / z));
	elseif (z <= 6e+22)
		tmp = x + ((y * (b + (z * a))) / (0.607771387771 + (z * 11.9400905721)));
	else
		tmp = x + (y * 3.13060547623);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -0.085], N[(x + N[(N[(y * 3.13060547623), $MachinePrecision] - N[(N[(y * 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6e+22], N[(x + N[(N[(y * N[(b + N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(0.607771387771 + N[(z * 11.9400905721), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.0850000000000000061

   1. Initial program 19.5%

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

      1. associate-*l/ 20.8%

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

      2. *-commutative 20.8%

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

      3. fma-def 20.8%

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

      4. *-commutative 20.8%

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

      5. fma-def 20.8%

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

      6. *-commutative 20.8%

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

      7. fma-def 20.8%

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

      8. *-commutative 20.8%

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

      9. fma-def 20.8%

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

   3. Simplified 20.8%

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

   4. Taylor expanded in z around -inf 84.6%

      \[\leadsto x + \color{blue}{\left(-1 \cdot \frac{-11.1667541262 \cdot y - -47.69379582500642 \cdot y}{z} + 3.13060547623 \cdot y\right)} \]
   5. Step-by-step derivation

      1. +-commutative 84.6%

         \[\leadsto x + \color{blue}{\left(3.13060547623 \cdot y + -1 \cdot \frac{-11.1667541262 \cdot y - -47.69379582500642 \cdot y}{z}\right)} \]

      2. mul-1-neg 84.6%

         \[\leadsto x + \left(3.13060547623 \cdot y + \color{blue}{\left(-\frac{-11.1667541262 \cdot y - -47.69379582500642 \cdot y}{z}\right)}\right) \]

      3. unsub-neg 84.6%

         \[\leadsto x + \color{blue}{\left(3.13060547623 \cdot y - \frac{-11.1667541262 \cdot y - -47.69379582500642 \cdot y}{z}\right)} \]

      4. *-commutative 84.6%

         \[\leadsto x + \left(\color{blue}{y \cdot 3.13060547623} - \frac{-11.1667541262 \cdot y - -47.69379582500642 \cdot y}{z}\right) \]

      5. distribute-rgt-out-- 84.6%

         \[\leadsto x + \left(y \cdot 3.13060547623 - \frac{\color{blue}{y \cdot \left(-11.1667541262 - -47.69379582500642\right)}}{z}\right) \]

      6. metadata-eval 84.6%

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

   6. Simplified 84.6%

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

   if -0.0850000000000000061 < z < 6e22

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 91.8%

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

      1. associate-*r* 89.3%

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

      2. *-commutative 89.3%

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

      3. associate-*r* 93.1%

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

      4. distribute-lft-out 94.5%

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

      5. *-commutative 94.5%

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

   4. Simplified 94.5%

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

   5. Taylor expanded in z around 0 92.8%

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

      1. *-commutative 92.8%

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

   7. Simplified 92.8%

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

   if 6e22 < z

   1. Initial program 12.4%

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

      1. associate-*l/ 10.6%

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

      2. *-commutative 10.6%

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

      3. fma-def 10.6%

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

      4. *-commutative 10.6%

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

      5. fma-def 10.6%

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

      6. *-commutative 10.6%

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

      7. fma-def 10.6%

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

      8. *-commutative 10.6%

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

      9. fma-def 10.6%

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

   3. Simplified 10.6%

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

   4. Taylor expanded in z around inf 88.1%

      \[\leadsto x + \color{blue}{3.13060547623 \cdot y} \]
   5. Step-by-step derivation

      1. *-commutative 88.1%

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

   6. Simplified 88.1%

      \[\leadsto x + \color{blue}{y \cdot 3.13060547623} \]
3. Recombined 3 regimes into one program.

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.085:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 - \frac{y \cdot 36.52704169880642}{z}\right)\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+22}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot a\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \]

Alternative 11: 84.0% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.085:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 - \frac{y \cdot 36.52704169880642}{z}\right)\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+22}:\\ \;\;\;\;x + \left(y \cdot b\right) \cdot \frac{1}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -0.085)
   (+ x (- (* y 3.13060547623) (/ (* y 36.52704169880642) z)))
   (if (<= z 7.2e+22)
     (+ x (* (* y b) (/ 1.0 (+ 0.607771387771 (* z 11.9400905721)))))
     (+ x (* y 3.13060547623)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -0.085) {
		tmp = x + ((y * 3.13060547623) - ((y * 36.52704169880642) / z));
	} else if (z <= 7.2e+22) {
		tmp = x + ((y * b) * (1.0 / (0.607771387771 + (z * 11.9400905721))));
	} else {
		tmp = x + (y * 3.13060547623);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-0.085d0)) then
        tmp = x + ((y * 3.13060547623d0) - ((y * 36.52704169880642d0) / z))
    else if (z <= 7.2d+22) then
        tmp = x + ((y * b) * (1.0d0 / (0.607771387771d0 + (z * 11.9400905721d0))))
    else
        tmp = x + (y * 3.13060547623d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -0.085) {
		tmp = x + ((y * 3.13060547623) - ((y * 36.52704169880642) / z));
	} else if (z <= 7.2e+22) {
		tmp = x + ((y * b) * (1.0 / (0.607771387771 + (z * 11.9400905721))));
	} else {
		tmp = x + (y * 3.13060547623);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -0.085:
		tmp = x + ((y * 3.13060547623) - ((y * 36.52704169880642) / z))
	elif z <= 7.2e+22:
		tmp = x + ((y * b) * (1.0 / (0.607771387771 + (z * 11.9400905721))))
	else:
		tmp = x + (y * 3.13060547623)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -0.085)
		tmp = Float64(x + Float64(Float64(y * 3.13060547623) - Float64(Float64(y * 36.52704169880642) / z)));
	elseif (z <= 7.2e+22)
		tmp = Float64(x + Float64(Float64(y * b) * Float64(1.0 / Float64(0.607771387771 + Float64(z * 11.9400905721)))));
	else
		tmp = Float64(x + Float64(y * 3.13060547623));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -0.085)
		tmp = x + ((y * 3.13060547623) - ((y * 36.52704169880642) / z));
	elseif (z <= 7.2e+22)
		tmp = x + ((y * b) * (1.0 / (0.607771387771 + (z * 11.9400905721))));
	else
		tmp = x + (y * 3.13060547623);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -0.085], N[(x + N[(N[(y * 3.13060547623), $MachinePrecision] - N[(N[(y * 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.2e+22], N[(x + N[(N[(y * b), $MachinePrecision] * N[(1.0 / N[(0.607771387771 + N[(z * 11.9400905721), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.0850000000000000061

   1. Initial program 19.5%

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

      1. associate-*l/ 20.8%

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

      2. *-commutative 20.8%

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

      3. fma-def 20.8%

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

      4. *-commutative 20.8%

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

      5. fma-def 20.8%

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

      6. *-commutative 20.8%

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

      7. fma-def 20.8%

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

      8. *-commutative 20.8%

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

      9. fma-def 20.8%

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

   3. Simplified 20.8%

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

   4. Taylor expanded in z around -inf 84.6%

      \[\leadsto x + \color{blue}{\left(-1 \cdot \frac{-11.1667541262 \cdot y - -47.69379582500642 \cdot y}{z} + 3.13060547623 \cdot y\right)} \]
   5. Step-by-step derivation

      1. +-commutative 84.6%

         \[\leadsto x + \color{blue}{\left(3.13060547623 \cdot y + -1 \cdot \frac{-11.1667541262 \cdot y - -47.69379582500642 \cdot y}{z}\right)} \]

      2. mul-1-neg 84.6%

         \[\leadsto x + \left(3.13060547623 \cdot y + \color{blue}{\left(-\frac{-11.1667541262 \cdot y - -47.69379582500642 \cdot y}{z}\right)}\right) \]

      3. unsub-neg 84.6%

         \[\leadsto x + \color{blue}{\left(3.13060547623 \cdot y - \frac{-11.1667541262 \cdot y - -47.69379582500642 \cdot y}{z}\right)} \]

      4. *-commutative 84.6%

         \[\leadsto x + \left(\color{blue}{y \cdot 3.13060547623} - \frac{-11.1667541262 \cdot y - -47.69379582500642 \cdot y}{z}\right) \]

      5. distribute-rgt-out-- 84.6%

         \[\leadsto x + \left(y \cdot 3.13060547623 - \frac{\color{blue}{y \cdot \left(-11.1667541262 - -47.69379582500642\right)}}{z}\right) \]

      6. metadata-eval 84.6%

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

   6. Simplified 84.6%

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

   if -0.0850000000000000061 < z < 7.2e22

   1. Initial program 99.8%

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

      1. associate-/l* 99.7%

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

      2. fma-def 99.7%

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

      3. fma-def 99.7%

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

      4. fma-def 99.7%

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

      5. fma-def 99.8%

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

      6. fma-def 99.8%

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

      7. fma-def 99.8%

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

      8. fma-def 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around 0 81.1%

      \[\leadsto x + \frac{y}{\color{blue}{\left(11.9400905721 \cdot \frac{1}{b} - 0.607771387771 \cdot \frac{a}{{b}^{2}}\right) \cdot z + 0.607771387771 \cdot \frac{1}{b}}} \]

   5. Taylor expanded in b around inf 81.9%

      \[\leadsto x + \color{blue}{\frac{y \cdot b}{0.607771387771 + 11.9400905721 \cdot z}} \]
   6. Step-by-step derivation

      1. div-inv 81.9%

         \[\leadsto x + \color{blue}{\left(y \cdot b\right) \cdot \frac{1}{0.607771387771 + 11.9400905721 \cdot z}} \]

      2. *-commutative 81.9%

         \[\leadsto x + \left(y \cdot b\right) \cdot \frac{1}{0.607771387771 + \color{blue}{z \cdot 11.9400905721}} \]

   7. Applied egg-rr 81.9%

      \[\leadsto x + \color{blue}{\left(y \cdot b\right) \cdot \frac{1}{0.607771387771 + z \cdot 11.9400905721}} \]

   if 7.2e22 < z

   1. Initial program 12.4%

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

      1. associate-*l/ 10.6%

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

      2. *-commutative 10.6%

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

      3. fma-def 10.6%

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

      4. *-commutative 10.6%

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

      5. fma-def 10.6%

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

      6. *-commutative 10.6%

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

      7. fma-def 10.6%

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

      8. *-commutative 10.6%

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

      9. fma-def 10.6%

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

   3. Simplified 10.6%

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

   4. Taylor expanded in z around inf 88.1%

      \[\leadsto x + \color{blue}{3.13060547623 \cdot y} \]
   5. Step-by-step derivation

      1. *-commutative 88.1%

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

   6. Simplified 88.1%

      \[\leadsto x + \color{blue}{y \cdot 3.13060547623} \]
3. Recombined 3 regimes into one program.

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.085:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 - \frac{y \cdot 36.52704169880642}{z}\right)\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+22}:\\ \;\;\;\;x + \left(y \cdot b\right) \cdot \frac{1}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \]

Alternative 12: 83.9% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+21} \lor \neg \left(z \leq 4.5 \cdot 10^{+22}\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x + 1.6453555072203998 \cdot \left(y \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -6.5e+21) (not (<= z 4.5e+22)))
   (+ x (* y 3.13060547623))
   (+ x (* 1.6453555072203998 (* y b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -6.5e+21) || !(z <= 4.5e+22)) {
		tmp = x + (y * 3.13060547623);
	} 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 <= (-6.5d+21)) .or. (.not. (z <= 4.5d+22))) then
        tmp = x + (y * 3.13060547623d0)
    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 <= -6.5e+21) || !(z <= 4.5e+22)) {
		tmp = x + (y * 3.13060547623);
	} else {
		tmp = x + (1.6453555072203998 * (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -6.5e+21) or not (z <= 4.5e+22):
		tmp = x + (y * 3.13060547623)
	else:
		tmp = x + (1.6453555072203998 * (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -6.5e+21) || !(z <= 4.5e+22))
		tmp = Float64(x + Float64(y * 3.13060547623));
	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 <= -6.5e+21) || ~((z <= 4.5e+22)))
		tmp = x + (y * 3.13060547623);
	else
		tmp = x + (1.6453555072203998 * (y * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -6.5e+21], N[Not[LessEqual[z, 4.5e+22]], $MachinePrecision]], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision], N[(x + N[(1.6453555072203998 * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.5e21 or 4.4999999999999998e22 < z

   1. Initial program 10.8%

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

      1. associate-*l/ 10.8%

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

      2. *-commutative 10.8%

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

      3. fma-def 10.8%

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

      4. *-commutative 10.8%

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

      5. fma-def 10.8%

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

      6. *-commutative 10.8%

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

      7. fma-def 10.8%

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

      8. *-commutative 10.8%

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

      9. fma-def 10.8%

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

   3. Simplified 10.8%

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

   4. Taylor expanded in z around inf 88.0%

      \[\leadsto x + \color{blue}{3.13060547623 \cdot y} \]
   5. Step-by-step derivation

      1. *-commutative 88.0%

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

   6. Simplified 88.0%

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

   if -6.5e21 < z < 4.4999999999999998e22

   1. Initial program 99.8%

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

      1. associate-*l/ 99.8%

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

      2. *-commutative 99.8%

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

      3. fma-def 99.8%

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

      4. *-commutative 99.8%

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

      5. fma-def 99.8%

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

      6. *-commutative 99.8%

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

      7. fma-def 99.8%

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

      8. *-commutative 99.8%

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

      9. fma-def 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around 0 80.8%

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

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+21} \lor \neg \left(z \leq 4.5 \cdot 10^{+22}\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x + 1.6453555072203998 \cdot \left(y \cdot b\right)\\ \end{array} \]

Alternative 13: 64.2% accurate, 4.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{-66} \lor \neg \left(z \leq 8.8 \cdot 10^{-64}\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -6e-66) (not (<= z 8.8e-64))) (+ x (* y 3.13060547623)) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -6e-66) || !(z <= 8.8e-64)) {
		tmp = x + (y * 3.13060547623);
	} else {
		tmp = x;
	}
	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 <= (-6d-66)) .or. (.not. (z <= 8.8d-64))) then
        tmp = x + (y * 3.13060547623d0)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -6e-66) || !(z <= 8.8e-64)) {
		tmp = x + (y * 3.13060547623);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -6e-66) or not (z <= 8.8e-64):
		tmp = x + (y * 3.13060547623)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -6e-66) || !(z <= 8.8e-64))
		tmp = Float64(x + Float64(y * 3.13060547623));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -6e-66) || ~((z <= 8.8e-64)))
		tmp = x + (y * 3.13060547623);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -6e-66], N[Not[LessEqual[z, 8.8e-64]], $MachinePrecision]], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -6.0000000000000004e-66 or 8.7999999999999998e-64 < z

   1. Initial program 35.4%

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

      1. associate-*l/ 35.3%

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

      2. *-commutative 35.3%

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

      3. fma-def 35.3%

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

      4. *-commutative 35.3%

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

      5. fma-def 35.3%

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

      6. *-commutative 35.3%

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

      7. fma-def 35.3%

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

      8. *-commutative 35.3%

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

      9. fma-def 35.3%

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

   3. Simplified 35.3%

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

   4. Taylor expanded in z around inf 76.4%

      \[\leadsto x + \color{blue}{3.13060547623 \cdot y} \]
   5. Step-by-step derivation

      1. *-commutative 76.4%

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

   6. Simplified 76.4%

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

   if -6.0000000000000004e-66 < z < 8.7999999999999998e-64

   1. Initial program 99.8%

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

      1. associate-/l* 99.7%

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

      2. fma-def 99.7%

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

      3. fma-def 99.7%

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

      4. fma-def 99.7%

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

      5. fma-def 99.8%

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

      6. fma-def 99.8%

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

      7. fma-def 99.8%

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

      8. fma-def 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around 0 86.0%

      \[\leadsto x + \frac{y}{\color{blue}{\left(11.9400905721 \cdot \frac{1}{b} - 0.607771387771 \cdot \frac{a}{{b}^{2}}\right) \cdot z + 0.607771387771 \cdot \frac{1}{b}}} \]

   5. Taylor expanded in b around inf 86.9%

      \[\leadsto x + \color{blue}{\frac{y \cdot b}{0.607771387771 + 11.9400905721 \cdot z}} \]

   6. Taylor expanded in x around inf 57.4%

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

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{-66} \lor \neg \left(z \leq 8.8 \cdot 10^{-64}\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 14: 45.0% 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 63.3%

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

   1. associate-/l* 63.6%

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

   2. fma-def 63.6%

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

   3. fma-def 63.6%

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

   4. fma-def 63.6%

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

   5. fma-def 63.6%

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

   6. fma-def 63.6%

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

   7. fma-def 63.6%

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

   8. fma-def 63.6%

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

3. Simplified 63.6%

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

4. Taylor expanded in z around 0 66.7%

   \[\leadsto x + \frac{y}{\color{blue}{\left(11.9400905721 \cdot \frac{1}{b} - 0.607771387771 \cdot \frac{a}{{b}^{2}}\right) \cdot z + 0.607771387771 \cdot \frac{1}{b}}} \]

5. Taylor expanded in b around inf 67.1%

   \[\leadsto x + \color{blue}{\frac{y \cdot b}{0.607771387771 + 11.9400905721 \cdot z}} \]

6. Taylor expanded in x around inf 51.9%

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

7. Final simplification 51.9%

   \[\leadsto x \]

Developer target: 98.5% 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 2023224 
(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))))