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

Percentage Accurate: 58.7% → 97.1%

Time: 20.0s

Alternatives: 18

Speedup: 5.2×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 58.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.1% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771} \leq \infty:\\ \;\;\;\;x + \frac{y}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)} \cdot \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(\mathsf{fma}\left(y, 3.13060547623, \frac{t}{\frac{{z}^{2}}{y}}\right) - \frac{y \cdot 36.52704169880642}{z}\right) - \mathsf{fma}\left(98.5170599679272, \frac{y}{{z}^{2}}, \frac{y \cdot -556.47806218377}{{z}^{2}}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<=
      (/
       (*
        y
        (+
         (* z (+ (* z (+ (* z (+ (* z 3.13060547623) 11.1667541262)) t)) a))
         b))
       (+
        (*
         z
         (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721))
        0.607771387771))
      INFINITY)
   (+
    x
    (*
     (/
      y
      (fma
       z
       (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721)
       0.607771387771))
     (fma z (fma z (fma z (fma z 3.13060547623 11.1667541262) t) a) b)))
   (+
    x
    (-
     (-
      (fma y 3.13060547623 (/ t (/ (pow z 2.0) y)))
      (/ (* y 36.52704169880642) z))
     (fma
      98.5170599679272
      (/ y (pow z 2.0))
      (/ (* y -556.47806218377) (pow z 2.0)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)) <= ((double) INFINITY)) {
		tmp = x + ((y / fma(z, fma(z, fma(z, (z + 15.234687407), 31.4690115749), 11.9400905721), 0.607771387771)) * fma(z, fma(z, fma(z, fma(z, 3.13060547623, 11.1667541262), t), a), b));
	} else {
		tmp = x + ((fma(y, 3.13060547623, (t / (pow(z, 2.0) / y))) - ((y * 36.52704169880642) / z)) - fma(98.5170599679272, (y / pow(z, 2.0)), ((y * -556.47806218377) / pow(z, 2.0))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(Float64(y * Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)) <= Inf)
		tmp = Float64(x + Float64(Float64(y / fma(z, fma(z, fma(z, Float64(z + 15.234687407), 31.4690115749), 11.9400905721), 0.607771387771)) * fma(z, fma(z, fma(z, fma(z, 3.13060547623, 11.1667541262), t), a), b)));
	else
		tmp = Float64(x + Float64(Float64(fma(y, 3.13060547623, Float64(t / Float64((z ^ 2.0) / y))) - Float64(Float64(y * 36.52704169880642) / z)) - fma(98.5170599679272, Float64(y / (z ^ 2.0)), Float64(Float64(y * -556.47806218377) / (z ^ 2.0)))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(N[(y * N[(N[(z * N[(N[(z * N[(N[(z * N[(N[(z * 3.13060547623), $MachinePrecision] + 11.1667541262), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(N[(z * N[(N[(z * N[(N[(z * N[(z + 15.234687407), $MachinePrecision]), $MachinePrecision] + 31.4690115749), $MachinePrecision]), $MachinePrecision] + 11.9400905721), $MachinePrecision]), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision], Infinity], N[(x + N[(N[(y / N[(z * N[(z * N[(z * N[(z + 15.234687407), $MachinePrecision] + 31.4690115749), $MachinePrecision] + 11.9400905721), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision] * N[(z * N[(z * N[(z * N[(z * 3.13060547623 + 11.1667541262), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(N[(y * 3.13060547623 + N[(t / N[(N[Power[z, 2.0], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y * 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] - N[(98.5170599679272 * N[(y / N[Power[z, 2.0], $MachinePrecision]), $MachinePrecision] + N[(N[(y * -556.47806218377), $MachinePrecision] / N[Power[z, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 93.2%

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

   3. Simplified 97.8%

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

   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. Taylor expanded in b around 0 0.0%

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

   3. Taylor expanded in z around 0 0.0%

      \[\leadsto x + \frac{b \cdot y + y \cdot \left(z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + 3.13060547623 \cdot z\right)\right)\right)\right)}{\left(\left(\color{blue}{\left(15.234687407 \cdot z + {z}^{2}\right)} + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

   4. Taylor expanded in z around -inf 85.6%

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

      1. +-commutative 85.6%

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

      2. mul-1-neg 85.6%

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

      3. unsub-neg 85.6%

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

      4. *-commutative 85.6%

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

      5. fma-def 85.6%

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

      6. associate-/l* 98.2%

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

      7. distribute-rgt-out-- 98.2%

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

      8. metadata-eval 98.2%

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

      9. +-commutative 98.2%

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

      10. fma-def 98.2%

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

      11. associate-*r/ 98.2%

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

   6. Simplified 98.2%

      \[\leadsto x + \color{blue}{\left(\left(\mathsf{fma}\left(y, 3.13060547623, \frac{t}{\frac{{z}^{2}}{y}}\right) - \frac{y \cdot 36.52704169880642}{z}\right) - \mathsf{fma}\left(98.5170599679272, \frac{y}{{z}^{2}}, \frac{y \cdot -556.47806218377}{{z}^{2}}\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 97.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771} \leq \infty:\\ \;\;\;\;x + \frac{y}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)} \cdot \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(\mathsf{fma}\left(y, 3.13060547623, \frac{t}{\frac{{z}^{2}}{y}}\right) - \frac{y \cdot 36.52704169880642}{z}\right) - \mathsf{fma}\left(98.5170599679272, \frac{y}{{z}^{2}}, \frac{y \cdot -556.47806218377}{{z}^{2}}\right)\right)\\ \end{array} \]

Alternative 2: 96.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+36}:\\ \;\;\;\;x + \left(\left(\mathsf{fma}\left(y, 3.13060547623, \frac{t}{\frac{{z}^{2}}{y}}\right) - \frac{y \cdot 36.52704169880642}{z}\right) - \mathsf{fma}\left(98.5170599679272, \frac{y}{{z}^{2}}, \frac{y \cdot -556.47806218377}{{z}^{2}}\right)\right)\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{+42}:\\ \;\;\;\;x + \frac{y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right)}{0.607771387771 + \mathsf{fma}\left(z, 11.9400905721, \mathsf{fma}\left(15.234687407, {z}^{3}, \mathsf{fma}\left(31.4690115749, {z}^{2}, {z}^{4}\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -6e+36)
   (+
    x
    (-
     (-
      (fma y 3.13060547623 (/ t (/ (pow z 2.0) y)))
      (/ (* y 36.52704169880642) z))
     (fma
      98.5170599679272
      (/ y (pow z 2.0))
      (/ (* y -556.47806218377) (pow z 2.0)))))
   (if (<= z 8.6e+42)
     (+
      x
      (/
       (*
        y
        (+
         (* z (+ (* z (+ (* z (+ (* z 3.13060547623) 11.1667541262)) t)) a))
         b))
       (+
        0.607771387771
        (fma
         z
         11.9400905721
         (fma
          15.234687407
          (pow z 3.0)
          (fma 31.4690115749 (pow z 2.0) (pow z 4.0)))))))
     (+ x (* y 3.13060547623)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -6e+36) {
		tmp = x + ((fma(y, 3.13060547623, (t / (pow(z, 2.0) / y))) - ((y * 36.52704169880642) / z)) - fma(98.5170599679272, (y / pow(z, 2.0)), ((y * -556.47806218377) / pow(z, 2.0))));
	} else if (z <= 8.6e+42) {
		tmp = x + ((y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / (0.607771387771 + fma(z, 11.9400905721, fma(15.234687407, pow(z, 3.0), fma(31.4690115749, pow(z, 2.0), pow(z, 4.0))))));
	} else {
		tmp = x + (y * 3.13060547623);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -6e+36)
		tmp = Float64(x + Float64(Float64(fma(y, 3.13060547623, Float64(t / Float64((z ^ 2.0) / y))) - Float64(Float64(y * 36.52704169880642) / z)) - fma(98.5170599679272, Float64(y / (z ^ 2.0)), Float64(Float64(y * -556.47806218377) / (z ^ 2.0)))));
	elseif (z <= 8.6e+42)
		tmp = Float64(x + Float64(Float64(y * Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / Float64(0.607771387771 + fma(z, 11.9400905721, fma(15.234687407, (z ^ 3.0), fma(31.4690115749, (z ^ 2.0), (z ^ 4.0)))))));
	else
		tmp = Float64(x + Float64(y * 3.13060547623));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -6e+36], N[(x + N[(N[(N[(y * 3.13060547623 + N[(t / N[(N[Power[z, 2.0], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y * 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] - N[(98.5170599679272 * N[(y / N[Power[z, 2.0], $MachinePrecision]), $MachinePrecision] + N[(N[(y * -556.47806218377), $MachinePrecision] / N[Power[z, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.6e+42], N[(x + N[(N[(y * N[(N[(z * N[(N[(z * N[(N[(z * N[(N[(z * 3.13060547623), $MachinePrecision] + 11.1667541262), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(0.607771387771 + N[(z * 11.9400905721 + N[(15.234687407 * N[Power[z, 3.0], $MachinePrecision] + N[(31.4690115749 * N[Power[z, 2.0], $MachinePrecision] + N[Power[z, 4.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6e36

   1. Initial program 4.3%

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

   2. Taylor expanded in b around 0 4.3%

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

   3. Taylor expanded in z around 0 4.3%

      \[\leadsto x + \frac{b \cdot y + y \cdot \left(z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + 3.13060547623 \cdot z\right)\right)\right)\right)}{\left(\left(\color{blue}{\left(15.234687407 \cdot z + {z}^{2}\right)} + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

   4. Taylor expanded in z around -inf 78.5%

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

      1. +-commutative 78.5%

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

      2. mul-1-neg 78.5%

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

      3. unsub-neg 78.5%

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

      4. *-commutative 78.5%

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

      5. fma-def 78.5%

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

      6. associate-/l* 92.5%

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

      7. distribute-rgt-out-- 92.5%

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

      8. metadata-eval 92.5%

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

      9. +-commutative 92.5%

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

      10. fma-def 92.5%

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

      11. associate-*r/ 92.5%

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

   6. Simplified 92.5%

      \[\leadsto x + \color{blue}{\left(\left(\mathsf{fma}\left(y, 3.13060547623, \frac{t}{\frac{{z}^{2}}{y}}\right) - \frac{y \cdot 36.52704169880642}{z}\right) - \mathsf{fma}\left(98.5170599679272, \frac{y}{{z}^{2}}, \frac{y \cdot -556.47806218377}{{z}^{2}}\right)\right)} \]

   if -6e36 < z < 8.5999999999999996e42

   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 99.1%

      \[\leadsto x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\color{blue}{\left(11.9400905721 \cdot z + \left(15.234687407 \cdot {z}^{3} + \left(31.4690115749 \cdot {z}^{2} + {z}^{4}\right)\right)\right)} + 0.607771387771} \]
   3. Step-by-step derivation

      1. *-commutative 99.1%

         \[\leadsto x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\color{blue}{z \cdot 11.9400905721} + \left(15.234687407 \cdot {z}^{3} + \left(31.4690115749 \cdot {z}^{2} + {z}^{4}\right)\right)\right) + 0.607771387771} \]

      2. fma-def 99.1%

         \[\leadsto x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\color{blue}{\mathsf{fma}\left(z, 11.9400905721, 15.234687407 \cdot {z}^{3} + \left(31.4690115749 \cdot {z}^{2} + {z}^{4}\right)\right)} + 0.607771387771} \]

      3. fma-def 99.2%

         \[\leadsto x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\mathsf{fma}\left(z, 11.9400905721, \color{blue}{\mathsf{fma}\left(15.234687407, {z}^{3}, 31.4690115749 \cdot {z}^{2} + {z}^{4}\right)}\right) + 0.607771387771} \]

      4. fma-def 99.2%

         \[\leadsto x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\mathsf{fma}\left(z, 11.9400905721, \mathsf{fma}\left(15.234687407, {z}^{3}, \color{blue}{\mathsf{fma}\left(31.4690115749, {z}^{2}, {z}^{4}\right)}\right)\right) + 0.607771387771} \]

   4. Simplified 99.2%

      \[\leadsto x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\color{blue}{\mathsf{fma}\left(z, 11.9400905721, \mathsf{fma}\left(15.234687407, {z}^{3}, \mathsf{fma}\left(31.4690115749, {z}^{2}, {z}^{4}\right)\right)\right)} + 0.607771387771} \]

   if 8.5999999999999996e42 < z

   1. Initial program 10.0%

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

   3. Simplified 11.2%

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

   4. Taylor expanded in z around inf 95.3%

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

      1. +-commutative 95.3%

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

      2. *-commutative 95.3%

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

   6. Simplified 95.3%

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

4. Final simplification 97.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+36}:\\ \;\;\;\;x + \left(\left(\mathsf{fma}\left(y, 3.13060547623, \frac{t}{\frac{{z}^{2}}{y}}\right) - \frac{y \cdot 36.52704169880642}{z}\right) - \mathsf{fma}\left(98.5170599679272, \frac{y}{{z}^{2}}, \frac{y \cdot -556.47806218377}{{z}^{2}}\right)\right)\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{+42}:\\ \;\;\;\;x + \frac{y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right)}{0.607771387771 + \mathsf{fma}\left(z, 11.9400905721, \mathsf{fma}\left(15.234687407, {z}^{3}, \mathsf{fma}\left(31.4690115749, {z}^{2}, {z}^{4}\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \]

Alternative 3: 96.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+36}:\\ \;\;\;\;x + \left(\left(\mathsf{fma}\left(y, 3.13060547623, \frac{t}{\frac{{z}^{2}}{y}}\right) - \frac{y \cdot 36.52704169880642}{z}\right) - \mathsf{fma}\left(98.5170599679272, \frac{y}{{z}^{2}}, \frac{y \cdot -556.47806218377}{{z}^{2}}\right)\right)\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+41}:\\ \;\;\;\;x + \frac{y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right)}{0.607771387771 + \left(z \cdot 11.9400905721 + \left(15.234687407 \cdot {z}^{3} + \left({z}^{4} + 31.4690115749 \cdot {z}^{2}\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.2e+36)
   (+
    x
    (-
     (-
      (fma y 3.13060547623 (/ t (/ (pow z 2.0) y)))
      (/ (* y 36.52704169880642) z))
     (fma
      98.5170599679272
      (/ y (pow z 2.0))
      (/ (* y -556.47806218377) (pow z 2.0)))))
   (if (<= z 3.5e+41)
     (+
      x
      (/
       (*
        y
        (+
         (* z (+ (* z (+ (* z (+ (* z 3.13060547623) 11.1667541262)) t)) a))
         b))
       (+
        0.607771387771
        (+
         (* z 11.9400905721)
         (+
          (* 15.234687407 (pow z 3.0))
          (+ (pow z 4.0) (* 31.4690115749 (pow z 2.0))))))))
     (+ x (* y 3.13060547623)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.2e+36) {
		tmp = x + ((fma(y, 3.13060547623, (t / (pow(z, 2.0) / y))) - ((y * 36.52704169880642) / z)) - fma(98.5170599679272, (y / pow(z, 2.0)), ((y * -556.47806218377) / pow(z, 2.0))));
	} else if (z <= 3.5e+41) {
		tmp = x + ((y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / (0.607771387771 + ((z * 11.9400905721) + ((15.234687407 * pow(z, 3.0)) + (pow(z, 4.0) + (31.4690115749 * pow(z, 2.0)))))));
	} else {
		tmp = x + (y * 3.13060547623);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.2e+36)
		tmp = Float64(x + Float64(Float64(fma(y, 3.13060547623, Float64(t / Float64((z ^ 2.0) / y))) - Float64(Float64(y * 36.52704169880642) / z)) - fma(98.5170599679272, Float64(y / (z ^ 2.0)), Float64(Float64(y * -556.47806218377) / (z ^ 2.0)))));
	elseif (z <= 3.5e+41)
		tmp = Float64(x + Float64(Float64(y * Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / Float64(0.607771387771 + Float64(Float64(z * 11.9400905721) + Float64(Float64(15.234687407 * (z ^ 3.0)) + Float64((z ^ 4.0) + Float64(31.4690115749 * (z ^ 2.0))))))));
	else
		tmp = Float64(x + Float64(y * 3.13060547623));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.2e+36], N[(x + N[(N[(N[(y * 3.13060547623 + N[(t / N[(N[Power[z, 2.0], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y * 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] - N[(98.5170599679272 * N[(y / N[Power[z, 2.0], $MachinePrecision]), $MachinePrecision] + N[(N[(y * -556.47806218377), $MachinePrecision] / N[Power[z, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.5e+41], N[(x + N[(N[(y * N[(N[(z * N[(N[(z * N[(N[(z * N[(N[(z * 3.13060547623), $MachinePrecision] + 11.1667541262), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(0.607771387771 + N[(N[(z * 11.9400905721), $MachinePrecision] + N[(N[(15.234687407 * N[Power[z, 3.0], $MachinePrecision]), $MachinePrecision] + N[(N[Power[z, 4.0], $MachinePrecision] + N[(31.4690115749 * N[Power[z, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.19999999999999996e36

   1. Initial program 4.3%

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

   2. Taylor expanded in b around 0 4.3%

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

   3. Taylor expanded in z around 0 4.3%

      \[\leadsto x + \frac{b \cdot y + y \cdot \left(z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + 3.13060547623 \cdot z\right)\right)\right)\right)}{\left(\left(\color{blue}{\left(15.234687407 \cdot z + {z}^{2}\right)} + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

   4. Taylor expanded in z around -inf 78.5%

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

      1. +-commutative 78.5%

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

      2. mul-1-neg 78.5%

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

      3. unsub-neg 78.5%

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

      4. *-commutative 78.5%

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

      5. fma-def 78.5%

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

      6. associate-/l* 92.5%

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

      7. distribute-rgt-out-- 92.5%

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

      8. metadata-eval 92.5%

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

      9. +-commutative 92.5%

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

      10. fma-def 92.5%

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

      11. associate-*r/ 92.5%

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

   6. Simplified 92.5%

      \[\leadsto x + \color{blue}{\left(\left(\mathsf{fma}\left(y, 3.13060547623, \frac{t}{\frac{{z}^{2}}{y}}\right) - \frac{y \cdot 36.52704169880642}{z}\right) - \mathsf{fma}\left(98.5170599679272, \frac{y}{{z}^{2}}, \frac{y \cdot -556.47806218377}{{z}^{2}}\right)\right)} \]

   if -1.19999999999999996e36 < z < 3.4999999999999999e41

   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 99.1%

      \[\leadsto x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\color{blue}{\left(11.9400905721 \cdot z + \left(15.234687407 \cdot {z}^{3} + \left(31.4690115749 \cdot {z}^{2} + {z}^{4}\right)\right)\right)} + 0.607771387771} \]

   if 3.4999999999999999e41 < z

   1. Initial program 10.0%

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

   3. Simplified 11.2%

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

   4. Taylor expanded in z around inf 95.3%

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

      1. +-commutative 95.3%

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

      2. *-commutative 95.3%

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

   6. Simplified 95.3%

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

4. Final simplification 97.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+36}:\\ \;\;\;\;x + \left(\left(\mathsf{fma}\left(y, 3.13060547623, \frac{t}{\frac{{z}^{2}}{y}}\right) - \frac{y \cdot 36.52704169880642}{z}\right) - \mathsf{fma}\left(98.5170599679272, \frac{y}{{z}^{2}}, \frac{y \cdot -556.47806218377}{{z}^{2}}\right)\right)\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+41}:\\ \;\;\;\;x + \frac{y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right)}{0.607771387771 + \left(z \cdot 11.9400905721 + \left(15.234687407 \cdot {z}^{3} + \left({z}^{4} + 31.4690115749 \cdot {z}^{2}\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \]

Alternative 4: 95.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right)\\ \mathbf{if}\;\frac{t_1}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771} \leq \infty:\\ \;\;\;\;x + \frac{t_1}{0.607771387771 + \left(z \cdot 11.9400905721 + \left(15.234687407 \cdot {z}^{3} + \left({z}^{4} + 31.4690115749 \cdot {z}^{2}\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (*
          y
          (+
           (* z (+ (* z (+ (* z (+ (* z 3.13060547623) 11.1667541262)) t)) a))
           b))))
   (if (<=
        (/
         t_1
         (+
          (*
           z
           (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721))
          0.607771387771))
        INFINITY)
     (+
      x
      (/
       t_1
       (+
        0.607771387771
        (+
         (* z 11.9400905721)
         (+
          (* 15.234687407 (pow z 3.0))
          (+ (pow z 4.0) (* 31.4690115749 (pow z 2.0))))))))
     (fma y 3.13060547623 x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b);
	double tmp;
	if ((t_1 / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)) <= ((double) INFINITY)) {
		tmp = x + (t_1 / (0.607771387771 + ((z * 11.9400905721) + ((15.234687407 * pow(z, 3.0)) + (pow(z, 4.0) + (31.4690115749 * pow(z, 2.0)))))));
	} else {
		tmp = fma(y, 3.13060547623, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b))
	tmp = 0.0
	if (Float64(t_1 / Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)) <= Inf)
		tmp = Float64(x + Float64(t_1 / Float64(0.607771387771 + Float64(Float64(z * 11.9400905721) + Float64(Float64(15.234687407 * (z ^ 3.0)) + Float64((z ^ 4.0) + Float64(31.4690115749 * (z ^ 2.0))))))));
	else
		tmp = fma(y, 3.13060547623, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(N[(z * N[(N[(z * N[(N[(z * N[(N[(z * 3.13060547623), $MachinePrecision] + 11.1667541262), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$1 / 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[(t$95$1 / N[(0.607771387771 + N[(N[(z * 11.9400905721), $MachinePrecision] + N[(N[(15.234687407 * N[Power[z, 3.0], $MachinePrecision]), $MachinePrecision] + N[(N[Power[z, 4.0], $MachinePrecision] + N[(31.4690115749 * N[Power[z, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * 3.13060547623 + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 93.2%

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

   2. Taylor expanded in z around 0 93.2%

      \[\leadsto x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\color{blue}{\left(11.9400905721 \cdot z + \left(15.234687407 \cdot {z}^{3} + \left(31.4690115749 \cdot {z}^{2} + {z}^{4}\right)\right)\right)} + 0.607771387771} \]

   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%

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

   3. Simplified 0.0%

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

   4. Taylor expanded in z around inf 97.0%

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

      1. +-commutative 97.0%

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

      2. *-commutative 97.0%

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

      3. fma-def 97.1%

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

   6. Simplified 97.1%

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

4. Final simplification 94.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771} \leq \infty:\\ \;\;\;\;x + \frac{y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right)}{0.607771387771 + \left(z \cdot 11.9400905721 + \left(15.234687407 \cdot {z}^{3} + \left({z}^{4} + 31.4690115749 \cdot {z}^{2}\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623, x\right)\\ \end{array} \]

Alternative 5: 95.4% accurate, 0.3× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771);
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1 + x;
	} else {
		tmp = fma(y, 3.13060547623, x);
	}
	return tmp;
}

Julia

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y * N[(N[(z * N[(N[(z * N[(N[(z * N[(N[(z * 3.13060547623), $MachinePrecision] + 11.1667541262), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(N[(z * N[(N[(z * N[(N[(z * N[(z + 15.234687407), $MachinePrecision]), $MachinePrecision] + 31.4690115749), $MachinePrecision]), $MachinePrecision] + 11.9400905721), $MachinePrecision]), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], N[(t$95$1 + x), $MachinePrecision], N[(y * 3.13060547623 + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 93.2%

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

   if +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%

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

   3. Simplified 0.0%

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

   4. Taylor expanded in z around inf 97.0%

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

      1. +-commutative 97.0%

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

      2. *-commutative 97.0%

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

      3. fma-def 97.1%

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

   6. Simplified 97.1%

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

4. Final simplification 94.4%

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

Alternative 6: 95.3% accurate, 0.5× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771);
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1 + x;
	} else {
		tmp = x + (y * 3.13060547623);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771);
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1 + x;
	} else {
		tmp = x + (y * 3.13060547623);
	}
	return tmp;
}

Python

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

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y * Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = Float64(t_1 + x);
	else
		tmp = Float64(x + Float64(y * 3.13060547623));
	end
	return tmp
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y * N[(N[(z * N[(N[(z * N[(N[(z * N[(N[(z * 3.13060547623), $MachinePrecision] + 11.1667541262), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(N[(z * N[(N[(z * N[(N[(z * N[(z + 15.234687407), $MachinePrecision]), $MachinePrecision] + 31.4690115749), $MachinePrecision]), $MachinePrecision] + 11.9400905721), $MachinePrecision]), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], N[(t$95$1 + x), $MachinePrecision], N[(x + N[(y * 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 93.2%

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

   if +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%

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

   3. Simplified 0.0%

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

   4. Taylor expanded in z around inf 97.0%

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

      1. +-commutative 97.0%

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

      2. *-commutative 97.0%

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

   6. Simplified 97.0%

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

4. Final simplification 94.4%

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

Alternative 7: 95.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{+43} \lor \neg \left(z \leq 1.5 \cdot 10^{+39}\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot 11.1667541262\right)\right)\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -6.4e+43) (not (<= z 1.5e+39)))
   (+ x (* y 3.13060547623))
   (+
    x
    (/
     (* y (+ b (* z (+ a (* z (+ t (* z 11.1667541262)))))))
     (+
      (* 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 <= -6.4e+43) || !(z <= 1.5e+39)) {
		tmp = x + (y * 3.13060547623);
	} else {
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))) / ((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 <= (-6.4d+43)) .or. (.not. (z <= 1.5d+39))) then
        tmp = x + (y * 3.13060547623d0)
    else
        tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262d0))))))) / ((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 <= -6.4e+43) || !(z <= 1.5e+39)) {
		tmp = x + (y * 3.13060547623);
	} else {
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))) / ((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 <= -6.4e+43) or not (z <= 1.5e+39):
		tmp = x + (y * 3.13060547623)
	else:
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))) / ((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 <= -6.4e+43) || !(z <= 1.5e+39))
		tmp = Float64(x + Float64(y * 3.13060547623));
	else
		tmp = Float64(x + Float64(Float64(y * Float64(b + Float64(z * Float64(a + Float64(z * Float64(t + Float64(z * 11.1667541262))))))) / Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -6.4e+43) || ~((z <= 1.5e+39)))
		tmp = x + (y * 3.13060547623);
	else
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))) / ((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, -6.4e+43], N[Not[LessEqual[z, 1.5e+39]], $MachinePrecision]], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * N[(b + N[(z * N[(a + N[(z * N[(t + N[(z * 11.1667541262), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(z * N[(N[(z * N[(N[(z * N[(z + 15.234687407), $MachinePrecision]), $MachinePrecision] + 31.4690115749), $MachinePrecision]), $MachinePrecision] + 11.9400905721), $MachinePrecision]), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.40000000000000029e43 or 1.5e39 < z

   1. Initial program 6.7%

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

   3. Simplified 11.9%

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

   4. Taylor expanded in z around inf 89.7%

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

      1. +-commutative 89.7%

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

      2. *-commutative 89.7%

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

   6. Simplified 89.7%

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

   if -6.40000000000000029e43 < z < 1.5e39

   1. Initial program 97.9%

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

   2. Taylor expanded in z around 0 97.6%

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

      1. *-commutative 97.6%

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

   4. Simplified 97.6%

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

4. Final simplification 94.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{+43} \lor \neg \left(z \leq 1.5 \cdot 10^{+39}\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot 11.1667541262\right)\right)\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\\ \end{array} \]

Alternative 8: 93.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.415:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 - \frac{y \cdot 36.52704169880642}{z}\right)\\ \mathbf{elif}\;z \leq 1.38 \cdot 10^{+26}:\\ \;\;\;\;x + \frac{y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -0.415)
   (+ x (- (* y 3.13060547623) (/ (* y 36.52704169880642) z)))
   (if (<= z 1.38e+26)
     (+
      x
      (/
       (*
        y
        (+
         (* z (+ (* z (+ (* z (+ (* z 3.13060547623) 11.1667541262)) t)) a))
         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 <= -0.415) {
		tmp = x + ((y * 3.13060547623) - ((y * 36.52704169880642) / z));
	} else if (z <= 1.38e+26) {
		tmp = x + ((y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + 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 <= (-0.415d0)) then
        tmp = x + ((y * 3.13060547623d0) - ((y * 36.52704169880642d0) / z))
    else if (z <= 1.38d+26) then
        tmp = x + ((y * ((z * ((z * ((z * ((z * 3.13060547623d0) + 11.1667541262d0)) + t)) + a)) + 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 <= -0.415) {
		tmp = x + ((y * 3.13060547623) - ((y * 36.52704169880642) / z));
	} else if (z <= 1.38e+26) {
		tmp = x + ((y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + 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 <= -0.415:
		tmp = x + ((y * 3.13060547623) - ((y * 36.52704169880642) / z))
	elif z <= 1.38e+26:
		tmp = x + ((y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + 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 <= -0.415)
		tmp = Float64(x + Float64(Float64(y * 3.13060547623) - Float64(Float64(y * 36.52704169880642) / z)));
	elseif (z <= 1.38e+26)
		tmp = Float64(x + Float64(Float64(y * Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * 3.13060547623) + 11.1667541262)) + t)) + a)) + 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 <= -0.415)
		tmp = x + ((y * 3.13060547623) - ((y * 36.52704169880642) / z));
	elseif (z <= 1.38e+26)
		tmp = x + ((y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + 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, -0.415], N[(x + N[(N[(y * 3.13060547623), $MachinePrecision] - N[(N[(y * 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.38e+26], N[(x + N[(N[(y * N[(N[(z * N[(N[(z * N[(N[(z * N[(N[(z * 3.13060547623), $MachinePrecision] + 11.1667541262), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(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 < -0.41499999999999998

   1. Initial program 11.7%

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

   3. Simplified 21.8%

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

   4. Taylor expanded in z around -inf 81.2%

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

      1. +-commutative 81.2%

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

      2. mul-1-neg 81.2%

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

      3. unsub-neg 81.2%

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

      4. *-commutative 81.2%

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

      5. cancel-sign-sub-inv 81.2%

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

      6. metadata-eval 81.2%

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

      7. distribute-rgt-out 81.2%

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

      8. metadata-eval 81.2%

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

   6. Simplified 81.2%

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

   if -0.41499999999999998 < z < 1.38e26

   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 99.0%

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

      1. *-commutative 85.3%

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

   4. Simplified 99.0%

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

   if 1.38e26 < z

   1. Initial program 14.1%

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

   3. Simplified 17.4%

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

   4. Taylor expanded in z around inf 93.4%

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

      1. +-commutative 93.4%

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

      2. *-commutative 93.4%

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

   6. Simplified 93.4%

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

4. Final simplification 93.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.415:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 - \frac{y \cdot 36.52704169880642}{z}\right)\\ \mathbf{elif}\;z \leq 1.38 \cdot 10^{+26}:\\ \;\;\;\;x + \frac{y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \]

Alternative 9: 92.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+15} \lor \neg \left(z \leq 1.8 \cdot 10^{+15}\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot b + y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right)\right)}{0.607771387771}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.75e+15) (not (<= z 1.8e+15)))
   (+ x (* y 3.13060547623))
   (+
    x
    (/
     (+
      (* y b)
      (*
       y
       (* z (+ (* z (+ (* z (+ (* z 3.13060547623) 11.1667541262)) t)) a))))
     0.607771387771))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.75e+15) || !(z <= 1.8e+15)) {
		tmp = x + (y * 3.13060547623);
	} else {
		tmp = x + (((y * b) + (y * (z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)))) / 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 <= (-1.75d+15)) .or. (.not. (z <= 1.8d+15))) then
        tmp = x + (y * 3.13060547623d0)
    else
        tmp = x + (((y * b) + (y * (z * ((z * ((z * ((z * 3.13060547623d0) + 11.1667541262d0)) + t)) + a)))) / 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 <= -1.75e+15) || !(z <= 1.8e+15)) {
		tmp = x + (y * 3.13060547623);
	} else {
		tmp = x + (((y * b) + (y * (z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)))) / 0.607771387771);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.75e+15) or not (z <= 1.8e+15):
		tmp = x + (y * 3.13060547623)
	else:
		tmp = x + (((y * b) + (y * (z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)))) / 0.607771387771)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.75e+15) || !(z <= 1.8e+15))
		tmp = Float64(x + Float64(y * 3.13060547623));
	else
		tmp = Float64(x + Float64(Float64(Float64(y * b) + Float64(y * Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * 3.13060547623) + 11.1667541262)) + t)) + a)))) / 0.607771387771));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.75e+15) || ~((z <= 1.8e+15)))
		tmp = x + (y * 3.13060547623);
	else
		tmp = x + (((y * b) + (y * (z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)))) / 0.607771387771);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.75e+15], N[Not[LessEqual[z, 1.8e+15]], $MachinePrecision]], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(N[(y * b), $MachinePrecision] + N[(y * N[(z * N[(N[(z * N[(N[(z * N[(N[(z * 3.13060547623), $MachinePrecision] + 11.1667541262), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / 0.607771387771), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.75e15 or 1.8e15 < z

   1. Initial program 13.5%

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

   3. Simplified 20.8%

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

   4. Taylor expanded in z around inf 87.1%

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

      1. +-commutative 87.1%

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

      2. *-commutative 87.1%

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

   6. Simplified 87.1%

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

   if -1.75e15 < z < 1.8e15

   1. Initial program 99.7%

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

   2. Taylor expanded in b around 0 98.4%

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

   3. Taylor expanded in z around 0 96.3%

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

      1. *-commutative 83.8%

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

   5. Simplified 96.3%

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

   6. Taylor expanded in z around 0 95.9%

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

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+15} \lor \neg \left(z \leq 1.8 \cdot 10^{+15}\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot b + y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right)\right)}{0.607771387771}\\ \end{array} \]

Alternative 10: 89.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.415:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 - \frac{y \cdot 36.52704169880642}{z}\right)\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+20}:\\ \;\;\;\;x + \frac{y \cdot b + a \cdot \left(y \cdot z\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -0.415)
   (+ x (- (* y 3.13060547623) (/ (* y 36.52704169880642) z)))
   (if (<= z 2.05e+20)
     (+ x (/ (+ (* y b) (* a (* y z))) (+ 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 <= -0.415) {
		tmp = x + ((y * 3.13060547623) - ((y * 36.52704169880642) / z));
	} else if (z <= 2.05e+20) {
		tmp = x + (((y * b) + (a * (y * z))) / (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 <= (-0.415d0)) then
        tmp = x + ((y * 3.13060547623d0) - ((y * 36.52704169880642d0) / z))
    else if (z <= 2.05d+20) then
        tmp = x + (((y * b) + (a * (y * z))) / (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 <= -0.415) {
		tmp = x + ((y * 3.13060547623) - ((y * 36.52704169880642) / z));
	} else if (z <= 2.05e+20) {
		tmp = x + (((y * b) + (a * (y * z))) / (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 <= -0.415:
		tmp = x + ((y * 3.13060547623) - ((y * 36.52704169880642) / z))
	elif z <= 2.05e+20:
		tmp = x + (((y * b) + (a * (y * z))) / (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 <= -0.415)
		tmp = Float64(x + Float64(Float64(y * 3.13060547623) - Float64(Float64(y * 36.52704169880642) / z)));
	elseif (z <= 2.05e+20)
		tmp = Float64(x + Float64(Float64(Float64(y * b) + Float64(a * Float64(y * z))) / 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 <= -0.415)
		tmp = x + ((y * 3.13060547623) - ((y * 36.52704169880642) / z));
	elseif (z <= 2.05e+20)
		tmp = x + (((y * b) + (a * (y * z))) / (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, -0.415], N[(x + N[(N[(y * 3.13060547623), $MachinePrecision] - N[(N[(y * 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.05e+20], N[(x + N[(N[(N[(y * b), $MachinePrecision] + N[(a * N[(y * z), $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 < -0.41499999999999998

   1. Initial program 11.7%

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

   3. Simplified 21.8%

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

   4. Taylor expanded in z around -inf 81.2%

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

      1. +-commutative 81.2%

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

      2. mul-1-neg 81.2%

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

      3. unsub-neg 81.2%

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

      4. *-commutative 81.2%

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

      5. cancel-sign-sub-inv 81.2%

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

      6. metadata-eval 81.2%

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

      7. distribute-rgt-out 81.2%

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

      8. metadata-eval 81.2%

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

   6. Simplified 81.2%

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

   if -0.41499999999999998 < z < 2.05e20

   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 b around 0 98.4%

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

   3. Taylor expanded in z around 0 97.6%

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

      1. *-commutative 84.9%

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

   5. Simplified 97.6%

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

   6. Taylor expanded in z around 0 95.9%

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

      1. *-commutative 95.9%

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

   8. Simplified 95.9%

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

   if 2.05e20 < z

   1. Initial program 19.7%

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

   3. Simplified 22.8%

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

   4. Taylor expanded in z around inf 91.8%

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

      1. +-commutative 91.8%

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

      2. *-commutative 91.8%

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

   6. Simplified 91.8%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.415:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 - \frac{y \cdot 36.52704169880642}{z}\right)\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+20}:\\ \;\;\;\;x + \frac{y \cdot b + a \cdot \left(y \cdot z\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \]

Alternative 11: 81.9% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot 3.13060547623\\ \mathbf{if}\;z \leq -6200:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-174}:\\ \;\;\;\;x + b \cdot \left(y \cdot 1.6453555072203998\right)\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-78}:\\ \;\;\;\;x + \left(a \cdot \left(y \cdot z\right)\right) \cdot 1.6453555072203998\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+28}:\\ \;\;\;\;x + \frac{y \cdot b}{0.607771387771}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* y 3.13060547623))))
   (if (<= z -6200.0)
     t_1
     (if (<= z 9.5e-174)
       (+ x (* b (* y 1.6453555072203998)))
       (if (<= z 9e-78)
         (+ x (* (* a (* y z)) 1.6453555072203998))
         (if (<= z 1.8e+28) (+ x (/ (* y b) 0.607771387771)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * 3.13060547623);
	double tmp;
	if (z <= -6200.0) {
		tmp = t_1;
	} else if (z <= 9.5e-174) {
		tmp = x + (b * (y * 1.6453555072203998));
	} else if (z <= 9e-78) {
		tmp = x + ((a * (y * z)) * 1.6453555072203998);
	} else if (z <= 1.8e+28) {
		tmp = x + ((y * b) / 0.607771387771);
	} 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 + (y * 3.13060547623d0)
    if (z <= (-6200.0d0)) then
        tmp = t_1
    else if (z <= 9.5d-174) then
        tmp = x + (b * (y * 1.6453555072203998d0))
    else if (z <= 9d-78) then
        tmp = x + ((a * (y * z)) * 1.6453555072203998d0)
    else if (z <= 1.8d+28) then
        tmp = x + ((y * b) / 0.607771387771d0)
    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 + (y * 3.13060547623);
	double tmp;
	if (z <= -6200.0) {
		tmp = t_1;
	} else if (z <= 9.5e-174) {
		tmp = x + (b * (y * 1.6453555072203998));
	} else if (z <= 9e-78) {
		tmp = x + ((a * (y * z)) * 1.6453555072203998);
	} else if (z <= 1.8e+28) {
		tmp = x + ((y * b) / 0.607771387771);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y * 3.13060547623)
	tmp = 0
	if z <= -6200.0:
		tmp = t_1
	elif z <= 9.5e-174:
		tmp = x + (b * (y * 1.6453555072203998))
	elif z <= 9e-78:
		tmp = x + ((a * (y * z)) * 1.6453555072203998)
	elif z <= 1.8e+28:
		tmp = x + ((y * b) / 0.607771387771)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y * 3.13060547623))
	tmp = 0.0
	if (z <= -6200.0)
		tmp = t_1;
	elseif (z <= 9.5e-174)
		tmp = Float64(x + Float64(b * Float64(y * 1.6453555072203998)));
	elseif (z <= 9e-78)
		tmp = Float64(x + Float64(Float64(a * Float64(y * z)) * 1.6453555072203998));
	elseif (z <= 1.8e+28)
		tmp = Float64(x + Float64(Float64(y * b) / 0.607771387771));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (y * 3.13060547623);
	tmp = 0.0;
	if (z <= -6200.0)
		tmp = t_1;
	elseif (z <= 9.5e-174)
		tmp = x + (b * (y * 1.6453555072203998));
	elseif (z <= 9e-78)
		tmp = x + ((a * (y * z)) * 1.6453555072203998);
	elseif (z <= 1.8e+28)
		tmp = x + ((y * b) / 0.607771387771);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6200.0], t$95$1, If[LessEqual[z, 9.5e-174], N[(x + N[(b * N[(y * 1.6453555072203998), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9e-78], N[(x + N[(N[(a * N[(y * z), $MachinePrecision]), $MachinePrecision] * 1.6453555072203998), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.8e+28], N[(x + N[(N[(y * b), $MachinePrecision] / 0.607771387771), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6200 or 1.8e28 < z

   1. Initial program 11.9%

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

   3. Simplified 19.3%

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

   4. Taylor expanded in z around inf 86.8%

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

      1. +-commutative 86.8%

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

      2. *-commutative 86.8%

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

   6. Simplified 86.8%

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

   if -6200 < z < 9.50000000000000075e-174

   1. Initial program 99.7%

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

   2. Taylor expanded in z around 0 90.5%

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

      1. *-commutative 90.5%

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

   4. Simplified 90.5%

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

   5. Taylor expanded in z around 0 90.4%

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

      1. *-commutative 90.4%

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

   7. Simplified 90.4%

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

   8. Taylor expanded in z around 0 90.5%

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

      1. associate-*r* 90.5%

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

      2. *-commutative 90.5%

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

      3. associate-*l* 90.6%

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

   10. Simplified 90.6%

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

   if 9.50000000000000075e-174 < z < 9e-78

   1. Initial program 99.7%

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

   2. Taylor expanded in a around inf 83.4%

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

   3. Taylor expanded in z around 0 83.5%

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

   if 9e-78 < z < 1.8e28

   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 73.4%

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

      1. *-commutative 73.4%

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

   4. Simplified 73.4%

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

   5. Taylor expanded in z around 0 73.4%

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

      1. *-commutative 73.4%

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

   7. Simplified 73.4%

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

   8. Taylor expanded in z around 0 73.4%

      \[\leadsto x + \frac{y \cdot b}{\color{blue}{0.607771387771}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6200:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-174}:\\ \;\;\;\;x + b \cdot \left(y \cdot 1.6453555072203998\right)\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-78}:\\ \;\;\;\;x + \left(a \cdot \left(y \cdot z\right)\right) \cdot 1.6453555072203998\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+28}:\\ \;\;\;\;x + \frac{y \cdot b}{0.607771387771}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \]

Alternative 12: 82.0% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot 3.13060547623\\ \mathbf{if}\;z \leq -180:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-174}:\\ \;\;\;\;x + b \cdot \left(y \cdot 1.6453555072203998\right)\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-79}:\\ \;\;\;\;x + 1.6453555072203998 \cdot \left(y \cdot \left(z \cdot a\right)\right)\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+26}:\\ \;\;\;\;x + \frac{y \cdot b}{0.607771387771}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* y 3.13060547623))))
   (if (<= z -180.0)
     t_1
     (if (<= z 9.5e-174)
       (+ x (* b (* y 1.6453555072203998)))
       (if (<= z 2.6e-79)
         (+ x (* 1.6453555072203998 (* y (* z a))))
         (if (<= z 4.4e+26) (+ x (/ (* y b) 0.607771387771)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * 3.13060547623);
	double tmp;
	if (z <= -180.0) {
		tmp = t_1;
	} else if (z <= 9.5e-174) {
		tmp = x + (b * (y * 1.6453555072203998));
	} else if (z <= 2.6e-79) {
		tmp = x + (1.6453555072203998 * (y * (z * a)));
	} else if (z <= 4.4e+26) {
		tmp = x + ((y * b) / 0.607771387771);
	} 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 + (y * 3.13060547623d0)
    if (z <= (-180.0d0)) then
        tmp = t_1
    else if (z <= 9.5d-174) then
        tmp = x + (b * (y * 1.6453555072203998d0))
    else if (z <= 2.6d-79) then
        tmp = x + (1.6453555072203998d0 * (y * (z * a)))
    else if (z <= 4.4d+26) then
        tmp = x + ((y * b) / 0.607771387771d0)
    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 + (y * 3.13060547623);
	double tmp;
	if (z <= -180.0) {
		tmp = t_1;
	} else if (z <= 9.5e-174) {
		tmp = x + (b * (y * 1.6453555072203998));
	} else if (z <= 2.6e-79) {
		tmp = x + (1.6453555072203998 * (y * (z * a)));
	} else if (z <= 4.4e+26) {
		tmp = x + ((y * b) / 0.607771387771);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y * 3.13060547623)
	tmp = 0
	if z <= -180.0:
		tmp = t_1
	elif z <= 9.5e-174:
		tmp = x + (b * (y * 1.6453555072203998))
	elif z <= 2.6e-79:
		tmp = x + (1.6453555072203998 * (y * (z * a)))
	elif z <= 4.4e+26:
		tmp = x + ((y * b) / 0.607771387771)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y * 3.13060547623))
	tmp = 0.0
	if (z <= -180.0)
		tmp = t_1;
	elseif (z <= 9.5e-174)
		tmp = Float64(x + Float64(b * Float64(y * 1.6453555072203998)));
	elseif (z <= 2.6e-79)
		tmp = Float64(x + Float64(1.6453555072203998 * Float64(y * Float64(z * a))));
	elseif (z <= 4.4e+26)
		tmp = Float64(x + Float64(Float64(y * b) / 0.607771387771));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (y * 3.13060547623);
	tmp = 0.0;
	if (z <= -180.0)
		tmp = t_1;
	elseif (z <= 9.5e-174)
		tmp = x + (b * (y * 1.6453555072203998));
	elseif (z <= 2.6e-79)
		tmp = x + (1.6453555072203998 * (y * (z * a)));
	elseif (z <= 4.4e+26)
		tmp = x + ((y * b) / 0.607771387771);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -180.0], t$95$1, If[LessEqual[z, 9.5e-174], N[(x + N[(b * N[(y * 1.6453555072203998), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.6e-79], N[(x + N[(1.6453555072203998 * N[(y * N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.4e+26], N[(x + N[(N[(y * b), $MachinePrecision] / 0.607771387771), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -180 or 4.40000000000000014e26 < z

   1. Initial program 11.9%

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

   3. Simplified 19.3%

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

   4. Taylor expanded in z around inf 86.8%

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

      1. +-commutative 86.8%

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

      2. *-commutative 86.8%

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

   6. Simplified 86.8%

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

   if -180 < z < 9.50000000000000075e-174

   1. Initial program 99.7%

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

   2. Taylor expanded in z around 0 90.5%

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

      1. *-commutative 90.5%

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

   4. Simplified 90.5%

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

   5. Taylor expanded in z around 0 90.4%

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

      1. *-commutative 90.4%

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

   7. Simplified 90.4%

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

   8. Taylor expanded in z around 0 90.5%

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

      1. associate-*r* 90.5%

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

      2. *-commutative 90.5%

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

      3. associate-*l* 90.6%

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

   10. Simplified 90.6%

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

   if 9.50000000000000075e-174 < z < 2.59999999999999994e-79

   1. Initial program 99.7%

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

   2. Taylor expanded in a around inf 83.4%

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

   3. Taylor expanded in z around 0 83.4%

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

      1. *-commutative 62.5%

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

   5. Simplified 83.4%

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

   6. Taylor expanded in z around 0 83.5%

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

      1. associate-*r* 65.7%

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

      2. *-commutative 65.7%

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

      3. associate-*l* 83.6%

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

   8. Simplified 83.6%

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

   if 2.59999999999999994e-79 < z < 4.40000000000000014e26

   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 73.4%

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

      1. *-commutative 73.4%

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

   4. Simplified 73.4%

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

   5. Taylor expanded in z around 0 73.4%

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

      1. *-commutative 73.4%

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

   7. Simplified 73.4%

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

   8. Taylor expanded in z around 0 73.4%

      \[\leadsto x + \frac{y \cdot b}{\color{blue}{0.607771387771}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -180:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-174}:\\ \;\;\;\;x + b \cdot \left(y \cdot 1.6453555072203998\right)\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-79}:\\ \;\;\;\;x + 1.6453555072203998 \cdot \left(y \cdot \left(z \cdot a\right)\right)\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+26}:\\ \;\;\;\;x + \frac{y \cdot b}{0.607771387771}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \]

Alternative 13: 82.0% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -32000:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 - \frac{y \cdot 36.52704169880642}{z}\right)\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-174}:\\ \;\;\;\;x + b \cdot \left(y \cdot 1.6453555072203998\right)\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-79}:\\ \;\;\;\;x + 1.6453555072203998 \cdot \left(y \cdot \left(z \cdot a\right)\right)\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+25}:\\ \;\;\;\;x + \frac{y \cdot b}{0.607771387771}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -32000.0)
   (+ x (- (* y 3.13060547623) (/ (* y 36.52704169880642) z)))
   (if (<= z 9.5e-174)
     (+ x (* b (* y 1.6453555072203998)))
     (if (<= z 4.6e-79)
       (+ x (* 1.6453555072203998 (* y (* z a))))
       (if (<= z 6.8e+25)
         (+ x (/ (* y b) 0.607771387771))
         (+ x (* y 3.13060547623)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -32000.0) {
		tmp = x + ((y * 3.13060547623) - ((y * 36.52704169880642) / z));
	} else if (z <= 9.5e-174) {
		tmp = x + (b * (y * 1.6453555072203998));
	} else if (z <= 4.6e-79) {
		tmp = x + (1.6453555072203998 * (y * (z * a)));
	} else if (z <= 6.8e+25) {
		tmp = x + ((y * b) / 0.607771387771);
	} 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 <= (-32000.0d0)) then
        tmp = x + ((y * 3.13060547623d0) - ((y * 36.52704169880642d0) / z))
    else if (z <= 9.5d-174) then
        tmp = x + (b * (y * 1.6453555072203998d0))
    else if (z <= 4.6d-79) then
        tmp = x + (1.6453555072203998d0 * (y * (z * a)))
    else if (z <= 6.8d+25) then
        tmp = x + ((y * b) / 0.607771387771d0)
    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 <= -32000.0) {
		tmp = x + ((y * 3.13060547623) - ((y * 36.52704169880642) / z));
	} else if (z <= 9.5e-174) {
		tmp = x + (b * (y * 1.6453555072203998));
	} else if (z <= 4.6e-79) {
		tmp = x + (1.6453555072203998 * (y * (z * a)));
	} else if (z <= 6.8e+25) {
		tmp = x + ((y * b) / 0.607771387771);
	} else {
		tmp = x + (y * 3.13060547623);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -32000.0:
		tmp = x + ((y * 3.13060547623) - ((y * 36.52704169880642) / z))
	elif z <= 9.5e-174:
		tmp = x + (b * (y * 1.6453555072203998))
	elif z <= 4.6e-79:
		tmp = x + (1.6453555072203998 * (y * (z * a)))
	elif z <= 6.8e+25:
		tmp = x + ((y * b) / 0.607771387771)
	else:
		tmp = x + (y * 3.13060547623)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -32000.0)
		tmp = Float64(x + Float64(Float64(y * 3.13060547623) - Float64(Float64(y * 36.52704169880642) / z)));
	elseif (z <= 9.5e-174)
		tmp = Float64(x + Float64(b * Float64(y * 1.6453555072203998)));
	elseif (z <= 4.6e-79)
		tmp = Float64(x + Float64(1.6453555072203998 * Float64(y * Float64(z * a))));
	elseif (z <= 6.8e+25)
		tmp = Float64(x + Float64(Float64(y * b) / 0.607771387771));
	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 <= -32000.0)
		tmp = x + ((y * 3.13060547623) - ((y * 36.52704169880642) / z));
	elseif (z <= 9.5e-174)
		tmp = x + (b * (y * 1.6453555072203998));
	elseif (z <= 4.6e-79)
		tmp = x + (1.6453555072203998 * (y * (z * a)));
	elseif (z <= 6.8e+25)
		tmp = x + ((y * b) / 0.607771387771);
	else
		tmp = x + (y * 3.13060547623);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -32000.0], N[(x + N[(N[(y * 3.13060547623), $MachinePrecision] - N[(N[(y * 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.5e-174], N[(x + N[(b * N[(y * 1.6453555072203998), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.6e-79], N[(x + N[(1.6453555072203998 * N[(y * N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.8e+25], N[(x + N[(N[(y * b), $MachinePrecision] / 0.607771387771), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -32000

   1. Initial program 10.4%

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

   3. Simplified 20.6%

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

   4. Taylor expanded in z around -inf 82.4%

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

      1. +-commutative 82.4%

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

      2. mul-1-neg 82.4%

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

      3. unsub-neg 82.4%

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

      4. *-commutative 82.4%

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

      5. cancel-sign-sub-inv 82.4%

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

      6. metadata-eval 82.4%

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

      7. distribute-rgt-out 82.4%

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

      8. metadata-eval 82.4%

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

   6. Simplified 82.4%

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

   if -32000 < z < 9.50000000000000075e-174

   1. Initial program 99.7%

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

   2. Taylor expanded in z around 0 90.5%

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

      1. *-commutative 90.5%

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

   4. Simplified 90.5%

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

   5. Taylor expanded in z around 0 90.4%

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

      1. *-commutative 90.4%

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

   7. Simplified 90.4%

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

   8. Taylor expanded in z around 0 90.5%

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

      1. associate-*r* 90.5%

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

      2. *-commutative 90.5%

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

      3. associate-*l* 90.6%

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

   10. Simplified 90.6%

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

   if 9.50000000000000075e-174 < z < 4.60000000000000023e-79

   1. Initial program 99.7%

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

   2. Taylor expanded in a around inf 83.4%

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

   3. Taylor expanded in z around 0 83.4%

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

      1. *-commutative 62.5%

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

   5. Simplified 83.4%

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

   6. Taylor expanded in z around 0 83.5%

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

      1. associate-*r* 65.7%

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

      2. *-commutative 65.7%

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

      3. associate-*l* 83.6%

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

   8. Simplified 83.6%

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

   if 4.60000000000000023e-79 < z < 6.79999999999999967e25

   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 73.4%

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

      1. *-commutative 73.4%

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

   4. Simplified 73.4%

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

   5. Taylor expanded in z around 0 73.4%

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

      1. *-commutative 73.4%

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

   7. Simplified 73.4%

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

   8. Taylor expanded in z around 0 73.4%

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

   if 6.79999999999999967e25 < z

   1. Initial program 14.1%

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

   3. Simplified 17.4%

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

   4. Taylor expanded in z around inf 93.4%

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

      1. +-commutative 93.4%

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

      2. *-commutative 93.4%

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

   6. Simplified 93.4%

      \[\leadsto \color{blue}{y \cdot 3.13060547623 + x} \]
3. Recombined 5 regimes into one program.

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -32000:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 - \frac{y \cdot 36.52704169880642}{z}\right)\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-174}:\\ \;\;\;\;x + b \cdot \left(y \cdot 1.6453555072203998\right)\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-79}:\\ \;\;\;\;x + 1.6453555072203998 \cdot \left(y \cdot \left(z \cdot a\right)\right)\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+25}:\\ \;\;\;\;x + \frac{y \cdot b}{0.607771387771}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \]

Alternative 14: 83.7% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6200 \lor \neg \left(z \leq 2.95 \cdot 10^{+29}\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(y \cdot 1.6453555072203998\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -6200.0) (not (<= z 2.95e+29)))
   (+ x (* y 3.13060547623))
   (+ x (* b (* y 1.6453555072203998)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -6200.0) || !(z <= 2.95e+29)) {
		tmp = x + (y * 3.13060547623);
	} else {
		tmp = x + (b * (y * 1.6453555072203998));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-6200.0d0)) .or. (.not. (z <= 2.95d+29))) then
        tmp = x + (y * 3.13060547623d0)
    else
        tmp = x + (b * (y * 1.6453555072203998d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -6200.0) || !(z <= 2.95e+29)) {
		tmp = x + (y * 3.13060547623);
	} else {
		tmp = x + (b * (y * 1.6453555072203998));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -6200.0) or not (z <= 2.95e+29):
		tmp = x + (y * 3.13060547623)
	else:
		tmp = x + (b * (y * 1.6453555072203998))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -6200.0) || !(z <= 2.95e+29))
		tmp = Float64(x + Float64(y * 3.13060547623));
	else
		tmp = Float64(x + Float64(b * Float64(y * 1.6453555072203998)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -6200.0) || ~((z <= 2.95e+29)))
		tmp = x + (y * 3.13060547623);
	else
		tmp = x + (b * (y * 1.6453555072203998));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -6200.0], N[Not[LessEqual[z, 2.95e+29]], $MachinePrecision]], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision], N[(x + N[(b * N[(y * 1.6453555072203998), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6200 or 2.9499999999999999e29 < z

   1. Initial program 11.9%

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

   3. Simplified 19.3%

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

   4. Taylor expanded in z around inf 86.8%

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

      1. +-commutative 86.8%

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

      2. *-commutative 86.8%

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

   6. Simplified 86.8%

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

   if -6200 < z < 2.9499999999999999e29

   1. Initial program 99.7%

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

   2. Taylor expanded in z around 0 84.7%

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

      1. *-commutative 84.7%

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

   4. Simplified 84.7%

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

   5. Taylor expanded in z around 0 84.7%

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

      1. *-commutative 84.7%

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

   7. Simplified 84.7%

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

   8. Taylor expanded in z around 0 84.7%

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

      1. associate-*r* 84.8%

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

      2. *-commutative 84.8%

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

      3. associate-*l* 84.8%

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

   10. Simplified 84.8%

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

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6200 \lor \neg \left(z \leq 2.95 \cdot 10^{+29}\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(y \cdot 1.6453555072203998\right)\\ \end{array} \]

Alternative 15: 83.6% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -40000 \lor \neg \left(z \leq 1.95 \cdot 10^{+31}\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -40000.0) (not (<= z 1.95e+31)))
   (+ x (* y 3.13060547623))
   (+ x (* y (* b 1.6453555072203998)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -40000.0) || !(z <= 1.95e+31)) {
		tmp = x + (y * 3.13060547623);
	} else {
		tmp = x + (y * (b * 1.6453555072203998));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-40000.0d0)) .or. (.not. (z <= 1.95d+31))) then
        tmp = x + (y * 3.13060547623d0)
    else
        tmp = x + (y * (b * 1.6453555072203998d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -40000.0) || !(z <= 1.95e+31)) {
		tmp = x + (y * 3.13060547623);
	} else {
		tmp = x + (y * (b * 1.6453555072203998));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -40000.0) or not (z <= 1.95e+31):
		tmp = x + (y * 3.13060547623)
	else:
		tmp = x + (y * (b * 1.6453555072203998))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -40000.0) || !(z <= 1.95e+31))
		tmp = Float64(x + Float64(y * 3.13060547623));
	else
		tmp = Float64(x + Float64(y * Float64(b * 1.6453555072203998)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -40000.0) || ~((z <= 1.95e+31)))
		tmp = x + (y * 3.13060547623);
	else
		tmp = x + (y * (b * 1.6453555072203998));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -40000.0], N[Not[LessEqual[z, 1.95e+31]], $MachinePrecision]], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(b * 1.6453555072203998), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4e4 or 1.95e31 < z

   1. Initial program 11.9%

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

   3. Simplified 19.3%

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

   4. Taylor expanded in z around inf 86.8%

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

      1. +-commutative 86.8%

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

      2. *-commutative 86.8%

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

   6. Simplified 86.8%

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

   if -4e4 < z < 1.95e31

   1. Initial program 99.7%

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

   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 84.7%

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

      1. associate-*r* 84.8%

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

   6. Simplified 84.8%

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

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -40000 \lor \neg \left(z \leq 1.95 \cdot 10^{+31}\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998\right)\\ \end{array} \]

Alternative 16: 49.2% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.85 \cdot 10^{-128}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 110000000:\\ \;\;\;\;\left(y \cdot b\right) \cdot 1.6453555072203998\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -1.85e-128)
   x
   (if (<= x 110000000.0) (* (* y b) 1.6453555072203998) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.85e-128) {
		tmp = x;
	} else if (x <= 110000000.0) {
		tmp = (y * b) * 1.6453555072203998;
	} 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 (x <= (-1.85d-128)) then
        tmp = x
    else if (x <= 110000000.0d0) then
        tmp = (y * b) * 1.6453555072203998d0
    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 (x <= -1.85e-128) {
		tmp = x;
	} else if (x <= 110000000.0) {
		tmp = (y * b) * 1.6453555072203998;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -1.85e-128:
		tmp = x
	elif x <= 110000000.0:
		tmp = (y * b) * 1.6453555072203998
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -1.85e-128)
		tmp = x;
	elseif (x <= 110000000.0)
		tmp = Float64(Float64(y * b) * 1.6453555072203998);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -1.85e-128)
		tmp = x;
	elseif (x <= 110000000.0)
		tmp = (y * b) * 1.6453555072203998;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -1.85e-128], x, If[LessEqual[x, 110000000.0], N[(N[(y * b), $MachinePrecision] * 1.6453555072203998), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.85e-128 or 1.1e8 < x

   1. Initial program 63.7%

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

   3. Simplified 67.5%

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

   4. Taylor expanded in y around 0 63.9%

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

   if -1.85e-128 < x < 1.1e8

   1. Initial program 62.8%

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

   3. Simplified 65.0%

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

   4. Taylor expanded in z around 0 51.5%

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

      1. associate-*r* 51.5%

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

   6. Simplified 51.5%

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

      1. +-commutative 51.5%

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

      2. fma-def 51.5%

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

      3. *-commutative 51.5%

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

   8. Applied egg-rr 51.5%

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

   9. Taylor expanded in b around inf 38.5%

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

4. Final simplification 53.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.85 \cdot 10^{-128}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 110000000:\\ \;\;\;\;\left(y \cdot b\right) \cdot 1.6453555072203998\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 17: 61.9% accurate, 5.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+192}:\\ \;\;\;\;b \cdot \left(y \cdot 1.6453555072203998\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -2.1e+192)
   (* b (* y 1.6453555072203998))
   (+ x (* y 3.13060547623))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.1e+192) {
		tmp = b * (y * 1.6453555072203998);
	} 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 (y <= (-2.1d+192)) then
        tmp = b * (y * 1.6453555072203998d0)
    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 (y <= -2.1e+192) {
		tmp = b * (y * 1.6453555072203998);
	} else {
		tmp = x + (y * 3.13060547623);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -2.1e+192:
		tmp = b * (y * 1.6453555072203998)
	else:
		tmp = x + (y * 3.13060547623)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -2.1e+192)
		tmp = Float64(b * Float64(y * 1.6453555072203998));
	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 (y <= -2.1e+192)
		tmp = b * (y * 1.6453555072203998);
	else
		tmp = x + (y * 3.13060547623);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -2.1e+192], N[(b * N[(y * 1.6453555072203998), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.09999999999999995e192

   1. Initial program 64.8%

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

   3. Simplified 72.2%

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

   4. Taylor expanded in z around 0 55.0%

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

      1. associate-*r* 55.0%

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

   6. Simplified 55.0%

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

      1. +-commutative 55.0%

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

      2. fma-def 55.0%

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

      3. *-commutative 55.0%

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

   8. Applied egg-rr 55.0%

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

   9. Taylor expanded in b around inf 50.9%

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

       1. associate-*r* 50.9%

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

       2. *-commutative 50.9%

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

       3. associate-*r* 50.9%

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

   11. Simplified 50.9%

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

   if -2.09999999999999995e192 < y

   1. Initial program 63.2%

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

   3. Simplified 65.8%

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

   4. Taylor expanded in z around inf 62.4%

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

      1. +-commutative 62.4%

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

      2. *-commutative 62.4%

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

   6. Simplified 62.4%

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

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+192}:\\ \;\;\;\;b \cdot \left(y \cdot 1.6453555072203998\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \]

Alternative 18: 45.6% 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 63.4%

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

3. Simplified 66.5%

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

4. Taylor expanded in y around 0 44.5%

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

5. Final simplification 44.5%

   \[\leadsto x \]

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 2023310 
(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))))