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

Percentage Accurate: 58.7% → 98.0%

Time: 24.7s

Alternatives: 16

Speedup: 7.4×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 58.7% 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: 98.0% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771} \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right)}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \left(3.13060547623 + \frac{457.9610022158428}{{z}^{2}}\right) + \left(\frac{t}{{z}^{2}} + \frac{-36.52704169880642}{z}\right), x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<=
      (/
       (*
        y
        (+
         (* z (+ (* z (+ (* z (+ (* z 3.13060547623) 11.1667541262)) t)) a))
         b))
       (+
        (*
         z
         (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721))
        0.607771387771))
      INFINITY)
   (fma
    y
    (/
     (fma z (fma z (fma z (fma z 3.13060547623 11.1667541262) t) a) b)
     (fma
      z
      (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721)
      0.607771387771))
    x)
   (fma
    y
    (+
     (+ 3.13060547623 (/ 457.9610022158428 (pow z 2.0)))
     (+ (/ t (pow z 2.0)) (/ -36.52704169880642 z)))
    x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)) <= ((double) INFINITY)) {
		tmp = fma(y, (fma(z, fma(z, fma(z, fma(z, 3.13060547623, 11.1667541262), t), a), b) / fma(z, fma(z, fma(z, (z + 15.234687407), 31.4690115749), 11.9400905721), 0.607771387771)), x);
	} else {
		tmp = fma(y, ((3.13060547623 + (457.9610022158428 / pow(z, 2.0))) + ((t / pow(z, 2.0)) + (-36.52704169880642 / z))), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(Float64(y * Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)) <= Inf)
		tmp = fma(y, Float64(fma(z, fma(z, fma(z, fma(z, 3.13060547623, 11.1667541262), t), a), b) / fma(z, fma(z, fma(z, Float64(z + 15.234687407), 31.4690115749), 11.9400905721), 0.607771387771)), x);
	else
		tmp = fma(y, Float64(Float64(3.13060547623 + Float64(457.9610022158428 / (z ^ 2.0))) + Float64(Float64(t / (z ^ 2.0)) + Float64(-36.52704169880642 / z))), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(N[(y * N[(N[(z * N[(N[(z * N[(N[(z * N[(N[(z * 3.13060547623), $MachinePrecision] + 11.1667541262), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(N[(z * N[(N[(z * N[(N[(z * N[(z + 15.234687407), $MachinePrecision]), $MachinePrecision] + 31.4690115749), $MachinePrecision]), $MachinePrecision] + 11.9400905721), $MachinePrecision]), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision], Infinity], N[(y * N[(N[(z * N[(z * N[(z * N[(z * 3.13060547623 + 11.1667541262), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision] + b), $MachinePrecision] / N[(z * N[(z * N[(z * N[(z + 15.234687407), $MachinePrecision] + 31.4690115749), $MachinePrecision] + 11.9400905721), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(y * N[(N[(3.13060547623 + N[(457.9610022158428 / N[Power[z, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t / N[Power[z, 2.0], $MachinePrecision]), $MachinePrecision] + N[(-36.52704169880642 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 92.3%

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

   3. Simplified 96.8%

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

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

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in z around inf 99.9%

      \[\leadsto \mathsf{fma}\left(y, \color{blue}{\left(3.13060547623 + \left(\frac{457.9610022158428}{{z}^{2}} + \frac{t}{{z}^{2}}\right)\right) - 36.52704169880642 \cdot \frac{1}{z}}, x\right) \]
   6. Step-by-step derivation

      1. sub-neg 99.9%

         \[\leadsto \mathsf{fma}\left(y, \color{blue}{\left(3.13060547623 + \left(\frac{457.9610022158428}{{z}^{2}} + \frac{t}{{z}^{2}}\right)\right) + \left(-36.52704169880642 \cdot \frac{1}{z}\right)}, x\right) \]

      2. associate-+r+ 99.9%

         \[\leadsto \mathsf{fma}\left(y, \color{blue}{\left(\left(3.13060547623 + \frac{457.9610022158428}{{z}^{2}}\right) + \frac{t}{{z}^{2}}\right)} + \left(-36.52704169880642 \cdot \frac{1}{z}\right), x\right) \]

      3. associate-+l+ 99.9%

         \[\leadsto \mathsf{fma}\left(y, \color{blue}{\left(3.13060547623 + \frac{457.9610022158428}{{z}^{2}}\right) + \left(\frac{t}{{z}^{2}} + \left(-36.52704169880642 \cdot \frac{1}{z}\right)\right)}, x\right) \]

      4. associate-*r/ 99.9%

         \[\leadsto \mathsf{fma}\left(y, \left(3.13060547623 + \frac{457.9610022158428}{{z}^{2}}\right) + \left(\frac{t}{{z}^{2}} + \left(-\color{blue}{\frac{36.52704169880642 \cdot 1}{z}}\right)\right), x\right) \]

      5. metadata-eval 99.9%

         \[\leadsto \mathsf{fma}\left(y, \left(3.13060547623 + \frac{457.9610022158428}{{z}^{2}}\right) + \left(\frac{t}{{z}^{2}} + \left(-\frac{\color{blue}{36.52704169880642}}{z}\right)\right), x\right) \]

      6. distribute-neg-frac 99.9%

         \[\leadsto \mathsf{fma}\left(y, \left(3.13060547623 + \frac{457.9610022158428}{{z}^{2}}\right) + \left(\frac{t}{{z}^{2}} + \color{blue}{\frac{-36.52704169880642}{z}}\right), x\right) \]

      7. metadata-eval 99.9%

         \[\leadsto \mathsf{fma}\left(y, \left(3.13060547623 + \frac{457.9610022158428}{{z}^{2}}\right) + \left(\frac{t}{{z}^{2}} + \frac{\color{blue}{-36.52704169880642}}{z}\right), x\right) \]

   7. Simplified 99.9%

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

4. Final simplification 97.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771} \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right)}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \left(3.13060547623 + \frac{457.9610022158428}{{z}^{2}}\right) + \left(\frac{t}{{z}^{2}} + \frac{-36.52704169880642}{z}\right), x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 97.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771\\ \mathbf{if}\;\frac{y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right)}{t\_1} \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right), \frac{y}{t\_1}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \left(3.13060547623 + \frac{457.9610022158428}{{z}^{2}}\right) + \left(\frac{t}{{z}^{2}} + \frac{-36.52704169880642}{z}\right), x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+
          (*
           z
           (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721))
          0.607771387771)))
   (if (<=
        (/
         (*
          y
          (+
           (* z (+ (* z (+ (* z (+ (* z 3.13060547623) 11.1667541262)) t)) a))
           b))
         t_1)
        INFINITY)
     (fma
      (fma z (fma z (fma z (fma z 3.13060547623 11.1667541262) t) a) b)
      (/ y t_1)
      x)
     (fma
      y
      (+
       (+ 3.13060547623 (/ 457.9610022158428 (pow z 2.0)))
       (+ (/ t (pow z 2.0)) (/ -36.52704169880642 z)))
      x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771;
	double tmp;
	if (((y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / t_1) <= ((double) INFINITY)) {
		tmp = fma(fma(z, fma(z, fma(z, fma(z, 3.13060547623, 11.1667541262), t), a), b), (y / t_1), x);
	} else {
		tmp = fma(y, ((3.13060547623 + (457.9610022158428 / pow(z, 2.0))) + ((t / pow(z, 2.0)) + (-36.52704169880642 / z))), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)
	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)) / t_1) <= Inf)
		tmp = fma(fma(z, fma(z, fma(z, fma(z, 3.13060547623, 11.1667541262), t), a), b), Float64(y / t_1), x);
	else
		tmp = fma(y, Float64(Float64(3.13060547623 + Float64(457.9610022158428 / (z ^ 2.0))) + Float64(Float64(t / (z ^ 2.0)) + Float64(-36.52704169880642 / z))), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{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]}, 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] / t$95$1), $MachinePrecision], Infinity], N[(N[(z * N[(z * N[(z * N[(z * 3.13060547623 + 11.1667541262), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision] + b), $MachinePrecision] * N[(y / t$95$1), $MachinePrecision] + x), $MachinePrecision], N[(y * N[(N[(3.13060547623 + N[(457.9610022158428 / N[Power[z, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t / N[Power[z, 2.0], $MachinePrecision]), $MachinePrecision] + N[(-36.52704169880642 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 92.3%

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

   3. Simplified 96.3%

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

   5. Taylor expanded in y around 0 96.3%

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

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

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in z around inf 99.9%

      \[\leadsto \mathsf{fma}\left(y, \color{blue}{\left(3.13060547623 + \left(\frac{457.9610022158428}{{z}^{2}} + \frac{t}{{z}^{2}}\right)\right) - 36.52704169880642 \cdot \frac{1}{z}}, x\right) \]
   6. Step-by-step derivation

      1. sub-neg 99.9%

         \[\leadsto \mathsf{fma}\left(y, \color{blue}{\left(3.13060547623 + \left(\frac{457.9610022158428}{{z}^{2}} + \frac{t}{{z}^{2}}\right)\right) + \left(-36.52704169880642 \cdot \frac{1}{z}\right)}, x\right) \]

      2. associate-+r+ 99.9%

         \[\leadsto \mathsf{fma}\left(y, \color{blue}{\left(\left(3.13060547623 + \frac{457.9610022158428}{{z}^{2}}\right) + \frac{t}{{z}^{2}}\right)} + \left(-36.52704169880642 \cdot \frac{1}{z}\right), x\right) \]

      3. associate-+l+ 99.9%

         \[\leadsto \mathsf{fma}\left(y, \color{blue}{\left(3.13060547623 + \frac{457.9610022158428}{{z}^{2}}\right) + \left(\frac{t}{{z}^{2}} + \left(-36.52704169880642 \cdot \frac{1}{z}\right)\right)}, x\right) \]

      4. associate-*r/ 99.9%

         \[\leadsto \mathsf{fma}\left(y, \left(3.13060547623 + \frac{457.9610022158428}{{z}^{2}}\right) + \left(\frac{t}{{z}^{2}} + \left(-\color{blue}{\frac{36.52704169880642 \cdot 1}{z}}\right)\right), x\right) \]

      5. metadata-eval 99.9%

         \[\leadsto \mathsf{fma}\left(y, \left(3.13060547623 + \frac{457.9610022158428}{{z}^{2}}\right) + \left(\frac{t}{{z}^{2}} + \left(-\frac{\color{blue}{36.52704169880642}}{z}\right)\right), x\right) \]

      6. distribute-neg-frac 99.9%

         \[\leadsto \mathsf{fma}\left(y, \left(3.13060547623 + \frac{457.9610022158428}{{z}^{2}}\right) + \left(\frac{t}{{z}^{2}} + \color{blue}{\frac{-36.52704169880642}{z}}\right), x\right) \]

      7. metadata-eval 99.9%

         \[\leadsto \mathsf{fma}\left(y, \left(3.13060547623 + \frac{457.9610022158428}{{z}^{2}}\right) + \left(\frac{t}{{z}^{2}} + \frac{\color{blue}{-36.52704169880642}}{z}\right), x\right) \]

   7. Simplified 99.9%

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

4. Final simplification 97.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771} \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right), \frac{y}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \left(3.13060547623 + \frac{457.9610022158428}{{z}^{2}}\right) + \left(\frac{t}{{z}^{2}} + \frac{-36.52704169880642}{z}\right), x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 97.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+50}:\\ \;\;\;\;x + \left(y \cdot \frac{\frac{t + 457.9610022158428}{z} - 36.52704169880642}{z} + y \cdot 3.13060547623\right)\\ \mathbf{elif}\;z \leq 1.66 \cdot 10^{+25}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right)\right)\right)\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \left(3.13060547623 + \frac{457.9610022158428}{{z}^{2}}\right) + \left(\frac{t}{{z}^{2}} + \frac{-36.52704169880642}{z}\right), x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -4.5e+50)
   (+
    x
    (+
     (* y (/ (- (/ (+ t 457.9610022158428) z) 36.52704169880642) z))
     (* y 3.13060547623)))
   (if (<= z 1.66e+25)
     (+
      x
      (/
       (*
        y
        (+
         b
         (* z (+ a (* z (+ t (* z (fma z 3.13060547623 11.1667541262))))))))
       (+
        (*
         z
         (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721))
        0.607771387771)))
     (fma
      y
      (+
       (+ 3.13060547623 (/ 457.9610022158428 (pow z 2.0)))
       (+ (/ t (pow z 2.0)) (/ -36.52704169880642 z)))
      x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -4.5e+50) {
		tmp = x + ((y * ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)) + (y * 3.13060547623));
	} else if (z <= 1.66e+25) {
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * fma(z, 3.13060547623, 11.1667541262)))))))) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771));
	} else {
		tmp = fma(y, ((3.13060547623 + (457.9610022158428 / pow(z, 2.0))) + ((t / pow(z, 2.0)) + (-36.52704169880642 / z))), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -4.5e+50)
		tmp = Float64(x + Float64(Float64(y * Float64(Float64(Float64(Float64(t + 457.9610022158428) / z) - 36.52704169880642) / z)) + Float64(y * 3.13060547623)));
	elseif (z <= 1.66e+25)
		tmp = Float64(x + Float64(Float64(y * Float64(b + Float64(z * Float64(a + Float64(z * Float64(t + Float64(z * fma(z, 3.13060547623, 11.1667541262)))))))) / Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)));
	else
		tmp = fma(y, Float64(Float64(3.13060547623 + Float64(457.9610022158428 / (z ^ 2.0))) + Float64(Float64(t / (z ^ 2.0)) + Float64(-36.52704169880642 / z))), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -4.5e+50], N[(x + N[(N[(y * N[(N[(N[(N[(t + 457.9610022158428), $MachinePrecision] / z), $MachinePrecision] - 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.66e+25], N[(x + N[(N[(y * N[(b + N[(z * N[(a + N[(z * N[(t + N[(z * N[(z * 3.13060547623 + 11.1667541262), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(z * N[(N[(z * N[(N[(z * N[(z + 15.234687407), $MachinePrecision]), $MachinePrecision] + 31.4690115749), $MachinePrecision]), $MachinePrecision] + 11.9400905721), $MachinePrecision]), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(3.13060547623 + N[(457.9610022158428 / N[Power[z, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t / N[Power[z, 2.0], $MachinePrecision]), $MachinePrecision] + N[(-36.52704169880642 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.50000000000000014e50

   1. Initial program 4.4%

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

   3. Taylor expanded in z around -inf 87.6%

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

   4. Taylor expanded in y around 0 91.8%

      \[\leadsto x + \left(-1 \cdot \color{blue}{\frac{y \cdot \left(36.52704169880642 + -1 \cdot \frac{457.9610022158428 + t}{z}\right)}{z}} + 3.13060547623 \cdot y\right) \]
   5. Step-by-step derivation

      1. associate-/l* 100.0%

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

      2. mul-1-neg 100.0%

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

      3. unsub-neg 100.0%

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

      4. +-commutative 100.0%

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

   6. Simplified 100.0%

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

   if -4.50000000000000014e50 < z < 1.6600000000000001e25

   1. Initial program 96.5%

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

   3. Taylor expanded in z around 0 96.5%

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

      1. +-commutative 96.5%

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

      2. *-commutative 96.5%

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

      3. fma-undefine 96.5%

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

   5. Simplified 96.5%

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

   if 1.6600000000000001e25 < z

   1. Initial program 17.9%

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

   3. Simplified 22.2%

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

   5. Taylor expanded in z around inf 97.6%

      \[\leadsto \mathsf{fma}\left(y, \color{blue}{\left(3.13060547623 + \left(\frac{457.9610022158428}{{z}^{2}} + \frac{t}{{z}^{2}}\right)\right) - 36.52704169880642 \cdot \frac{1}{z}}, x\right) \]
   6. Step-by-step derivation

      1. sub-neg 97.6%

         \[\leadsto \mathsf{fma}\left(y, \color{blue}{\left(3.13060547623 + \left(\frac{457.9610022158428}{{z}^{2}} + \frac{t}{{z}^{2}}\right)\right) + \left(-36.52704169880642 \cdot \frac{1}{z}\right)}, x\right) \]

      2. associate-+r+ 97.6%

         \[\leadsto \mathsf{fma}\left(y, \color{blue}{\left(\left(3.13060547623 + \frac{457.9610022158428}{{z}^{2}}\right) + \frac{t}{{z}^{2}}\right)} + \left(-36.52704169880642 \cdot \frac{1}{z}\right), x\right) \]

      3. associate-+l+ 97.6%

         \[\leadsto \mathsf{fma}\left(y, \color{blue}{\left(3.13060547623 + \frac{457.9610022158428}{{z}^{2}}\right) + \left(\frac{t}{{z}^{2}} + \left(-36.52704169880642 \cdot \frac{1}{z}\right)\right)}, x\right) \]

      4. associate-*r/ 97.6%

         \[\leadsto \mathsf{fma}\left(y, \left(3.13060547623 + \frac{457.9610022158428}{{z}^{2}}\right) + \left(\frac{t}{{z}^{2}} + \left(-\color{blue}{\frac{36.52704169880642 \cdot 1}{z}}\right)\right), x\right) \]

      5. metadata-eval 97.6%

         \[\leadsto \mathsf{fma}\left(y, \left(3.13060547623 + \frac{457.9610022158428}{{z}^{2}}\right) + \left(\frac{t}{{z}^{2}} + \left(-\frac{\color{blue}{36.52704169880642}}{z}\right)\right), x\right) \]

      6. distribute-neg-frac 97.6%

         \[\leadsto \mathsf{fma}\left(y, \left(3.13060547623 + \frac{457.9610022158428}{{z}^{2}}\right) + \left(\frac{t}{{z}^{2}} + \color{blue}{\frac{-36.52704169880642}{z}}\right), x\right) \]

      7. metadata-eval 97.6%

         \[\leadsto \mathsf{fma}\left(y, \left(3.13060547623 + \frac{457.9610022158428}{{z}^{2}}\right) + \left(\frac{t}{{z}^{2}} + \frac{\color{blue}{-36.52704169880642}}{z}\right), x\right) \]

   7. Simplified 97.6%

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

4. Final simplification 97.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+50}:\\ \;\;\;\;x + \left(y \cdot \frac{\frac{t + 457.9610022158428}{z} - 36.52704169880642}{z} + y \cdot 3.13060547623\right)\\ \mathbf{elif}\;z \leq 1.66 \cdot 10^{+25}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right)\right)\right)\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \left(3.13060547623 + \frac{457.9610022158428}{{z}^{2}}\right) + \left(\frac{t}{{z}^{2}} + \frac{-36.52704169880642}{z}\right), x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 97.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+49} \lor \neg \left(z \leq 1.75 \cdot 10^{+25}\right):\\ \;\;\;\;x + \left(y \cdot \frac{\frac{t + 457.9610022158428}{z} - 36.52704169880642}{z} + y \cdot 3.13060547623\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right)\right)\right)\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -9.5e+49) (not (<= z 1.75e+25)))
   (+
    x
    (+
     (* y (/ (- (/ (+ t 457.9610022158428) z) 36.52704169880642) z))
     (* y 3.13060547623)))
   (+
    x
    (/
     (*
      y
      (+ b (* z (+ a (* z (+ t (* z (fma z 3.13060547623 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 <= -9.5e+49) || !(z <= 1.75e+25)) {
		tmp = x + ((y * ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)) + (y * 3.13060547623));
	} else {
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * fma(z, 3.13060547623, 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 <= -9.5e+49) || !(z <= 1.75e+25))
		tmp = Float64(x + Float64(Float64(y * Float64(Float64(Float64(Float64(t + 457.9610022158428) / z) - 36.52704169880642) / z)) + Float64(y * 3.13060547623)));
	else
		tmp = Float64(x + Float64(Float64(y * Float64(b + Float64(z * Float64(a + Float64(z * Float64(t + Float64(z * fma(z, 3.13060547623, 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

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -9.5e+49], N[Not[LessEqual[z, 1.75e+25]], $MachinePrecision]], N[(x + N[(N[(y * N[(N[(N[(N[(t + 457.9610022158428), $MachinePrecision] / z), $MachinePrecision] - 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * N[(b + N[(z * N[(a + N[(z * N[(t + N[(z * N[(z * 3.13060547623 + 11.1667541262), $MachinePrecision]), $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 < -9.49999999999999969e49 or 1.75e25 < z

   1. Initial program 12.2%

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

   3. Taylor expanded in z around -inf 85.3%

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

   4. Taylor expanded in y around 0 91.4%

      \[\leadsto x + \left(-1 \cdot \color{blue}{\frac{y \cdot \left(36.52704169880642 + -1 \cdot \frac{457.9610022158428 + t}{z}\right)}{z}} + 3.13060547623 \cdot y\right) \]
   5. Step-by-step derivation

      1. associate-/l* 98.6%

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

      2. mul-1-neg 98.6%

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

      3. unsub-neg 98.6%

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

      4. +-commutative 98.6%

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

   6. Simplified 98.6%

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

   if -9.49999999999999969e49 < z < 1.75e25

   1. Initial program 96.5%

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

   3. Taylor expanded in z around 0 96.5%

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

      1. +-commutative 96.5%

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

      2. *-commutative 96.5%

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

      3. fma-undefine 96.5%

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

   5. Simplified 96.5%

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

4. Final simplification 97.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+49} \lor \neg \left(z \leq 1.75 \cdot 10^{+25}\right):\\ \;\;\;\;x + \left(y \cdot \frac{\frac{t + 457.9610022158428}{z} - 36.52704169880642}{z} + y \cdot 3.13060547623\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right)\right)\right)\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 97.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.06 \cdot 10^{+50} \lor \neg \left(z \leq 2.1 \cdot 10^{+24}\right):\\ \;\;\;\;x + \left(y \cdot \frac{\frac{t + 457.9610022158428}{z} - 36.52704169880642}{z} + y \cdot 3.13060547623\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771} + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.06e+50) (not (<= z 2.1e+24)))
   (+
    x
    (+
     (* y (/ (- (/ (+ t 457.9610022158428) z) 36.52704169880642) z))
     (* y 3.13060547623)))
   (+
    (/
     (*
      y
      (+
       (* z (+ (* z (+ (* z (+ (* z 3.13060547623) 11.1667541262)) t)) a))
       b))
     (+
      (* z (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721))
      0.607771387771))
    x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.06e+50) || !(z <= 2.1e+24)) {
		tmp = x + ((y * ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)) + (y * 3.13060547623));
	} else {
		tmp = ((y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)) + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-1.06d+50)) .or. (.not. (z <= 2.1d+24))) then
        tmp = x + ((y * ((((t + 457.9610022158428d0) / z) - 36.52704169880642d0) / z)) + (y * 3.13060547623d0))
    else
        tmp = ((y * ((z * ((z * ((z * ((z * 3.13060547623d0) + 11.1667541262d0)) + t)) + a)) + b)) / ((z * ((z * ((z * (z + 15.234687407d0)) + 31.4690115749d0)) + 11.9400905721d0)) + 0.607771387771d0)) + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.06e+50) || !(z <= 2.1e+24)) {
		tmp = x + ((y * ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)) + (y * 3.13060547623));
	} else {
		tmp = ((y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)) + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.06e+50) or not (z <= 2.1e+24):
		tmp = x + ((y * ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)) + (y * 3.13060547623))
	else:
		tmp = ((y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)) + x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.06e+50) || !(z <= 2.1e+24))
		tmp = Float64(x + Float64(Float64(y * Float64(Float64(Float64(Float64(t + 457.9610022158428) / z) - 36.52704169880642) / z)) + Float64(y * 3.13060547623)));
	else
		tmp = Float64(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)) + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.06e+50) || ~((z <= 2.1e+24)))
		tmp = x + ((y * ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)) + (y * 3.13060547623));
	else
		tmp = ((y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)) + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.06e+50], N[Not[LessEqual[z, 2.1e+24]], $MachinePrecision]], N[(x + N[(N[(y * N[(N[(N[(N[(t + 457.9610022158428), $MachinePrecision] / z), $MachinePrecision] - 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(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] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.06e50 or 2.1000000000000001e24 < z

   1. Initial program 12.2%

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

   3. Taylor expanded in z around -inf 85.3%

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

   4. Taylor expanded in y around 0 91.4%

      \[\leadsto x + \left(-1 \cdot \color{blue}{\frac{y \cdot \left(36.52704169880642 + -1 \cdot \frac{457.9610022158428 + t}{z}\right)}{z}} + 3.13060547623 \cdot y\right) \]
   5. Step-by-step derivation

      1. associate-/l* 98.6%

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

      2. mul-1-neg 98.6%

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

      3. unsub-neg 98.6%

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

      4. +-commutative 98.6%

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

   6. Simplified 98.6%

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

   if -1.06e50 < z < 2.1000000000000001e24

   1. Initial program 96.5%

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

4. Final simplification 97.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.06 \cdot 10^{+50} \lor \neg \left(z \leq 2.1 \cdot 10^{+24}\right):\\ \;\;\;\;x + \left(y \cdot \frac{\frac{t + 457.9610022158428}{z} - 36.52704169880642}{z} + y \cdot 3.13060547623\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771} + x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 96.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.9 \cdot 10^{+26} \lor \neg \left(z \leq 24\right):\\ \;\;\;\;x + \left(y \cdot \frac{\frac{t + 457.9610022158428}{z} - 36.52704169880642}{z} + y \cdot 3.13060547623\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot 31.4690115749\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -4.9e+26) (not (<= z 24.0)))
   (+
    x
    (+
     (* y (/ (- (/ (+ t 457.9610022158428) z) 36.52704169880642) z))
     (* y 3.13060547623)))
   (+
    x
    (/
     (*
      y
      (+
       (* z (+ (* z (+ (* z (+ (* z 3.13060547623) 11.1667541262)) t)) a))
       b))
     (+ 0.607771387771 (* z (+ 11.9400905721 (* z 31.4690115749))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -4.9e+26) || !(z <= 24.0)) {
		tmp = x + ((y * ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)) + (y * 3.13060547623));
	} else {
		tmp = x + ((y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / (0.607771387771 + (z * (11.9400905721 + (z * 31.4690115749)))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-4.9d+26)) .or. (.not. (z <= 24.0d0))) then
        tmp = x + ((y * ((((t + 457.9610022158428d0) / z) - 36.52704169880642d0) / z)) + (y * 3.13060547623d0))
    else
        tmp = x + ((y * ((z * ((z * ((z * ((z * 3.13060547623d0) + 11.1667541262d0)) + t)) + a)) + b)) / (0.607771387771d0 + (z * (11.9400905721d0 + (z * 31.4690115749d0)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -4.9e+26) || !(z <= 24.0)) {
		tmp = x + ((y * ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)) + (y * 3.13060547623));
	} else {
		tmp = x + ((y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / (0.607771387771 + (z * (11.9400905721 + (z * 31.4690115749)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -4.9e+26) or not (z <= 24.0):
		tmp = x + ((y * ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)) + (y * 3.13060547623))
	else:
		tmp = x + ((y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / (0.607771387771 + (z * (11.9400905721 + (z * 31.4690115749)))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -4.9e+26) || !(z <= 24.0))
		tmp = Float64(x + Float64(Float64(y * Float64(Float64(Float64(Float64(t + 457.9610022158428) / z) - 36.52704169880642) / z)) + Float64(y * 3.13060547623)));
	else
		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 * Float64(11.9400905721 + Float64(z * 31.4690115749))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -4.9e+26) || ~((z <= 24.0)))
		tmp = x + ((y * ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)) + (y * 3.13060547623));
	else
		tmp = x + ((y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / (0.607771387771 + (z * (11.9400905721 + (z * 31.4690115749)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -4.9e+26], N[Not[LessEqual[z, 24.0]], $MachinePrecision]], N[(x + N[(N[(y * N[(N[(N[(N[(t + 457.9610022158428), $MachinePrecision] / z), $MachinePrecision] - 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 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 * N[(11.9400905721 + N[(z * 31.4690115749), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.89999999999999974e26 or 24 < z

   1. Initial program 18.3%

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

   3. Taylor expanded in z around -inf 80.8%

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

   4. Taylor expanded in y around 0 86.3%

      \[\leadsto x + \left(-1 \cdot \color{blue}{\frac{y \cdot \left(36.52704169880642 + -1 \cdot \frac{457.9610022158428 + t}{z}\right)}{z}} + 3.13060547623 \cdot y\right) \]
   5. Step-by-step derivation

      1. associate-/l* 92.6%

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

      2. mul-1-neg 92.6%

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

      3. unsub-neg 92.6%

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

      4. +-commutative 92.6%

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

   6. Simplified 92.6%

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

   if -4.89999999999999974e26 < z < 24

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0 97.6%

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

      1. *-commutative 97.6%

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

   5. Simplified 97.6%

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

4. Final simplification 95.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.9 \cdot 10^{+26} \lor \neg \left(z \leq 24\right):\\ \;\;\;\;x + \left(y \cdot \frac{\frac{t + 457.9610022158428}{z} - 36.52704169880642}{z} + y \cdot 3.13060547623\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot 31.4690115749\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 96.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -410 \lor \neg \left(z \leq 24\right):\\ \;\;\;\;x + \left(y \cdot \frac{\frac{t + 457.9610022158428}{z} - 36.52704169880642}{z} + y \cdot 3.13060547623\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -410.0) (not (<= z 24.0)))
   (+
    x
    (+
     (* y (/ (- (/ (+ t 457.9610022158428) z) 36.52704169880642) z))
     (* y 3.13060547623)))
   (+
    x
    (/
     (*
      y
      (+
       (* z (+ (* z (+ (* z (+ (* z 3.13060547623) 11.1667541262)) t)) a))
       b))
     (+ 0.607771387771 (* z 11.9400905721))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -410.0) || !(z <= 24.0)) {
		tmp = x + ((y * ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)) + (y * 3.13060547623));
	} else {
		tmp = x + ((y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / (0.607771387771 + (z * 11.9400905721)));
	}
	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 <= (-410.0d0)) .or. (.not. (z <= 24.0d0))) then
        tmp = x + ((y * ((((t + 457.9610022158428d0) / z) - 36.52704169880642d0) / z)) + (y * 3.13060547623d0))
    else
        tmp = x + ((y * ((z * ((z * ((z * ((z * 3.13060547623d0) + 11.1667541262d0)) + t)) + a)) + b)) / (0.607771387771d0 + (z * 11.9400905721d0)))
    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 <= -410.0) || !(z <= 24.0)) {
		tmp = x + ((y * ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)) + (y * 3.13060547623));
	} else {
		tmp = x + ((y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / (0.607771387771 + (z * 11.9400905721)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -410.0) or not (z <= 24.0):
		tmp = x + ((y * ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)) + (y * 3.13060547623))
	else:
		tmp = x + ((y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / (0.607771387771 + (z * 11.9400905721)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -410.0) || !(z <= 24.0))
		tmp = Float64(x + Float64(Float64(y * Float64(Float64(Float64(Float64(t + 457.9610022158428) / z) - 36.52704169880642) / z)) + Float64(y * 3.13060547623)));
	else
		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))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -410.0) || ~((z <= 24.0)))
		tmp = x + ((y * ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)) + (y * 3.13060547623));
	else
		tmp = x + ((y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / (0.607771387771 + (z * 11.9400905721)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -410.0], N[Not[LessEqual[z, 24.0]], $MachinePrecision]], N[(x + N[(N[(y * N[(N[(N[(N[(t + 457.9610022158428), $MachinePrecision] / z), $MachinePrecision] - 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 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]]

Derivation

1. Split input into 2 regimes

2. if z < -410 or 24 < z

   1. Initial program 21.5%

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

   3. Taylor expanded in z around -inf 79.3%

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

   4. Taylor expanded in y around 0 84.6%

      \[\leadsto x + \left(-1 \cdot \color{blue}{\frac{y \cdot \left(36.52704169880642 + -1 \cdot \frac{457.9610022158428 + t}{z}\right)}{z}} + 3.13060547623 \cdot y\right) \]
   5. Step-by-step derivation

      1. associate-/l* 90.7%

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

      2. mul-1-neg 90.7%

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

      3. unsub-neg 90.7%

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

      4. +-commutative 90.7%

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

   6. Simplified 90.7%

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

   if -410 < z < 24

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0 97.8%

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

      1. *-commutative 97.8%

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

   5. Simplified 97.8%

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

4. Final simplification 94.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -410 \lor \neg \left(z \leq 24\right):\\ \;\;\;\;x + \left(y \cdot \frac{\frac{t + 457.9610022158428}{z} - 36.52704169880642}{z} + y \cdot 3.13060547623\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 90.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+26} \lor \neg \left(z \leq 23\right):\\ \;\;\;\;x + \left(y \cdot \frac{\frac{t + 457.9610022158428}{z} - 36.52704169880642}{z} + y \cdot 3.13060547623\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(1.6453555072203998 \cdot \left(y \cdot b\right) + z \cdot \left(1.6453555072203998 \cdot \left(y \cdot a\right) + 1.6453555072203998 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -3.6e+26) (not (<= z 23.0)))
   (+
    x
    (+
     (* y (/ (- (/ (+ t 457.9610022158428) z) 36.52704169880642) z))
     (* y 3.13060547623)))
   (+
    x
    (+
     (* 1.6453555072203998 (* y b))
     (*
      z
      (+
       (* 1.6453555072203998 (* y a))
       (* 1.6453555072203998 (* t (* y z)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3.6e+26) || !(z <= 23.0)) {
		tmp = x + ((y * ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)) + (y * 3.13060547623));
	} else {
		tmp = x + ((1.6453555072203998 * (y * b)) + (z * ((1.6453555072203998 * (y * a)) + (1.6453555072203998 * (t * (y * z))))));
	}
	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 <= (-3.6d+26)) .or. (.not. (z <= 23.0d0))) then
        tmp = x + ((y * ((((t + 457.9610022158428d0) / z) - 36.52704169880642d0) / z)) + (y * 3.13060547623d0))
    else
        tmp = x + ((1.6453555072203998d0 * (y * b)) + (z * ((1.6453555072203998d0 * (y * a)) + (1.6453555072203998d0 * (t * (y * z))))))
    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 <= -3.6e+26) || !(z <= 23.0)) {
		tmp = x + ((y * ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)) + (y * 3.13060547623));
	} else {
		tmp = x + ((1.6453555072203998 * (y * b)) + (z * ((1.6453555072203998 * (y * a)) + (1.6453555072203998 * (t * (y * z))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -3.6e+26) or not (z <= 23.0):
		tmp = x + ((y * ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)) + (y * 3.13060547623))
	else:
		tmp = x + ((1.6453555072203998 * (y * b)) + (z * ((1.6453555072203998 * (y * a)) + (1.6453555072203998 * (t * (y * z))))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -3.6e+26) || !(z <= 23.0))
		tmp = Float64(x + Float64(Float64(y * Float64(Float64(Float64(Float64(t + 457.9610022158428) / z) - 36.52704169880642) / z)) + Float64(y * 3.13060547623)));
	else
		tmp = Float64(x + Float64(Float64(1.6453555072203998 * Float64(y * b)) + Float64(z * Float64(Float64(1.6453555072203998 * Float64(y * a)) + Float64(1.6453555072203998 * Float64(t * Float64(y * z)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -3.6e+26) || ~((z <= 23.0)))
		tmp = x + ((y * ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)) + (y * 3.13060547623));
	else
		tmp = x + ((1.6453555072203998 * (y * b)) + (z * ((1.6453555072203998 * (y * a)) + (1.6453555072203998 * (t * (y * z))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -3.6e+26], N[Not[LessEqual[z, 23.0]], $MachinePrecision]], N[(x + N[(N[(y * N[(N[(N[(N[(t + 457.9610022158428), $MachinePrecision] / z), $MachinePrecision] - 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(1.6453555072203998 * N[(y * b), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(1.6453555072203998 * N[(y * a), $MachinePrecision]), $MachinePrecision] + N[(1.6453555072203998 * N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.60000000000000024e26 or 23 < z

   1. Initial program 18.3%

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

   3. Taylor expanded in z around -inf 80.8%

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

   4. Taylor expanded in y around 0 86.3%

      \[\leadsto x + \left(-1 \cdot \color{blue}{\frac{y \cdot \left(36.52704169880642 + -1 \cdot \frac{457.9610022158428 + t}{z}\right)}{z}} + 3.13060547623 \cdot y\right) \]
   5. Step-by-step derivation

      1. associate-/l* 92.6%

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

      2. mul-1-neg 92.6%

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

      3. unsub-neg 92.6%

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

      4. +-commutative 92.6%

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

   6. Simplified 92.6%

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

   if -3.60000000000000024e26 < z < 23

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0 91.1%

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

   4. Taylor expanded in z around inf 89.8%

      \[\leadsto x + \frac{b \cdot y + z \cdot \left(a \cdot y + t \cdot \left(y \cdot z\right)\right)}{\color{blue}{{z}^{4} \cdot \left(1 + 15.234687407 \cdot \frac{1}{z}\right)} + 0.607771387771} \]
   5. Step-by-step derivation

      1. associate-*r/ 89.8%

         \[\leadsto x + \frac{b \cdot y + z \cdot \left(a \cdot y + t \cdot \left(y \cdot z\right)\right)}{{z}^{4} \cdot \left(1 + \color{blue}{\frac{15.234687407 \cdot 1}{z}}\right) + 0.607771387771} \]

      2. metadata-eval 89.8%

         \[\leadsto x + \frac{b \cdot y + z \cdot \left(a \cdot y + t \cdot \left(y \cdot z\right)\right)}{{z}^{4} \cdot \left(1 + \frac{\color{blue}{15.234687407}}{z}\right) + 0.607771387771} \]

   6. Simplified 89.8%

      \[\leadsto x + \frac{b \cdot y + z \cdot \left(a \cdot y + t \cdot \left(y \cdot z\right)\right)}{\color{blue}{{z}^{4} \cdot \left(1 + \frac{15.234687407}{z}\right)} + 0.607771387771} \]

   7. Taylor expanded in z around 0 89.1%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+26} \lor \neg \left(z \leq 23\right):\\ \;\;\;\;x + \left(y \cdot \frac{\frac{t + 457.9610022158428}{z} - 36.52704169880642}{z} + y \cdot 3.13060547623\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(1.6453555072203998 \cdot \left(y \cdot b\right) + z \cdot \left(1.6453555072203998 \cdot \left(y \cdot a\right) + 1.6453555072203998 \cdot \left(t \cdot \left(y \cdot z\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 96.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -410 \lor \neg \left(z \leq 22\right):\\ \;\;\;\;x + \left(y \cdot \frac{\frac{t + 457.9610022158428}{z} - 36.52704169880642}{z} + y \cdot 3.13060547623\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot 11.1667541262\right)\right)\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -410.0) (not (<= z 22.0)))
   (+
    x
    (+
     (* y (/ (- (/ (+ t 457.9610022158428) z) 36.52704169880642) z))
     (* y 3.13060547623)))
   (+
    x
    (/
     (* y (+ b (* z (+ a (* z (+ t (* z 11.1667541262)))))))
     (+ 0.607771387771 (* z 11.9400905721))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -410.0) || !(z <= 22.0)) {
		tmp = x + ((y * ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)) + (y * 3.13060547623));
	} else {
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))) / (0.607771387771 + (z * 11.9400905721)));
	}
	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 <= (-410.0d0)) .or. (.not. (z <= 22.0d0))) then
        tmp = x + ((y * ((((t + 457.9610022158428d0) / z) - 36.52704169880642d0) / z)) + (y * 3.13060547623d0))
    else
        tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262d0))))))) / (0.607771387771d0 + (z * 11.9400905721d0)))
    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 <= -410.0) || !(z <= 22.0)) {
		tmp = x + ((y * ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)) + (y * 3.13060547623));
	} else {
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))) / (0.607771387771 + (z * 11.9400905721)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -410.0) or not (z <= 22.0):
		tmp = x + ((y * ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)) + (y * 3.13060547623))
	else:
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))) / (0.607771387771 + (z * 11.9400905721)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -410.0) || !(z <= 22.0))
		tmp = Float64(x + Float64(Float64(y * Float64(Float64(Float64(Float64(t + 457.9610022158428) / z) - 36.52704169880642) / z)) + 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(0.607771387771 + Float64(z * 11.9400905721))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -410.0) || ~((z <= 22.0)))
		tmp = x + ((y * ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)) + (y * 3.13060547623));
	else
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))) / (0.607771387771 + (z * 11.9400905721)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -410.0], N[Not[LessEqual[z, 22.0]], $MachinePrecision]], N[(x + N[(N[(y * N[(N[(N[(N[(t + 457.9610022158428), $MachinePrecision] / z), $MachinePrecision] - 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(y * 3.13060547623), $MachinePrecision]), $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[(0.607771387771 + N[(z * 11.9400905721), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -410 or 22 < z

   1. Initial program 21.5%

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

   3. Taylor expanded in z around -inf 79.3%

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

   4. Taylor expanded in y around 0 84.6%

      \[\leadsto x + \left(-1 \cdot \color{blue}{\frac{y \cdot \left(36.52704169880642 + -1 \cdot \frac{457.9610022158428 + t}{z}\right)}{z}} + 3.13060547623 \cdot y\right) \]
   5. Step-by-step derivation

      1. associate-/l* 90.7%

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

      2. mul-1-neg 90.7%

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

      3. unsub-neg 90.7%

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

      4. +-commutative 90.7%

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

   6. Simplified 90.7%

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

   if -410 < z < 22

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0 97.8%

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

      1. *-commutative 97.8%

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

   5. Simplified 97.8%

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

   6. Taylor expanded in z around 0 97.6%

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

      1. *-commutative 97.6%

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

   8. Simplified 97.6%

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

4. Final simplification 94.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -410 \lor \neg \left(z \leq 22\right):\\ \;\;\;\;x + \left(y \cdot \frac{\frac{t + 457.9610022158428}{z} - 36.52704169880642}{z} + y \cdot 3.13060547623\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot 11.1667541262\right)\right)\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 81.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot 3.13060547623\\ \mathbf{if}\;z \leq -2.4 \cdot 10^{+70}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-186}:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998\right)\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{-148}:\\ \;\;\;\;x + z \cdot \left(y \cdot \left(a \cdot 1.6453555072203998\right)\right)\\ \mathbf{elif}\;z \leq 1.7:\\ \;\;\;\;x + 1.6453555072203998 \cdot \left(y \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* y 3.13060547623))))
   (if (<= z -2.4e+70)
     t_1
     (if (<= z 4.2e-186)
       (+ x (* y (* b 1.6453555072203998)))
       (if (<= z 7.4e-148)
         (+ x (* z (* y (* a 1.6453555072203998))))
         (if (<= z 1.7) (+ x (* 1.6453555072203998 (* y b))) 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 <= -2.4e+70) {
		tmp = t_1;
	} else if (z <= 4.2e-186) {
		tmp = x + (y * (b * 1.6453555072203998));
	} else if (z <= 7.4e-148) {
		tmp = x + (z * (y * (a * 1.6453555072203998)));
	} else if (z <= 1.7) {
		tmp = x + (1.6453555072203998 * (y * 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 + (y * 3.13060547623d0)
    if (z <= (-2.4d+70)) then
        tmp = t_1
    else if (z <= 4.2d-186) then
        tmp = x + (y * (b * 1.6453555072203998d0))
    else if (z <= 7.4d-148) then
        tmp = x + (z * (y * (a * 1.6453555072203998d0)))
    else if (z <= 1.7d0) then
        tmp = x + (1.6453555072203998d0 * (y * 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 + (y * 3.13060547623);
	double tmp;
	if (z <= -2.4e+70) {
		tmp = t_1;
	} else if (z <= 4.2e-186) {
		tmp = x + (y * (b * 1.6453555072203998));
	} else if (z <= 7.4e-148) {
		tmp = x + (z * (y * (a * 1.6453555072203998)));
	} else if (z <= 1.7) {
		tmp = x + (1.6453555072203998 * (y * b));
	} 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 <= -2.4e+70:
		tmp = t_1
	elif z <= 4.2e-186:
		tmp = x + (y * (b * 1.6453555072203998))
	elif z <= 7.4e-148:
		tmp = x + (z * (y * (a * 1.6453555072203998)))
	elif z <= 1.7:
		tmp = x + (1.6453555072203998 * (y * b))
	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 <= -2.4e+70)
		tmp = t_1;
	elseif (z <= 4.2e-186)
		tmp = Float64(x + Float64(y * Float64(b * 1.6453555072203998)));
	elseif (z <= 7.4e-148)
		tmp = Float64(x + Float64(z * Float64(y * Float64(a * 1.6453555072203998))));
	elseif (z <= 1.7)
		tmp = Float64(x + Float64(1.6453555072203998 * Float64(y * b)));
	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 <= -2.4e+70)
		tmp = t_1;
	elseif (z <= 4.2e-186)
		tmp = x + (y * (b * 1.6453555072203998));
	elseif (z <= 7.4e-148)
		tmp = x + (z * (y * (a * 1.6453555072203998)));
	elseif (z <= 1.7)
		tmp = x + (1.6453555072203998 * (y * 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[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.4e+70], t$95$1, If[LessEqual[z, 4.2e-186], N[(x + N[(y * N[(b * 1.6453555072203998), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.4e-148], N[(x + N[(z * N[(y * N[(a * 1.6453555072203998), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.7], N[(x + N[(1.6453555072203998 * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.39999999999999987e70 or 1.69999999999999996 < z

   1. Initial program 12.4%

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

   3. Simplified 14.9%

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

   5. Taylor expanded in z around inf 86.8%

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

      1. +-commutative 86.8%

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

      2. *-commutative 86.8%

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

   7. Simplified 86.8%

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

   if -2.39999999999999987e70 < z < 4.2000000000000004e-186

   1. Initial program 93.9%

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

   3. Taylor expanded in z around 0 73.5%

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

      1. associate-*r* 73.5%

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

      2. *-commutative 73.5%

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

   5. Simplified 73.5%

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

   if 4.2000000000000004e-186 < z < 7.40000000000000067e-148

   1. Initial program 99.6%

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

   3. Taylor expanded in z around 0 99.6%

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

      1. *-commutative 99.6%

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

   5. Simplified 99.6%

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

   6. Taylor expanded in a around inf 80.1%

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

      1. associate-*r* 85.3%

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

      2. *-commutative 85.3%

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

   8. Simplified 85.3%

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

   9. Taylor expanded in z around 0 80.5%

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

       1. associate-*r* 85.6%

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

       2. associate-*r* 85.6%

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

       3. *-commutative 85.6%

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

       4. *-commutative 85.6%

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

       5. *-commutative 85.6%

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

       6. associate-*l* 85.6%

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

   11. Simplified 85.6%

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

   if 7.40000000000000067e-148 < z < 1.69999999999999996

   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 99.7%

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

   5. Taylor expanded in z around 0 72.5%

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

      1. +-commutative 72.5%

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

      2. *-commutative 72.5%

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

   7. Simplified 72.5%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+70}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-186}:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998\right)\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{-148}:\\ \;\;\;\;x + z \cdot \left(y \cdot \left(a \cdot 1.6453555072203998\right)\right)\\ \mathbf{elif}\;z \leq 1.7:\\ \;\;\;\;x + 1.6453555072203998 \cdot \left(y \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 92.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+26} \lor \neg \left(z \leq 20.5\right):\\ \;\;\;\;x + \left(y \cdot \frac{\frac{t + 457.9610022158428}{z} - 36.52704169880642}{z} + y \cdot 3.13060547623\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1.6453555072203998 \cdot \left(y \cdot \left(b + z \cdot a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -3.1e+26) (not (<= z 20.5)))
   (+
    x
    (+
     (* y (/ (- (/ (+ t 457.9610022158428) z) 36.52704169880642) z))
     (* y 3.13060547623)))
   (+ x (* 1.6453555072203998 (* y (+ b (* z a)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3.1e+26) || !(z <= 20.5)) {
		tmp = x + ((y * ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)) + (y * 3.13060547623));
	} else {
		tmp = x + (1.6453555072203998 * (y * (b + (z * a))));
	}
	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 <= (-3.1d+26)) .or. (.not. (z <= 20.5d0))) then
        tmp = x + ((y * ((((t + 457.9610022158428d0) / z) - 36.52704169880642d0) / z)) + (y * 3.13060547623d0))
    else
        tmp = x + (1.6453555072203998d0 * (y * (b + (z * a))))
    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 <= -3.1e+26) || !(z <= 20.5)) {
		tmp = x + ((y * ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)) + (y * 3.13060547623));
	} else {
		tmp = x + (1.6453555072203998 * (y * (b + (z * a))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -3.1e+26) or not (z <= 20.5):
		tmp = x + ((y * ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)) + (y * 3.13060547623))
	else:
		tmp = x + (1.6453555072203998 * (y * (b + (z * a))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -3.1e+26) || !(z <= 20.5))
		tmp = Float64(x + Float64(Float64(y * Float64(Float64(Float64(Float64(t + 457.9610022158428) / z) - 36.52704169880642) / z)) + Float64(y * 3.13060547623)));
	else
		tmp = Float64(x + Float64(1.6453555072203998 * Float64(y * Float64(b + Float64(z * a)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -3.1e+26) || ~((z <= 20.5)))
		tmp = x + ((y * ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)) + (y * 3.13060547623));
	else
		tmp = x + (1.6453555072203998 * (y * (b + (z * a))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -3.1e+26], N[Not[LessEqual[z, 20.5]], $MachinePrecision]], N[(x + N[(N[(y * N[(N[(N[(N[(t + 457.9610022158428), $MachinePrecision] / z), $MachinePrecision] - 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(1.6453555072203998 * N[(y * N[(b + N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.1e26 or 20.5 < z

   1. Initial program 18.3%

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

   3. Taylor expanded in z around -inf 80.8%

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

   4. Taylor expanded in y around 0 86.3%

      \[\leadsto x + \left(-1 \cdot \color{blue}{\frac{y \cdot \left(36.52704169880642 + -1 \cdot \frac{457.9610022158428 + t}{z}\right)}{z}} + 3.13060547623 \cdot y\right) \]
   5. Step-by-step derivation

      1. associate-/l* 92.6%

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

      2. mul-1-neg 92.6%

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

      3. unsub-neg 92.6%

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

      4. +-commutative 92.6%

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

   6. Simplified 92.6%

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

   if -3.1e26 < z < 20.5

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0 91.1%

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

   4. Taylor expanded in z around inf 89.8%

      \[\leadsto x + \frac{b \cdot y + z \cdot \left(a \cdot y + t \cdot \left(y \cdot z\right)\right)}{\color{blue}{{z}^{4} \cdot \left(1 + 15.234687407 \cdot \frac{1}{z}\right)} + 0.607771387771} \]
   5. Step-by-step derivation

      1. associate-*r/ 89.8%

         \[\leadsto x + \frac{b \cdot y + z \cdot \left(a \cdot y + t \cdot \left(y \cdot z\right)\right)}{{z}^{4} \cdot \left(1 + \color{blue}{\frac{15.234687407 \cdot 1}{z}}\right) + 0.607771387771} \]

      2. metadata-eval 89.8%

         \[\leadsto x + \frac{b \cdot y + z \cdot \left(a \cdot y + t \cdot \left(y \cdot z\right)\right)}{{z}^{4} \cdot \left(1 + \frac{\color{blue}{15.234687407}}{z}\right) + 0.607771387771} \]

   6. Simplified 89.8%

      \[\leadsto x + \frac{b \cdot y + z \cdot \left(a \cdot y + t \cdot \left(y \cdot z\right)\right)}{\color{blue}{{z}^{4} \cdot \left(1 + \frac{15.234687407}{z}\right)} + 0.607771387771} \]

   7. Taylor expanded in z around 0 86.2%

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

      1. distribute-lft-out 86.2%

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

      2. +-commutative 86.2%

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

      3. *-commutative 86.2%

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

      4. associate-*r* 83.7%

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

      5. *-commutative 83.7%

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

      6. associate-*r* 87.2%

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

      7. distribute-lft-out 87.9%

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

      8. *-commutative 87.9%

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

   9. Simplified 87.9%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+26} \lor \neg \left(z \leq 20.5\right):\\ \;\;\;\;x + \left(y \cdot \frac{\frac{t + 457.9610022158428}{z} - 36.52704169880642}{z} + y \cdot 3.13060547623\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1.6453555072203998 \cdot \left(y \cdot \left(b + z \cdot a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 89.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+34} \lor \neg \left(z \leq 24\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x + 1.6453555072203998 \cdot \left(y \cdot \left(b + z \cdot a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -6.8e+34) (not (<= z 24.0)))
   (+ x (* y 3.13060547623))
   (+ x (* 1.6453555072203998 (* y (+ b (* z a)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -6.8e+34) || !(z <= 24.0)) {
		tmp = x + (y * 3.13060547623);
	} else {
		tmp = x + (1.6453555072203998 * (y * (b + (z * a))));
	}
	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 <= (-6.8d+34)) .or. (.not. (z <= 24.0d0))) then
        tmp = x + (y * 3.13060547623d0)
    else
        tmp = x + (1.6453555072203998d0 * (y * (b + (z * a))))
    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 <= -6.8e+34) || !(z <= 24.0)) {
		tmp = x + (y * 3.13060547623);
	} else {
		tmp = x + (1.6453555072203998 * (y * (b + (z * a))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -6.8e+34) or not (z <= 24.0):
		tmp = x + (y * 3.13060547623)
	else:
		tmp = x + (1.6453555072203998 * (y * (b + (z * a))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -6.8e+34) || !(z <= 24.0))
		tmp = Float64(x + Float64(y * 3.13060547623));
	else
		tmp = Float64(x + Float64(1.6453555072203998 * Float64(y * Float64(b + Float64(z * a)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -6.8e+34) || ~((z <= 24.0)))
		tmp = x + (y * 3.13060547623);
	else
		tmp = x + (1.6453555072203998 * (y * (b + (z * a))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -6.8e+34], N[Not[LessEqual[z, 24.0]], $MachinePrecision]], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision], N[(x + N[(1.6453555072203998 * N[(y * N[(b + N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.7999999999999999e34 or 24 < z

   1. Initial program 15.7%

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

   3. Simplified 21.3%

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

   5. Taylor expanded in z around inf 84.0%

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

      1. +-commutative 84.0%

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

      2. *-commutative 84.0%

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

   7. Simplified 84.0%

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

   if -6.7999999999999999e34 < z < 24

   1. Initial program 98.4%

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

   3. Taylor expanded in z around 0 89.4%

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

   4. Taylor expanded in z around inf 88.2%

      \[\leadsto x + \frac{b \cdot y + z \cdot \left(a \cdot y + t \cdot \left(y \cdot z\right)\right)}{\color{blue}{{z}^{4} \cdot \left(1 + 15.234687407 \cdot \frac{1}{z}\right)} + 0.607771387771} \]
   5. Step-by-step derivation

      1. associate-*r/ 88.2%

         \[\leadsto x + \frac{b \cdot y + z \cdot \left(a \cdot y + t \cdot \left(y \cdot z\right)\right)}{{z}^{4} \cdot \left(1 + \color{blue}{\frac{15.234687407 \cdot 1}{z}}\right) + 0.607771387771} \]

      2. metadata-eval 88.2%

         \[\leadsto x + \frac{b \cdot y + z \cdot \left(a \cdot y + t \cdot \left(y \cdot z\right)\right)}{{z}^{4} \cdot \left(1 + \frac{\color{blue}{15.234687407}}{z}\right) + 0.607771387771} \]

   6. Simplified 88.2%

      \[\leadsto x + \frac{b \cdot y + z \cdot \left(a \cdot y + t \cdot \left(y \cdot z\right)\right)}{\color{blue}{{z}^{4} \cdot \left(1 + \frac{15.234687407}{z}\right)} + 0.607771387771} \]

   7. Taylor expanded in z around 0 84.1%

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

      1. distribute-lft-out 84.1%

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

      2. +-commutative 84.1%

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

      3. *-commutative 84.1%

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

      4. associate-*r* 81.6%

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

      5. *-commutative 81.6%

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

      6. associate-*r* 85.0%

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

      7. distribute-lft-out 85.7%

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

      8. *-commutative 85.7%

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

   9. Simplified 85.7%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+34} \lor \neg \left(z \leq 24\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x + 1.6453555072203998 \cdot \left(y \cdot \left(b + z \cdot a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 89.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+34}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{elif}\;z \leq 24:\\ \;\;\;\;x + 1.6453555072203998 \cdot \left(y \cdot \left(b + z \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 - \frac{y \cdot 36.52704169880642}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -6.8e+34)
   (+ x (* y 3.13060547623))
   (if (<= z 24.0)
     (+ x (* 1.6453555072203998 (* y (+ b (* z a)))))
     (+ x (- (* y 3.13060547623) (/ (* y 36.52704169880642) z))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -6.8e+34) {
		tmp = x + (y * 3.13060547623);
	} else if (z <= 24.0) {
		tmp = x + (1.6453555072203998 * (y * (b + (z * a))));
	} else {
		tmp = x + ((y * 3.13060547623) - ((y * 36.52704169880642) / z));
	}
	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 <= (-6.8d+34)) then
        tmp = x + (y * 3.13060547623d0)
    else if (z <= 24.0d0) then
        tmp = x + (1.6453555072203998d0 * (y * (b + (z * a))))
    else
        tmp = x + ((y * 3.13060547623d0) - ((y * 36.52704169880642d0) / z))
    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 <= -6.8e+34) {
		tmp = x + (y * 3.13060547623);
	} else if (z <= 24.0) {
		tmp = x + (1.6453555072203998 * (y * (b + (z * a))));
	} else {
		tmp = x + ((y * 3.13060547623) - ((y * 36.52704169880642) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -6.8e+34:
		tmp = x + (y * 3.13060547623)
	elif z <= 24.0:
		tmp = x + (1.6453555072203998 * (y * (b + (z * a))))
	else:
		tmp = x + ((y * 3.13060547623) - ((y * 36.52704169880642) / z))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -6.8e+34)
		tmp = Float64(x + Float64(y * 3.13060547623));
	elseif (z <= 24.0)
		tmp = Float64(x + Float64(1.6453555072203998 * Float64(y * Float64(b + Float64(z * a)))));
	else
		tmp = Float64(x + Float64(Float64(y * 3.13060547623) - Float64(Float64(y * 36.52704169880642) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -6.8e+34)
		tmp = x + (y * 3.13060547623);
	elseif (z <= 24.0)
		tmp = x + (1.6453555072203998 * (y * (b + (z * a))));
	else
		tmp = x + ((y * 3.13060547623) - ((y * 36.52704169880642) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -6.8e+34], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 24.0], N[(x + N[(1.6453555072203998 * N[(y * N[(b + N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * 3.13060547623), $MachinePrecision] - N[(N[(y * 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.7999999999999999e34

   1. Initial program 9.9%

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

   3. Simplified 17.3%

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

   5. Taylor expanded in z around inf 87.1%

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

      1. +-commutative 87.1%

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

      2. *-commutative 87.1%

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

   7. Simplified 87.1%

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

   if -6.7999999999999999e34 < z < 24

   1. Initial program 98.4%

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

   3. Taylor expanded in z around 0 89.4%

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

   4. Taylor expanded in z around inf 88.2%

      \[\leadsto x + \frac{b \cdot y + z \cdot \left(a \cdot y + t \cdot \left(y \cdot z\right)\right)}{\color{blue}{{z}^{4} \cdot \left(1 + 15.234687407 \cdot \frac{1}{z}\right)} + 0.607771387771} \]
   5. Step-by-step derivation

      1. associate-*r/ 88.2%

         \[\leadsto x + \frac{b \cdot y + z \cdot \left(a \cdot y + t \cdot \left(y \cdot z\right)\right)}{{z}^{4} \cdot \left(1 + \color{blue}{\frac{15.234687407 \cdot 1}{z}}\right) + 0.607771387771} \]

      2. metadata-eval 88.2%

         \[\leadsto x + \frac{b \cdot y + z \cdot \left(a \cdot y + t \cdot \left(y \cdot z\right)\right)}{{z}^{4} \cdot \left(1 + \frac{\color{blue}{15.234687407}}{z}\right) + 0.607771387771} \]

   6. Simplified 88.2%

      \[\leadsto x + \frac{b \cdot y + z \cdot \left(a \cdot y + t \cdot \left(y \cdot z\right)\right)}{\color{blue}{{z}^{4} \cdot \left(1 + \frac{15.234687407}{z}\right)} + 0.607771387771} \]

   7. Taylor expanded in z around 0 84.1%

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

      1. distribute-lft-out 84.1%

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

      2. +-commutative 84.1%

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

      3. *-commutative 84.1%

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

      4. associate-*r* 81.6%

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

      5. *-commutative 81.6%

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

      6. associate-*r* 85.0%

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

      7. distribute-lft-out 85.7%

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

      8. *-commutative 85.7%

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

   9. Simplified 85.7%

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

   if 24 < z

   1. Initial program 20.4%

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

   3. Taylor expanded in z around -inf 81.6%

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

      1. +-commutative 81.6%

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

      2. mul-1-neg 81.6%

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

      3. unsub-neg 81.6%

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

      4. *-commutative 81.6%

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

      5. distribute-rgt-out-- 81.6%

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

      6. metadata-eval 81.6%

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

   5. Simplified 81.6%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+34}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{elif}\;z \leq 24:\\ \;\;\;\;x + 1.6453555072203998 \cdot \left(y \cdot \left(b + z \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 - \frac{y \cdot 36.52704169880642}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 82.5% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+70} \lor \neg \left(z \leq 24\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2.4e+70) (not (<= z 24.0)))
   (+ 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 <= -2.4e+70) || !(z <= 24.0)) {
		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 <= (-2.4d+70)) .or. (.not. (z <= 24.0d0))) 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 <= -2.4e+70) || !(z <= 24.0)) {
		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 <= -2.4e+70) or not (z <= 24.0):
		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 <= -2.4e+70) || !(z <= 24.0))
		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 <= -2.4e+70) || ~((z <= 24.0)))
		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, -2.4e+70], N[Not[LessEqual[z, 24.0]], $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 < -2.39999999999999987e70 or 24 < z

   1. Initial program 12.4%

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

   3. Simplified 14.9%

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

   5. Taylor expanded in z around inf 86.8%

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

      1. +-commutative 86.8%

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

      2. *-commutative 86.8%

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

   7. Simplified 86.8%

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

   if -2.39999999999999987e70 < z < 24

   1. Initial program 95.2%

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

   3. Taylor expanded in z around 0 71.1%

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

      1. associate-*r* 71.2%

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

      2. *-commutative 71.2%

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

   5. Simplified 71.2%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+70} \lor \neg \left(z \leq 24\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 62.2% accurate, 7.4× speedup

Math

\[\begin{array}{l} \\ x + y \cdot 3.13060547623 \end{array} \]

FPCore

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

C

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

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 * 3.13060547623d0)
end function

Java

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

Python

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

Julia

function code(x, y, z, t, a, b)
	return Float64(x + Float64(y * 3.13060547623))
end

MATLAB

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

Wolfram

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

Derivation

1. Initial program 60.6%

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

3. Simplified 63.5%

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

5. Taylor expanded in z around inf 60.6%

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

   1. +-commutative 60.6%

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

   2. *-commutative 60.6%

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

7. Simplified 60.6%

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

8. Final simplification 60.6%

   \[\leadsto x + y \cdot 3.13060547623 \]
9. Add Preprocessing

Alternative 16: 44.6% 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 60.6%

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

3. Simplified 63.5%

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

5. Taylor expanded in y around 0 43.6%

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

6. Final simplification 43.6%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 98.3% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024059 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, D"
  :precision binary64

  :alt
  (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))))