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

Percentage Accurate: 58.7% → 98.2%

Time: 18.8s

Alternatives: 14

Speedup: 2.5×

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: 98.2% accurate, 0.0× speedup

Math

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

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 (/ (- (/ (+ t 457.9610022158428) z) 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 + ((((t + 457.9610022158428) / z) - 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(3.13060547623 + Float64(Float64(Float64(Float64(t + 457.9610022158428) / z) - 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[(3.13060547623 + N[(N[(N[(N[(t + 457.9610022158428), $MachinePrecision] / z), $MachinePrecision] - 36.52704169880642), $MachinePrecision] / z), $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 93.7%

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

   3. Simplified 98.6%

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

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

      1. mul-1-neg 99.9%

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

      2. unsub-neg 99.9%

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

      3. mul-1-neg 99.9%

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

      4. unsub-neg 99.9%

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

      5. +-commutative 99.9%

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

   7. Simplified 99.9%

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

4. Final simplification 99.0%

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

Alternative 2: 96.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+36} \lor \neg \left(z \leq 2850000\right):\\ \;\;\;\;x + \left(\frac{\left(y \cdot \frac{\left(t + 457.9610022158428\right) + \frac{a + \left(1112.0901850848957 + \left(-6976.8927133548 + t \cdot -15.234687407\right)\right)}{z}}{z} - y \cdot -11.1667541262\right) + y \cdot -47.69379582500642}{z} + y \cdot 3.13060547623\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot t\right)\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1e+36) (not (<= z 2850000.0)))
   (+
    x
    (+
     (/
      (+
       (-
        (*
         y
         (/
          (+
           (+ t 457.9610022158428)
           (/
            (+
             a
             (+ 1112.0901850848957 (+ -6976.8927133548 (* t -15.234687407))))
            z))
          z))
        (* y -11.1667541262))
       (* y -47.69379582500642))
      z)
     (* y 3.13060547623)))
   (+
    x
    (/
     (* y (+ b (* z (+ a (* z t)))))
     (+
      (* 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 <= -1e+36) || !(z <= 2850000.0)) {
		tmp = x + (((((y * (((t + 457.9610022158428) + ((a + (1112.0901850848957 + (-6976.8927133548 + (t * -15.234687407)))) / z)) / z)) - (y * -11.1667541262)) + (y * -47.69379582500642)) / z) + (y * 3.13060547623));
	} else {
		tmp = x + ((y * (b + (z * (a + (z * t))))) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-1d+36)) .or. (.not. (z <= 2850000.0d0))) then
        tmp = x + (((((y * (((t + 457.9610022158428d0) + ((a + (1112.0901850848957d0 + ((-6976.8927133548d0) + (t * (-15.234687407d0))))) / z)) / z)) - (y * (-11.1667541262d0))) + (y * (-47.69379582500642d0))) / z) + (y * 3.13060547623d0))
    else
        tmp = x + ((y * (b + (z * (a + (z * t))))) / ((z * ((z * ((z * (z + 15.234687407d0)) + 31.4690115749d0)) + 11.9400905721d0)) + 0.607771387771d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1e+36) || !(z <= 2850000.0)) {
		tmp = x + (((((y * (((t + 457.9610022158428) + ((a + (1112.0901850848957 + (-6976.8927133548 + (t * -15.234687407)))) / z)) / z)) - (y * -11.1667541262)) + (y * -47.69379582500642)) / z) + (y * 3.13060547623));
	} else {
		tmp = x + ((y * (b + (z * (a + (z * t))))) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1e+36) or not (z <= 2850000.0):
		tmp = x + (((((y * (((t + 457.9610022158428) + ((a + (1112.0901850848957 + (-6976.8927133548 + (t * -15.234687407)))) / z)) / z)) - (y * -11.1667541262)) + (y * -47.69379582500642)) / z) + (y * 3.13060547623))
	else:
		tmp = x + ((y * (b + (z * (a + (z * t))))) / ((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 <= -1e+36) || !(z <= 2850000.0))
		tmp = Float64(x + Float64(Float64(Float64(Float64(Float64(y * Float64(Float64(Float64(t + 457.9610022158428) + Float64(Float64(a + Float64(1112.0901850848957 + Float64(-6976.8927133548 + Float64(t * -15.234687407)))) / z)) / z)) - Float64(y * -11.1667541262)) + Float64(y * -47.69379582500642)) / z) + Float64(y * 3.13060547623)));
	else
		tmp = Float64(x + Float64(Float64(y * Float64(b + Float64(z * Float64(a + Float64(z * t))))) / Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1e+36) || ~((z <= 2850000.0)))
		tmp = x + (((((y * (((t + 457.9610022158428) + ((a + (1112.0901850848957 + (-6976.8927133548 + (t * -15.234687407)))) / z)) / z)) - (y * -11.1667541262)) + (y * -47.69379582500642)) / z) + (y * 3.13060547623));
	else
		tmp = x + ((y * (b + (z * (a + (z * t))))) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1e+36], N[Not[LessEqual[z, 2850000.0]], $MachinePrecision]], N[(x + N[(N[(N[(N[(N[(y * N[(N[(N[(t + 457.9610022158428), $MachinePrecision] + N[(N[(a + N[(1112.0901850848957 + N[(-6976.8927133548 + N[(t * -15.234687407), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] - N[(y * -11.1667541262), $MachinePrecision]), $MachinePrecision] + N[(y * -47.69379582500642), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * N[(b + N[(z * N[(a + N[(z * t), $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 < -1.00000000000000004e36 or 2.85e6 < z

   1. Initial program 13.4%

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

   3. Simplified 19.6%

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

   5. Taylor expanded in z around -inf 79.6%

      \[\leadsto \color{blue}{x + \left(-1 \cdot \frac{\left(-11.1667541262 \cdot y + -1 \cdot \frac{\left(-1 \cdot \frac{-1 \cdot \left(a \cdot y\right) - \left(-37.37971293169846 \cdot y + \left(-15.234687407 \cdot \left(t \cdot y - \left(-15.234687407 \cdot \left(-11.1667541262 \cdot y - -47.69379582500642 \cdot y\right) + 98.5170599679272 \cdot y\right)\right) + 31.4690115749 \cdot \left(-11.1667541262 \cdot y - -47.69379582500642 \cdot y\right)\right)\right)}{z} + t \cdot y\right) - \left(-15.234687407 \cdot \left(-11.1667541262 \cdot y - -47.69379582500642 \cdot y\right) + 98.5170599679272 \cdot y\right)}{z}\right) - -47.69379582500642 \cdot y}{z} + 3.13060547623 \cdot y\right)} \]

   6. Taylor expanded in y around 0 87.2%

      \[\leadsto x + \left(-1 \cdot \frac{\left(-11.1667541262 \cdot y + \color{blue}{-1 \cdot \frac{y \cdot \left(457.9610022158428 + \left(t + -1 \cdot \frac{-1 \cdot a - \left(1112.0901850848957 + -15.234687407 \cdot \left(457.9610022158428 + t\right)\right)}{z}\right)\right)}{z}}\right) - -47.69379582500642 \cdot y}{z} + 3.13060547623 \cdot y\right) \]
   7. Step-by-step derivation

      1. mul-1-neg 87.2%

         \[\leadsto x + \left(-1 \cdot \frac{\left(-11.1667541262 \cdot y + \color{blue}{\left(-\frac{y \cdot \left(457.9610022158428 + \left(t + -1 \cdot \frac{-1 \cdot a - \left(1112.0901850848957 + -15.234687407 \cdot \left(457.9610022158428 + t\right)\right)}{z}\right)\right)}{z}\right)}\right) - -47.69379582500642 \cdot y}{z} + 3.13060547623 \cdot y\right) \]

      2. associate-/l* 98.9%

         \[\leadsto x + \left(-1 \cdot \frac{\left(-11.1667541262 \cdot y + \left(-\color{blue}{y \cdot \frac{457.9610022158428 + \left(t + -1 \cdot \frac{-1 \cdot a - \left(1112.0901850848957 + -15.234687407 \cdot \left(457.9610022158428 + t\right)\right)}{z}\right)}{z}}\right)\right) - -47.69379582500642 \cdot y}{z} + 3.13060547623 \cdot y\right) \]

      3. associate-+r+ 98.9%

         \[\leadsto x + \left(-1 \cdot \frac{\left(-11.1667541262 \cdot y + \left(-y \cdot \frac{\color{blue}{\left(457.9610022158428 + t\right) + -1 \cdot \frac{-1 \cdot a - \left(1112.0901850848957 + -15.234687407 \cdot \left(457.9610022158428 + t\right)\right)}{z}}}{z}\right)\right) - -47.69379582500642 \cdot y}{z} + 3.13060547623 \cdot y\right) \]

      4. +-commutative 98.9%

         \[\leadsto x + \left(-1 \cdot \frac{\left(-11.1667541262 \cdot y + \left(-y \cdot \frac{\color{blue}{\left(t + 457.9610022158428\right)} + -1 \cdot \frac{-1 \cdot a - \left(1112.0901850848957 + -15.234687407 \cdot \left(457.9610022158428 + t\right)\right)}{z}}{z}\right)\right) - -47.69379582500642 \cdot y}{z} + 3.13060547623 \cdot y\right) \]

      5. mul-1-neg 98.9%

         \[\leadsto x + \left(-1 \cdot \frac{\left(-11.1667541262 \cdot y + \left(-y \cdot \frac{\left(t + 457.9610022158428\right) + \color{blue}{\left(-\frac{-1 \cdot a - \left(1112.0901850848957 + -15.234687407 \cdot \left(457.9610022158428 + t\right)\right)}{z}\right)}}{z}\right)\right) - -47.69379582500642 \cdot y}{z} + 3.13060547623 \cdot y\right) \]

      6. mul-1-neg 98.9%

         \[\leadsto x + \left(-1 \cdot \frac{\left(-11.1667541262 \cdot y + \left(-y \cdot \frac{\left(t + 457.9610022158428\right) + \left(-\frac{\color{blue}{\left(-a\right)} - \left(1112.0901850848957 + -15.234687407 \cdot \left(457.9610022158428 + t\right)\right)}{z}\right)}{z}\right)\right) - -47.69379582500642 \cdot y}{z} + 3.13060547623 \cdot y\right) \]

      7. distribute-lft-in 98.9%

         \[\leadsto x + \left(-1 \cdot \frac{\left(-11.1667541262 \cdot y + \left(-y \cdot \frac{\left(t + 457.9610022158428\right) + \left(-\frac{\left(-a\right) - \left(1112.0901850848957 + \color{blue}{\left(-15.234687407 \cdot 457.9610022158428 + -15.234687407 \cdot t\right)}\right)}{z}\right)}{z}\right)\right) - -47.69379582500642 \cdot y}{z} + 3.13060547623 \cdot y\right) \]

      8. metadata-eval 98.9%

         \[\leadsto x + \left(-1 \cdot \frac{\left(-11.1667541262 \cdot y + \left(-y \cdot \frac{\left(t + 457.9610022158428\right) + \left(-\frac{\left(-a\right) - \left(1112.0901850848957 + \left(\color{blue}{-6976.8927133548} + -15.234687407 \cdot t\right)\right)}{z}\right)}{z}\right)\right) - -47.69379582500642 \cdot y}{z} + 3.13060547623 \cdot y\right) \]

   8. Simplified 98.9%

      \[\leadsto x + \left(-1 \cdot \frac{\left(-11.1667541262 \cdot y + \color{blue}{\left(-y \cdot \frac{\left(t + 457.9610022158428\right) + \left(-\frac{\left(-a\right) - \left(1112.0901850848957 + \left(-6976.8927133548 + -15.234687407 \cdot t\right)\right)}{z}\right)}{z}\right)}\right) - -47.69379582500642 \cdot y}{z} + 3.13060547623 \cdot y\right) \]

   if -1.00000000000000004e36 < z < 2.85e6

   1. Initial program 98.5%

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

   3. Taylor expanded in z around 0 92.0%

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

   4. Taylor expanded in y around 0 98.5%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+36} \lor \neg \left(z \leq 2850000\right):\\ \;\;\;\;x + \left(\frac{\left(y \cdot \frac{\left(t + 457.9610022158428\right) + \frac{a + \left(1112.0901850848957 + \left(-6976.8927133548 + t \cdot -15.234687407\right)\right)}{z}}{z} - y \cdot -11.1667541262\right) + y \cdot -47.69379582500642}{z} + y \cdot 3.13060547623\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot t\right)\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 95.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+36} \lor \neg \left(z \leq 67000000\right):\\ \;\;\;\;x + \left(y \cdot 3.13060547623 + \frac{y \cdot -47.69379582500642 + \left(t \cdot \frac{y - \frac{y \cdot 15.234687407}{z}}{z} - y \cdot -11.1667541262\right)}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot t\right)\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.3e+36) (not (<= z 67000000.0)))
   (+
    x
    (+
     (* y 3.13060547623)
     (/
      (+
       (* y -47.69379582500642)
       (- (* t (/ (- y (/ (* y 15.234687407) z)) z)) (* y -11.1667541262)))
      z)))
   (+
    x
    (/
     (* y (+ b (* z (+ a (* z t)))))
     (+
      (* 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 <= -1.3e+36) || !(z <= 67000000.0)) {
		tmp = x + ((y * 3.13060547623) + (((y * -47.69379582500642) + ((t * ((y - ((y * 15.234687407) / z)) / z)) - (y * -11.1667541262))) / z));
	} else {
		tmp = x + ((y * (b + (z * (a + (z * t))))) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-1.3d+36)) .or. (.not. (z <= 67000000.0d0))) then
        tmp = x + ((y * 3.13060547623d0) + (((y * (-47.69379582500642d0)) + ((t * ((y - ((y * 15.234687407d0) / z)) / z)) - (y * (-11.1667541262d0)))) / z))
    else
        tmp = x + ((y * (b + (z * (a + (z * t))))) / ((z * ((z * ((z * (z + 15.234687407d0)) + 31.4690115749d0)) + 11.9400905721d0)) + 0.607771387771d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.3e+36) || !(z <= 67000000.0)) {
		tmp = x + ((y * 3.13060547623) + (((y * -47.69379582500642) + ((t * ((y - ((y * 15.234687407) / z)) / z)) - (y * -11.1667541262))) / z));
	} else {
		tmp = x + ((y * (b + (z * (a + (z * t))))) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.3e+36) or not (z <= 67000000.0):
		tmp = x + ((y * 3.13060547623) + (((y * -47.69379582500642) + ((t * ((y - ((y * 15.234687407) / z)) / z)) - (y * -11.1667541262))) / z))
	else:
		tmp = x + ((y * (b + (z * (a + (z * t))))) / ((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 <= -1.3e+36) || !(z <= 67000000.0))
		tmp = Float64(x + Float64(Float64(y * 3.13060547623) + Float64(Float64(Float64(y * -47.69379582500642) + Float64(Float64(t * Float64(Float64(y - Float64(Float64(y * 15.234687407) / z)) / z)) - Float64(y * -11.1667541262))) / z)));
	else
		tmp = Float64(x + Float64(Float64(y * Float64(b + Float64(z * Float64(a + Float64(z * t))))) / Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.3e+36) || ~((z <= 67000000.0)))
		tmp = x + ((y * 3.13060547623) + (((y * -47.69379582500642) + ((t * ((y - ((y * 15.234687407) / z)) / z)) - (y * -11.1667541262))) / z));
	else
		tmp = x + ((y * (b + (z * (a + (z * t))))) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.3e+36], N[Not[LessEqual[z, 67000000.0]], $MachinePrecision]], N[(x + N[(N[(y * 3.13060547623), $MachinePrecision] + N[(N[(N[(y * -47.69379582500642), $MachinePrecision] + N[(N[(t * N[(N[(y - N[(N[(y * 15.234687407), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] - N[(y * -11.1667541262), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * N[(b + N[(z * N[(a + N[(z * t), $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 < -1.3000000000000001e36 or 6.7e7 < z

   1. Initial program 13.4%

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

   3. Simplified 19.6%

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

   5. Taylor expanded in z around -inf 79.6%

      \[\leadsto \color{blue}{x + \left(-1 \cdot \frac{\left(-11.1667541262 \cdot y + -1 \cdot \frac{\left(-1 \cdot \frac{-1 \cdot \left(a \cdot y\right) - \left(-37.37971293169846 \cdot y + \left(-15.234687407 \cdot \left(t \cdot y - \left(-15.234687407 \cdot \left(-11.1667541262 \cdot y - -47.69379582500642 \cdot y\right) + 98.5170599679272 \cdot y\right)\right) + 31.4690115749 \cdot \left(-11.1667541262 \cdot y - -47.69379582500642 \cdot y\right)\right)\right)}{z} + t \cdot y\right) - \left(-15.234687407 \cdot \left(-11.1667541262 \cdot y - -47.69379582500642 \cdot y\right) + 98.5170599679272 \cdot y\right)}{z}\right) - -47.69379582500642 \cdot y}{z} + 3.13060547623 \cdot y\right)} \]

   6. Taylor expanded in t around -inf 88.2%

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

      1. associate-/l* 96.1%

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

      2. +-commutative 96.1%

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

      3. mul-1-neg 96.1%

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

      4. unsub-neg 96.1%

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

      5. associate-*r/ 96.1%

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

      6. *-commutative 96.1%

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

   8. Simplified 96.1%

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

   if -1.3000000000000001e36 < z < 6.7e7

   1. Initial program 98.5%

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

   3. Taylor expanded in z around 0 92.0%

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

   4. Taylor expanded in y around 0 98.5%

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

4. Final simplification 97.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+36} \lor \neg \left(z \leq 67000000\right):\\ \;\;\;\;x + \left(y \cdot 3.13060547623 + \frac{y \cdot -47.69379582500642 + \left(t \cdot \frac{y - \frac{y \cdot 15.234687407}{z}}{z} - y \cdot -11.1667541262\right)}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot t\right)\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 94.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+34} \lor \neg \left(z \leq 18000\right):\\ \;\;\;\;x + \left(y \cdot 3.13060547623 + \frac{y \cdot -47.69379582500642 + \left(t \cdot \frac{y - \frac{y \cdot 15.234687407}{z}}{z} - y \cdot -11.1667541262\right)}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot t\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot 31.4690115749\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.05e+34) (not (<= z 18000.0)))
   (+
    x
    (+
     (* y 3.13060547623)
     (/
      (+
       (* y -47.69379582500642)
       (- (* t (/ (- y (/ (* y 15.234687407) z)) z)) (* y -11.1667541262)))
      z)))
   (+
    x
    (/
     (* y (+ b (* z (+ a (* z t)))))
     (+ 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 <= -1.05e+34) || !(z <= 18000.0)) {
		tmp = x + ((y * 3.13060547623) + (((y * -47.69379582500642) + ((t * ((y - ((y * 15.234687407) / z)) / z)) - (y * -11.1667541262))) / z));
	} else {
		tmp = x + ((y * (b + (z * (a + (z * t))))) / (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 <= (-1.05d+34)) .or. (.not. (z <= 18000.0d0))) then
        tmp = x + ((y * 3.13060547623d0) + (((y * (-47.69379582500642d0)) + ((t * ((y - ((y * 15.234687407d0) / z)) / z)) - (y * (-11.1667541262d0)))) / z))
    else
        tmp = x + ((y * (b + (z * (a + (z * t))))) / (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 <= -1.05e+34) || !(z <= 18000.0)) {
		tmp = x + ((y * 3.13060547623) + (((y * -47.69379582500642) + ((t * ((y - ((y * 15.234687407) / z)) / z)) - (y * -11.1667541262))) / z));
	} else {
		tmp = x + ((y * (b + (z * (a + (z * t))))) / (0.607771387771 + (z * (11.9400905721 + (z * 31.4690115749)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.05e+34) or not (z <= 18000.0):
		tmp = x + ((y * 3.13060547623) + (((y * -47.69379582500642) + ((t * ((y - ((y * 15.234687407) / z)) / z)) - (y * -11.1667541262))) / z))
	else:
		tmp = x + ((y * (b + (z * (a + (z * t))))) / (0.607771387771 + (z * (11.9400905721 + (z * 31.4690115749)))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.05e+34) || !(z <= 18000.0))
		tmp = Float64(x + Float64(Float64(y * 3.13060547623) + Float64(Float64(Float64(y * -47.69379582500642) + Float64(Float64(t * Float64(Float64(y - Float64(Float64(y * 15.234687407) / z)) / z)) - Float64(y * -11.1667541262))) / z)));
	else
		tmp = Float64(x + Float64(Float64(y * Float64(b + Float64(z * Float64(a + Float64(z * t))))) / 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 <= -1.05e+34) || ~((z <= 18000.0)))
		tmp = x + ((y * 3.13060547623) + (((y * -47.69379582500642) + ((t * ((y - ((y * 15.234687407) / z)) / z)) - (y * -11.1667541262))) / z));
	else
		tmp = x + ((y * (b + (z * (a + (z * t))))) / (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, -1.05e+34], N[Not[LessEqual[z, 18000.0]], $MachinePrecision]], N[(x + N[(N[(y * 3.13060547623), $MachinePrecision] + N[(N[(N[(y * -47.69379582500642), $MachinePrecision] + N[(N[(t * N[(N[(y - N[(N[(y * 15.234687407), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] - N[(y * -11.1667541262), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * N[(b + N[(z * N[(a + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $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 < -1.05000000000000009e34 or 18000 < z

   1. Initial program 15.8%

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

   3. Simplified 21.8%

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

   5. Taylor expanded in z around -inf 79.8%

      \[\leadsto \color{blue}{x + \left(-1 \cdot \frac{\left(-11.1667541262 \cdot y + -1 \cdot \frac{\left(-1 \cdot \frac{-1 \cdot \left(a \cdot y\right) - \left(-37.37971293169846 \cdot y + \left(-15.234687407 \cdot \left(t \cdot y - \left(-15.234687407 \cdot \left(-11.1667541262 \cdot y - -47.69379582500642 \cdot y\right) + 98.5170599679272 \cdot y\right)\right) + 31.4690115749 \cdot \left(-11.1667541262 \cdot y - -47.69379582500642 \cdot y\right)\right)\right)}{z} + t \cdot y\right) - \left(-15.234687407 \cdot \left(-11.1667541262 \cdot y - -47.69379582500642 \cdot y\right) + 98.5170599679272 \cdot y\right)}{z}\right) - -47.69379582500642 \cdot y}{z} + 3.13060547623 \cdot y\right)} \]

   6. Taylor expanded in t around -inf 88.1%

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

      1. associate-/l* 95.8%

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

      2. +-commutative 95.8%

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

      3. mul-1-neg 95.8%

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

      4. unsub-neg 95.8%

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

      5. associate-*r/ 95.8%

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

      6. *-commutative 95.8%

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

   8. Simplified 95.8%

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

   if -1.05000000000000009e34 < z < 18000

   1. Initial program 98.5%

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

   3. Taylor expanded in z around 0 91.8%

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

   4. Taylor expanded in y around 0 98.5%

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

   5. Taylor expanded in z around 0 98.1%

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

4. Final simplification 97.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+34} \lor \neg \left(z \leq 18000\right):\\ \;\;\;\;x + \left(y \cdot 3.13060547623 + \frac{y \cdot -47.69379582500642 + \left(t \cdot \frac{y - \frac{y \cdot 15.234687407}{z}}{z} - y \cdot -11.1667541262\right)}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot t\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot 31.4690115749\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 93.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot 3.13060547623\\ \mathbf{if}\;z \leq -7.2 \cdot 10^{+34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 14500000000000:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot t\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot 31.4690115749\right)}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+120}:\\ \;\;\;\;y \cdot \left(\left(3.13060547623 + \frac{\frac{t + 457.9610022158428}{z} - 36.52704169880642}{z}\right) + \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* y 3.13060547623))))
   (if (<= z -7.2e+34)
     t_1
     (if (<= z 14500000000000.0)
       (+
        x
        (/
         (* y (+ b (* z (+ a (* z t)))))
         (+ 0.607771387771 (* z (+ 11.9400905721 (* z 31.4690115749))))))
       (if (<= z 9e+120)
         (*
          y
          (+
           (+
            3.13060547623
            (/ (- (/ (+ t 457.9610022158428) z) 36.52704169880642) z))
           (/ x y)))
         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 <= -7.2e+34) {
		tmp = t_1;
	} else if (z <= 14500000000000.0) {
		tmp = x + ((y * (b + (z * (a + (z * t))))) / (0.607771387771 + (z * (11.9400905721 + (z * 31.4690115749)))));
	} else if (z <= 9e+120) {
		tmp = y * ((3.13060547623 + ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)) + (x / y));
	} 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 <= (-7.2d+34)) then
        tmp = t_1
    else if (z <= 14500000000000.0d0) then
        tmp = x + ((y * (b + (z * (a + (z * t))))) / (0.607771387771d0 + (z * (11.9400905721d0 + (z * 31.4690115749d0)))))
    else if (z <= 9d+120) then
        tmp = y * ((3.13060547623d0 + ((((t + 457.9610022158428d0) / z) - 36.52704169880642d0) / z)) + (x / y))
    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 <= -7.2e+34) {
		tmp = t_1;
	} else if (z <= 14500000000000.0) {
		tmp = x + ((y * (b + (z * (a + (z * t))))) / (0.607771387771 + (z * (11.9400905721 + (z * 31.4690115749)))));
	} else if (z <= 9e+120) {
		tmp = y * ((3.13060547623 + ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)) + (x / y));
	} 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 <= -7.2e+34:
		tmp = t_1
	elif z <= 14500000000000.0:
		tmp = x + ((y * (b + (z * (a + (z * t))))) / (0.607771387771 + (z * (11.9400905721 + (z * 31.4690115749)))))
	elif z <= 9e+120:
		tmp = y * ((3.13060547623 + ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)) + (x / y))
	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 <= -7.2e+34)
		tmp = t_1;
	elseif (z <= 14500000000000.0)
		tmp = Float64(x + Float64(Float64(y * Float64(b + Float64(z * Float64(a + Float64(z * t))))) / Float64(0.607771387771 + Float64(z * Float64(11.9400905721 + Float64(z * 31.4690115749))))));
	elseif (z <= 9e+120)
		tmp = Float64(y * Float64(Float64(3.13060547623 + Float64(Float64(Float64(Float64(t + 457.9610022158428) / z) - 36.52704169880642) / z)) + Float64(x / y)));
	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 <= -7.2e+34)
		tmp = t_1;
	elseif (z <= 14500000000000.0)
		tmp = x + ((y * (b + (z * (a + (z * t))))) / (0.607771387771 + (z * (11.9400905721 + (z * 31.4690115749)))));
	elseif (z <= 9e+120)
		tmp = y * ((3.13060547623 + ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)) + (x / y));
	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, -7.2e+34], t$95$1, If[LessEqual[z, 14500000000000.0], N[(x + N[(N[(y * N[(b + N[(z * N[(a + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(0.607771387771 + N[(z * N[(11.9400905721 + N[(z * 31.4690115749), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9e+120], N[(y * N[(N[(3.13060547623 + N[(N[(N[(N[(t + 457.9610022158428), $MachinePrecision] / z), $MachinePrecision] - 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.2000000000000001e34 or 8.99999999999999953e120 < z

   1. Initial program 10.8%

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

   3. Simplified 13.9%

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

   5. Taylor expanded in z around inf 96.9%

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

   if -7.2000000000000001e34 < z < 1.45e13

   1. Initial program 98.5%

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

   3. Taylor expanded in z around 0 92.0%

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

   4. Taylor expanded in y around 0 98.5%

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

   5. Taylor expanded in z around 0 97.5%

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

   if 1.45e13 < z < 8.99999999999999953e120

   1. Initial program 32.1%

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

   3. Simplified 61.3%

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

   5. Taylor expanded in y around -inf 61.3%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(-1 \cdot \frac{x}{y} + -1 \cdot \frac{b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + 3.13060547623 \cdot z\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right)}\right)\right)} \]

   6. Taylor expanded in z around -inf 92.6%

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

      1. mul-1-neg 92.6%

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

      2. unsub-neg 92.6%

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

      3. mul-1-neg 92.6%

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

      4. unsub-neg 92.6%

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

      5. +-commutative 92.6%

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

   8. Simplified 92.6%

      \[\leadsto -1 \cdot \left(y \cdot \left(-1 \cdot \frac{x}{y} + -1 \cdot \color{blue}{\left(3.13060547623 - \frac{36.52704169880642 - \frac{t + 457.9610022158428}{z}}{z}\right)}\right)\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 97.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+34}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{elif}\;z \leq 14500000000000:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot t\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot 31.4690115749\right)}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+120}:\\ \;\;\;\;y \cdot \left(\left(3.13060547623 + \frac{\frac{t + 457.9610022158428}{z} - 36.52704169880642}{z}\right) + \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 93.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot 3.13060547623\\ \mathbf{if}\;z \leq -13:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 9000000000000:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot t\right)\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{+121}:\\ \;\;\;\;y \cdot \left(\left(3.13060547623 + \frac{\frac{t + 457.9610022158428}{z} - 36.52704169880642}{z}\right) + \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* y 3.13060547623))))
   (if (<= z -13.0)
     t_1
     (if (<= z 9000000000000.0)
       (+
        x
        (/
         (* y (+ b (* z (+ a (* z t)))))
         (+ 0.607771387771 (* z 11.9400905721))))
       (if (<= z 1.02e+121)
         (*
          y
          (+
           (+
            3.13060547623
            (/ (- (/ (+ t 457.9610022158428) z) 36.52704169880642) z))
           (/ x y)))
         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 <= -13.0) {
		tmp = t_1;
	} else if (z <= 9000000000000.0) {
		tmp = x + ((y * (b + (z * (a + (z * t))))) / (0.607771387771 + (z * 11.9400905721)));
	} else if (z <= 1.02e+121) {
		tmp = y * ((3.13060547623 + ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)) + (x / y));
	} 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 <= (-13.0d0)) then
        tmp = t_1
    else if (z <= 9000000000000.0d0) then
        tmp = x + ((y * (b + (z * (a + (z * t))))) / (0.607771387771d0 + (z * 11.9400905721d0)))
    else if (z <= 1.02d+121) then
        tmp = y * ((3.13060547623d0 + ((((t + 457.9610022158428d0) / z) - 36.52704169880642d0) / z)) + (x / y))
    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 <= -13.0) {
		tmp = t_1;
	} else if (z <= 9000000000000.0) {
		tmp = x + ((y * (b + (z * (a + (z * t))))) / (0.607771387771 + (z * 11.9400905721)));
	} else if (z <= 1.02e+121) {
		tmp = y * ((3.13060547623 + ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)) + (x / y));
	} 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 <= -13.0:
		tmp = t_1
	elif z <= 9000000000000.0:
		tmp = x + ((y * (b + (z * (a + (z * t))))) / (0.607771387771 + (z * 11.9400905721)))
	elif z <= 1.02e+121:
		tmp = y * ((3.13060547623 + ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)) + (x / y))
	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 <= -13.0)
		tmp = t_1;
	elseif (z <= 9000000000000.0)
		tmp = Float64(x + Float64(Float64(y * Float64(b + Float64(z * Float64(a + Float64(z * t))))) / Float64(0.607771387771 + Float64(z * 11.9400905721))));
	elseif (z <= 1.02e+121)
		tmp = Float64(y * Float64(Float64(3.13060547623 + Float64(Float64(Float64(Float64(t + 457.9610022158428) / z) - 36.52704169880642) / z)) + Float64(x / y)));
	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 <= -13.0)
		tmp = t_1;
	elseif (z <= 9000000000000.0)
		tmp = x + ((y * (b + (z * (a + (z * t))))) / (0.607771387771 + (z * 11.9400905721)));
	elseif (z <= 1.02e+121)
		tmp = y * ((3.13060547623 + ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)) + (x / y));
	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, -13.0], t$95$1, If[LessEqual[z, 9000000000000.0], N[(x + N[(N[(y * N[(b + N[(z * N[(a + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(0.607771387771 + N[(z * 11.9400905721), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.02e+121], N[(y * N[(N[(3.13060547623 + N[(N[(N[(N[(t + 457.9610022158428), $MachinePrecision] / z), $MachinePrecision] - 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -13 or 1.02000000000000005e121 < z

   1. Initial program 12.6%

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

   3. Simplified 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 93.0%

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

   if -13 < z < 9e12

   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 94.4%

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

   4. Taylor expanded in y around 0 99.7%

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

   5. Taylor expanded in z around 0 98.5%

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

      1. *-commutative 98.5%

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

   7. Simplified 98.5%

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

   if 9e12 < z < 1.02000000000000005e121

   1. Initial program 32.1%

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

   3. Simplified 61.3%

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

   5. Taylor expanded in y around -inf 61.3%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(-1 \cdot \frac{x}{y} + -1 \cdot \frac{b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + 3.13060547623 \cdot z\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right)}\right)\right)} \]

   6. Taylor expanded in z around -inf 92.6%

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

      1. mul-1-neg 92.6%

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

      2. unsub-neg 92.6%

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

      3. mul-1-neg 92.6%

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

      4. unsub-neg 92.6%

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

      5. +-commutative 92.6%

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

   8. Simplified 92.6%

      \[\leadsto -1 \cdot \left(y \cdot \left(-1 \cdot \frac{x}{y} + -1 \cdot \color{blue}{\left(3.13060547623 - \frac{36.52704169880642 - \frac{t + 457.9610022158428}{z}}{z}\right)}\right)\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 96.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -13:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{elif}\;z \leq 9000000000000:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot t\right)\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{+121}:\\ \;\;\;\;y \cdot \left(\left(3.13060547623 + \frac{\frac{t + 457.9610022158428}{z} - 36.52704169880642}{z}\right) + \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 92.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -13 \lor \neg \left(z \leq 70000000\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot t\right)\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -13.0) (not (<= z 70000000.0)))
   (+ x (* y 3.13060547623))
   (+
    x
    (/
     (* y (+ b (* z (+ a (* z t)))))
     (+ 0.607771387771 (* z 11.9400905721))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -13.0) || !(z <= 70000000.0)) {
		tmp = x + (y * 3.13060547623);
	} else {
		tmp = x + ((y * (b + (z * (a + (z * t))))) / (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 <= (-13.0d0)) .or. (.not. (z <= 70000000.0d0))) then
        tmp = x + (y * 3.13060547623d0)
    else
        tmp = x + ((y * (b + (z * (a + (z * t))))) / (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 <= -13.0) || !(z <= 70000000.0)) {
		tmp = x + (y * 3.13060547623);
	} else {
		tmp = x + ((y * (b + (z * (a + (z * t))))) / (0.607771387771 + (z * 11.9400905721)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -13.0) or not (z <= 70000000.0):
		tmp = x + (y * 3.13060547623)
	else:
		tmp = x + ((y * (b + (z * (a + (z * t))))) / (0.607771387771 + (z * 11.9400905721)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -13.0) || !(z <= 70000000.0))
		tmp = Float64(x + Float64(y * 3.13060547623));
	else
		tmp = Float64(x + Float64(Float64(y * Float64(b + Float64(z * Float64(a + Float64(z * t))))) / 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 <= -13.0) || ~((z <= 70000000.0)))
		tmp = x + (y * 3.13060547623);
	else
		tmp = x + ((y * (b + (z * (a + (z * t))))) / (0.607771387771 + (z * 11.9400905721)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -13.0], N[Not[LessEqual[z, 70000000.0]], $MachinePrecision]], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * N[(b + N[(z * N[(a + N[(z * t), $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 < -13 or 7e7 < z

   1. Initial program 15.6%

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

   3. Simplified 23.2%

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

   5. Taylor expanded in z around inf 89.1%

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

   if -13 < z < 7e7

   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 94.4%

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

   4. Taylor expanded in y around 0 99.7%

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

   5. Taylor expanded in z around 0 98.5%

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

      1. *-commutative 98.5%

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

   7. Simplified 98.5%

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

4. Final simplification 94.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -13 \lor \neg \left(z \leq 70000000\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot t\right)\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 89.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+33} \lor \neg \left(z \leq 20000\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot a\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -3.8e+33) (not (<= z 20000.0)))
   (+ x (* y 3.13060547623))
   (+ x (/ (* y (+ b (* z a))) (+ 0.607771387771 (* z 11.9400905721))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3.8e+33) || !(z <= 20000.0)) {
		tmp = x + (y * 3.13060547623);
	} else {
		tmp = x + ((y * (b + (z * a))) / (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 <= (-3.8d+33)) .or. (.not. (z <= 20000.0d0))) then
        tmp = x + (y * 3.13060547623d0)
    else
        tmp = x + ((y * (b + (z * a))) / (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 <= -3.8e+33) || !(z <= 20000.0)) {
		tmp = x + (y * 3.13060547623);
	} else {
		tmp = x + ((y * (b + (z * a))) / (0.607771387771 + (z * 11.9400905721)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -3.8e+33) or not (z <= 20000.0):
		tmp = x + (y * 3.13060547623)
	else:
		tmp = x + ((y * (b + (z * a))) / (0.607771387771 + (z * 11.9400905721)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -3.8e+33) || !(z <= 20000.0))
		tmp = Float64(x + Float64(y * 3.13060547623));
	else
		tmp = Float64(x + Float64(Float64(y * Float64(b + Float64(z * a))) / 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 <= -3.8e+33) || ~((z <= 20000.0)))
		tmp = x + (y * 3.13060547623);
	else
		tmp = x + ((y * (b + (z * a))) / (0.607771387771 + (z * 11.9400905721)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -3.8e+33], N[Not[LessEqual[z, 20000.0]], $MachinePrecision]], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * N[(b + N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(0.607771387771 + N[(z * 11.9400905721), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.80000000000000002e33 or 2e4 < z

   1. Initial program 16.5%

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

   3. Simplified 22.5%

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

   5. Taylor expanded in z around inf 90.8%

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

   if -3.80000000000000002e33 < z < 2e4

   1. Initial program 98.5%

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

   3. Taylor expanded in z around 0 92.4%

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

   4. Taylor expanded in y around 0 98.5%

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

   5. Taylor expanded in z around 0 97.0%

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

      1. *-commutative 97.0%

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

   7. Simplified 97.0%

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

   8. Taylor expanded in z around 0 85.6%

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

      1. associate-*r* 82.9%

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

      2. *-commutative 82.9%

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

      3. associate-*r* 86.9%

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

      4. *-commutative 86.9%

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

      5. distribute-rgt-in 86.9%

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

   10. Simplified 86.9%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+33} \lor \neg \left(z \leq 20000\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot a\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 83.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot 3.13060547623\\ \mathbf{if}\;z \leq -1.05 \cdot 10^{+34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-62}:\\ \;\;\;\;x + \frac{a \cdot \left(y \cdot z\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{elif}\;z \leq 20000:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* y 3.13060547623))))
   (if (<= z -1.05e+34)
     t_1
     (if (<= z -1.35e-62)
       (+ x (/ (* a (* y z)) (+ 0.607771387771 (* z 11.9400905721))))
       (if (<= z 20000.0) (+ x (* y (* b 1.6453555072203998))) 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 <= -1.05e+34) {
		tmp = t_1;
	} else if (z <= -1.35e-62) {
		tmp = x + ((a * (y * z)) / (0.607771387771 + (z * 11.9400905721)));
	} else if (z <= 20000.0) {
		tmp = x + (y * (b * 1.6453555072203998));
	} 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 <= (-1.05d+34)) then
        tmp = t_1
    else if (z <= (-1.35d-62)) then
        tmp = x + ((a * (y * z)) / (0.607771387771d0 + (z * 11.9400905721d0)))
    else if (z <= 20000.0d0) then
        tmp = x + (y * (b * 1.6453555072203998d0))
    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 <= -1.05e+34) {
		tmp = t_1;
	} else if (z <= -1.35e-62) {
		tmp = x + ((a * (y * z)) / (0.607771387771 + (z * 11.9400905721)));
	} else if (z <= 20000.0) {
		tmp = x + (y * (b * 1.6453555072203998));
	} 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 <= -1.05e+34:
		tmp = t_1
	elif z <= -1.35e-62:
		tmp = x + ((a * (y * z)) / (0.607771387771 + (z * 11.9400905721)))
	elif z <= 20000.0:
		tmp = x + (y * (b * 1.6453555072203998))
	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 <= -1.05e+34)
		tmp = t_1;
	elseif (z <= -1.35e-62)
		tmp = Float64(x + Float64(Float64(a * Float64(y * z)) / Float64(0.607771387771 + Float64(z * 11.9400905721))));
	elseif (z <= 20000.0)
		tmp = Float64(x + Float64(y * Float64(b * 1.6453555072203998)));
	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 <= -1.05e+34)
		tmp = t_1;
	elseif (z <= -1.35e-62)
		tmp = x + ((a * (y * z)) / (0.607771387771 + (z * 11.9400905721)));
	elseif (z <= 20000.0)
		tmp = x + (y * (b * 1.6453555072203998));
	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, -1.05e+34], t$95$1, If[LessEqual[z, -1.35e-62], N[(x + N[(N[(a * N[(y * z), $MachinePrecision]), $MachinePrecision] / N[(0.607771387771 + N[(z * 11.9400905721), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 20000.0], N[(x + N[(y * N[(b * 1.6453555072203998), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.05000000000000009e34 or 2e4 < z

   1. Initial program 15.8%

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

   3. Simplified 21.8%

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

   5. Taylor expanded in z around inf 91.7%

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

   if -1.05000000000000009e34 < z < -1.3500000000000001e-62

   1. Initial program 90.1%

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

   3. Taylor expanded in z around 0 78.9%

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

   4. Taylor expanded in y around 0 90.1%

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

   5. Taylor expanded in z around 0 74.9%

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

      1. *-commutative 74.9%

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

   7. Simplified 74.9%

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

   8. Taylor expanded in a around inf 65.0%

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

   if -1.3500000000000001e-62 < z < 2e4

   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 78.1%

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

      1. associate-*r* 78.2%

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

      2. *-commutative 78.2%

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

   7. Simplified 78.2%

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

4. Final simplification 83.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+34}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-62}:\\ \;\;\;\;x + \frac{a \cdot \left(y \cdot z\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{elif}\;z \leq 20000:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 83.5% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+36} \lor \neg \left(z \leq 20000\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1e+36) (not (<= z 20000.0)))
   (+ 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 <= -1e+36) || !(z <= 20000.0)) {
		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 <= (-1d+36)) .or. (.not. (z <= 20000.0d0))) 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 <= -1e+36) || !(z <= 20000.0)) {
		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 <= -1e+36) or not (z <= 20000.0):
		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 <= -1e+36) || !(z <= 20000.0))
		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 <= -1e+36) || ~((z <= 20000.0)))
		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, -1e+36], N[Not[LessEqual[z, 20000.0]], $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 < -1.00000000000000004e36 or 2e4 < z

   1. Initial program 15.0%

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

   3. Simplified 21.1%

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

   5. Taylor expanded in z around inf 91.6%

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

   if -1.00000000000000004e36 < z < 2e4

   1. Initial program 98.5%

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

   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 72.6%

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

      1. associate-*r* 72.6%

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

      2. *-commutative 72.6%

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

   7. Simplified 72.6%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+36} \lor \neg \left(z \leq 20000\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 83.5% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+37} \lor \neg \left(z \leq 17000\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x + 1.6453555072203998 \cdot \left(y \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -3.3e+37) (not (<= z 17000.0)))
   (+ x (* y 3.13060547623))
   (+ x (* 1.6453555072203998 (* y b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3.3e+37) || !(z <= 17000.0)) {
		tmp = x + (y * 3.13060547623);
	} else {
		tmp = x + (1.6453555072203998 * (y * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-3.3d+37)) .or. (.not. (z <= 17000.0d0))) then
        tmp = x + (y * 3.13060547623d0)
    else
        tmp = x + (1.6453555072203998d0 * (y * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3.3e+37) || !(z <= 17000.0)) {
		tmp = x + (y * 3.13060547623);
	} else {
		tmp = x + (1.6453555072203998 * (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -3.3e+37) or not (z <= 17000.0):
		tmp = x + (y * 3.13060547623)
	else:
		tmp = x + (1.6453555072203998 * (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -3.3e+37) || !(z <= 17000.0))
		tmp = Float64(x + Float64(y * 3.13060547623));
	else
		tmp = Float64(x + Float64(1.6453555072203998 * Float64(y * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -3.3e+37) || ~((z <= 17000.0)))
		tmp = x + (y * 3.13060547623);
	else
		tmp = x + (1.6453555072203998 * (y * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -3.3e+37], N[Not[LessEqual[z, 17000.0]], $MachinePrecision]], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision], N[(x + N[(1.6453555072203998 * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.3000000000000001e37 or 17000 < z

   1. Initial program 15.0%

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

   3. Simplified 21.1%

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

   5. Taylor expanded in z around inf 91.6%

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

   if -3.3000000000000001e37 < z < 17000

   1. Initial program 98.5%

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

   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 72.6%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+37} \lor \neg \left(z \leq 17000\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x + 1.6453555072203998 \cdot \left(y \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 65.1% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+36} \lor \neg \left(z \leq 7.9 \cdot 10^{-84}\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1e+36) (not (<= z 7.9e-84))) (+ x (* y 3.13060547623)) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1e+36) || !(z <= 7.9e-84)) {
		tmp = x + (y * 3.13060547623);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-1d+36)) .or. (.not. (z <= 7.9d-84))) then
        tmp = x + (y * 3.13060547623d0)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1e+36) || !(z <= 7.9e-84)) {
		tmp = x + (y * 3.13060547623);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1e+36) or not (z <= 7.9e-84):
		tmp = x + (y * 3.13060547623)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1e+36) || !(z <= 7.9e-84))
		tmp = Float64(x + Float64(y * 3.13060547623));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1e+36) || ~((z <= 7.9e-84)))
		tmp = x + (y * 3.13060547623);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1e+36], N[Not[LessEqual[z, 7.9e-84]], $MachinePrecision]], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.00000000000000004e36 or 7.89999999999999991e-84 < z

   1. Initial program 28.7%

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

   3. Simplified 33.7%

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

   5. Taylor expanded in z around inf 79.5%

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

   if -1.00000000000000004e36 < z < 7.89999999999999991e-84

   1. Initial program 98.3%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 46.3%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+36} \lor \neg \left(z \leq 7.9 \cdot 10^{-84}\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 51.9% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{+113} \lor \neg \left(y \leq 1.85 \cdot 10^{+74}\right):\\ \;\;\;\;y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.75e+113) (not (<= y 1.85e+74))) (* y 3.13060547623) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.75e+113) || !(y <= 1.85e+74)) {
		tmp = y * 3.13060547623;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-1.75d+113)) .or. (.not. (y <= 1.85d+74))) then
        tmp = y * 3.13060547623d0
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.75e+113) || !(y <= 1.85e+74)) {
		tmp = y * 3.13060547623;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.75e+113) or not (y <= 1.85e+74):
		tmp = y * 3.13060547623
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.75e+113) || !(y <= 1.85e+74))
		tmp = Float64(y * 3.13060547623);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.75e+113) || ~((y <= 1.85e+74)))
		tmp = y * 3.13060547623;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.75e+113], N[Not[LessEqual[y, 1.85e+74]], $MachinePrecision]], N[(y * 3.13060547623), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.75e113 or 1.8500000000000001e74 < y

   1. Initial program 55.9%

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

   3. Simplified 62.3%

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

   5. Taylor expanded in z around inf 48.4%

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

   6. Taylor expanded in x around 0 42.2%

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

   if -1.75e113 < y < 1.8500000000000001e74

   1. Initial program 66.6%

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

   3. Simplified 68.3%

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

   5. Taylor expanded in y around 0 59.6%

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

4. Final simplification 53.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{+113} \lor \neg \left(y \leq 1.85 \cdot 10^{+74}\right):\\ \;\;\;\;y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 45.8% 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 62.9%

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

3. Simplified 66.2%

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

5. Taylor expanded in y around 0 43.5%

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

Developer Target 1: 98.5% 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 2024177 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, D"
  :precision binary64

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

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