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

Percentage Accurate: 57.7% → 98.3%

Time: 54.2s

Alternatives: 19

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: 57.7% 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: 98.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -900000000:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 + y \cdot \frac{\frac{\left(t + 457.9610022158428\right) + \frac{\left(a - 5864.8025282699045\right) - t \cdot 15.234687407}{z}}{z} - 36.52704169880642}{z}\right)\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+36}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot 11.1667541262\right)\right)\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot \frac{\frac{457.9610022158428 + \left(t + \frac{a}{z}\right)}{z} - 36.52704169880642}{z} + y \cdot 3.13060547623\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -900000000.0)
   (+
    x
    (+
     (* y 3.13060547623)
     (*
      y
      (/
       (-
        (/
         (+
          (+ t 457.9610022158428)
          (/ (- (- a 5864.8025282699045) (* t 15.234687407)) z))
         z)
        36.52704169880642)
       z))))
   (if (<= z 4.1e+36)
     (+
      x
      (/
       (* y (+ b (* z (+ a (* z (+ t (* z 11.1667541262)))))))
       (+
        (*
         z
         (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721))
        0.607771387771)))
     (+
      x
      (+
       (*
        y
        (/ (- (/ (+ 457.9610022158428 (+ t (/ a z))) z) 36.52704169880642) z))
       (* y 3.13060547623))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -900000000.0) {
		tmp = x + ((y * 3.13060547623) + (y * (((((t + 457.9610022158428) + (((a - 5864.8025282699045) - (t * 15.234687407)) / z)) / z) - 36.52704169880642) / z)));
	} else if (z <= 4.1e+36) {
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771));
	} else {
		tmp = x + ((y * ((((457.9610022158428 + (t + (a / z))) / z) - 36.52704169880642) / z)) + (y * 3.13060547623));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-900000000.0d0)) then
        tmp = x + ((y * 3.13060547623d0) + (y * (((((t + 457.9610022158428d0) + (((a - 5864.8025282699045d0) - (t * 15.234687407d0)) / z)) / z) - 36.52704169880642d0) / z)))
    else if (z <= 4.1d+36) then
        tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262d0))))))) / ((z * ((z * ((z * (z + 15.234687407d0)) + 31.4690115749d0)) + 11.9400905721d0)) + 0.607771387771d0))
    else
        tmp = x + ((y * ((((457.9610022158428d0 + (t + (a / z))) / z) - 36.52704169880642d0) / z)) + (y * 3.13060547623d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -900000000.0) {
		tmp = x + ((y * 3.13060547623) + (y * (((((t + 457.9610022158428) + (((a - 5864.8025282699045) - (t * 15.234687407)) / z)) / z) - 36.52704169880642) / z)));
	} else if (z <= 4.1e+36) {
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771));
	} else {
		tmp = x + ((y * ((((457.9610022158428 + (t + (a / z))) / z) - 36.52704169880642) / z)) + (y * 3.13060547623));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -900000000.0:
		tmp = x + ((y * 3.13060547623) + (y * (((((t + 457.9610022158428) + (((a - 5864.8025282699045) - (t * 15.234687407)) / z)) / z) - 36.52704169880642) / z)))
	elif z <= 4.1e+36:
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771))
	else:
		tmp = x + ((y * ((((457.9610022158428 + (t + (a / z))) / z) - 36.52704169880642) / z)) + (y * 3.13060547623))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -900000000.0)
		tmp = Float64(x + Float64(Float64(y * 3.13060547623) + Float64(y * Float64(Float64(Float64(Float64(Float64(t + 457.9610022158428) + Float64(Float64(Float64(a - 5864.8025282699045) - Float64(t * 15.234687407)) / z)) / z) - 36.52704169880642) / z))));
	elseif (z <= 4.1e+36)
		tmp = Float64(x + Float64(Float64(y * Float64(b + Float64(z * Float64(a + Float64(z * Float64(t + Float64(z * 11.1667541262))))))) / Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)));
	else
		tmp = Float64(x + Float64(Float64(y * Float64(Float64(Float64(Float64(457.9610022158428 + Float64(t + Float64(a / z))) / z) - 36.52704169880642) / z)) + Float64(y * 3.13060547623)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -900000000.0)
		tmp = x + ((y * 3.13060547623) + (y * (((((t + 457.9610022158428) + (((a - 5864.8025282699045) - (t * 15.234687407)) / z)) / z) - 36.52704169880642) / z)));
	elseif (z <= 4.1e+36)
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771));
	else
		tmp = x + ((y * ((((457.9610022158428 + (t + (a / z))) / z) - 36.52704169880642) / z)) + (y * 3.13060547623));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -900000000.0], N[(x + N[(N[(y * 3.13060547623), $MachinePrecision] + N[(y * N[(N[(N[(N[(N[(t + 457.9610022158428), $MachinePrecision] + N[(N[(N[(a - 5864.8025282699045), $MachinePrecision] - N[(t * 15.234687407), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] - 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.1e+36], N[(x + N[(N[(y * N[(b + N[(z * N[(a + N[(z * N[(t + N[(z * 11.1667541262), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(z * N[(N[(z * N[(N[(z * N[(z + 15.234687407), $MachinePrecision]), $MachinePrecision] + 31.4690115749), $MachinePrecision]), $MachinePrecision] + 11.9400905721), $MachinePrecision]), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * N[(N[(N[(N[(457.9610022158428 + N[(t + N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] - 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -9e8

   1. Initial program 18.3%

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

   3. Taylor expanded in z around -inf 76.3%

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

   4. Taylor expanded in y around 0 97.8%

      \[\leadsto x + \left(-1 \cdot \color{blue}{\frac{y \cdot \left(36.52704169880642 + -1 \cdot \frac{457.9610022158428 + \left(t + -1 \cdot \frac{-1 \cdot a - \left(1112.0901850848957 + -15.234687407 \cdot \left(457.9610022158428 + t\right)\right)}{z}\right)}{z}\right)}{z}} + 3.13060547623 \cdot y\right) \]

   6. Simplified 97.8%

      \[\leadsto x + \left(-1 \cdot \color{blue}{\frac{y \cdot \left(36.52704169880642 + \left(-\frac{457.9610022158428 + \left(t + \left(-\frac{\left(-a\right) - \left(1112.0901850848957 + \left(-6976.8927133548 + -15.234687407 \cdot t\right)\right)}{z}\right)\right)}{z}\right)\right)}{z}} + 3.13060547623 \cdot y\right) \]

   8. Applied egg-rr 99.3%

      \[\leadsto x + \left(-1 \cdot \color{blue}{\left(y \cdot \frac{36.52704169880642 - \frac{457.9610022158428 + \left(t - \frac{\left(-a\right) - \left(-5864.8025282699045 + t \cdot -15.234687407\right)}{z}\right)}{z}}{z}\right)} + 3.13060547623 \cdot y\right) \]

   10. Simplified 99.3%

       \[\leadsto x + \left(-1 \cdot \color{blue}{\left(y \cdot \frac{36.52704169880642 - \frac{\left(t + 457.9610022158428\right) - \frac{\left(5864.8025282699045 - a\right) + 15.234687407 \cdot t}{z}}{z}}{z}\right)} + 3.13060547623 \cdot y\right) \]

   if -9e8 < z < 4.10000000000000013e36

   1. Initial program 98.3%

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

   3. Taylor expanded in z around 0 98.1%

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

      1. *-commutative 98.1%

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

   5. Simplified 98.1%

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

   if 4.10000000000000013e36 < z

   1. Initial program 7.1%

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

   3. Taylor expanded in z around -inf 62.7%

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

   4. Taylor expanded in y around 0 91.8%

      \[\leadsto x + \left(-1 \cdot \color{blue}{\frac{y \cdot \left(36.52704169880642 + -1 \cdot \frac{457.9610022158428 + \left(t + -1 \cdot \frac{-1 \cdot a - \left(1112.0901850848957 + -15.234687407 \cdot \left(457.9610022158428 + t\right)\right)}{z}\right)}{z}\right)}{z}} + 3.13060547623 \cdot y\right) \]

   6. Simplified 91.8%

      \[\leadsto x + \left(-1 \cdot \color{blue}{\frac{y \cdot \left(36.52704169880642 + \left(-\frac{457.9610022158428 + \left(t + \left(-\frac{\left(-a\right) - \left(1112.0901850848957 + \left(-6976.8927133548 + -15.234687407 \cdot t\right)\right)}{z}\right)\right)}{z}\right)\right)}{z}} + 3.13060547623 \cdot y\right) \]

   7. Taylor expanded in a around inf 91.8%

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

      1. mul-1-neg 91.8%

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

      2. distribute-frac-neg 91.8%

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

   9. Simplified 91.8%

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

       1. associate-/l* 98.4%

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

       2. unsub-neg 98.4%

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

       3. unsub-neg 98.4%

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

   11. Applied egg-rr 98.4%

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

       1. distribute-frac-neg 98.4%

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

       2. mul-1-neg 98.4%

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

       3. cancel-sign-sub-inv 98.4%

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

       4. metadata-eval 98.4%

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

       5. *-lft-identity 98.4%

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

   13. Simplified 98.4%

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

4. Final simplification 98.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -900000000:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 + y \cdot \frac{\frac{\left(t + 457.9610022158428\right) + \frac{\left(a - 5864.8025282699045\right) - t \cdot 15.234687407}{z}}{z} - 36.52704169880642}{z}\right)\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+36}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot 11.1667541262\right)\right)\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot \frac{\frac{457.9610022158428 + \left(t + \frac{a}{z}\right)}{z} - 36.52704169880642}{z} + y \cdot 3.13060547623\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 98.0% accurate, 0.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 95.4%

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

   3. Simplified 97.1%

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

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

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in z around inf 99.9%

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

      1. sub-neg 99.9%

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

      2. associate-+r+ 99.9%

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

      3. associate-+l+ 99.9%

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

      4. associate-*r/ 99.9%

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

      5. metadata-eval 99.9%

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

      6. distribute-neg-frac 99.9%

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

      7. metadata-eval 99.9%

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

   7. Simplified 99.9%

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

4. Final simplification 98.2%

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

Alternative 3: 95.6% accurate, 0.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 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 95.4%

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

      1. remove-double-neg 95.4%

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

      2. distribute-lft-neg-out 95.4%

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

      3. distribute-lft-neg-in 95.4%

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

      4. remove-double-neg 95.4%

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

      5. fma-define 95.4%

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

      6. fma-define 95.4%

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

      7. fma-define 95.4%

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

      8. fma-define 95.4%

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

   3. Simplified 95.4%

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

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

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in z around inf 99.9%

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

      1. sub-neg 99.9%

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

      2. associate-+r+ 99.9%

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

      3. associate-+l+ 99.9%

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

      4. associate-*r/ 99.9%

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

      5. metadata-eval 99.9%

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

      6. distribute-neg-frac 99.9%

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

      7. metadata-eval 99.9%

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

   7. Simplified 99.9%

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

4. Final simplification 97.2%

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

Alternative 4: 95.5% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y * Float64(b + Float64(z * Float64(a + Float64(z * Float64(t + Float64(z * Float64(11.1667541262 + Float64(z * 3.13060547623))))))))) / Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = Float64(t_1 + x);
	else
		tmp = fma(y, Float64(Float64(3.13060547623 + Float64(457.9610022158428 / (z ^ 2.0))) + Float64(Float64(t / (z ^ 2.0)) + Float64(-36.52704169880642 / z))), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y * N[(b + N[(z * N[(a + N[(z * N[(t + N[(z * N[(11.1667541262 + N[(z * 3.13060547623), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(z * N[(N[(z * N[(N[(z * N[(z + 15.234687407), $MachinePrecision]), $MachinePrecision] + 31.4690115749), $MachinePrecision]), $MachinePrecision] + 11.9400905721), $MachinePrecision]), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], N[(t$95$1 + x), $MachinePrecision], N[(y * N[(N[(3.13060547623 + N[(457.9610022158428 / N[Power[z, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t / N[Power[z, 2.0], $MachinePrecision]), $MachinePrecision] + N[(-36.52704169880642 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 95.4%

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

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

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in z around inf 99.9%

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

      1. sub-neg 99.9%

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

      2. associate-+r+ 99.9%

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

      3. associate-+l+ 99.9%

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

      4. associate-*r/ 99.9%

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

      5. metadata-eval 99.9%

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

      6. distribute-neg-frac 99.9%

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

      7. metadata-eval 99.9%

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

   7. Simplified 99.9%

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

4. Final simplification 97.2%

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

Alternative 5: 95.7% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * (b + (z * (a + (z * (t + (z * (11.1667541262 + (z * 3.13060547623))))))))) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771);
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1 + x;
	} else {
		tmp = x + ((y * ((((457.9610022158428 + (t + (a / z))) / z) - 36.52704169880642) / z)) + (y * 3.13060547623));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (y * (b + (z * (a + (z * (t + (z * (11.1667541262 + (z * 3.13060547623))))))))) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1 + x
	else:
		tmp = x + ((y * ((((457.9610022158428 + (t + (a / z))) / z) - 36.52704169880642) / z)) + (y * 3.13060547623))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y * Float64(b + Float64(z * Float64(a + Float64(z * Float64(t + Float64(z * Float64(11.1667541262 + Float64(z * 3.13060547623))))))))) / Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = Float64(t_1 + x);
	else
		tmp = Float64(x + Float64(Float64(y * Float64(Float64(Float64(Float64(457.9610022158428 + Float64(t + Float64(a / z))) / z) - 36.52704169880642) / z)) + Float64(y * 3.13060547623)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (y * (b + (z * (a + (z * (t + (z * (11.1667541262 + (z * 3.13060547623))))))))) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771);
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1 + x;
	else
		tmp = x + ((y * ((((457.9610022158428 + (t + (a / z))) / z) - 36.52704169880642) / z)) + (y * 3.13060547623));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y * N[(b + N[(z * N[(a + N[(z * N[(t + N[(z * N[(11.1667541262 + N[(z * 3.13060547623), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(z * N[(N[(z * N[(N[(z * N[(z + 15.234687407), $MachinePrecision]), $MachinePrecision] + 31.4690115749), $MachinePrecision]), $MachinePrecision] + 11.9400905721), $MachinePrecision]), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], N[(t$95$1 + x), $MachinePrecision], N[(x + N[(N[(y * N[(N[(N[(N[(457.9610022158428 + N[(t + N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] - 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]), $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 95.4%

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

   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%

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

   3. Taylor expanded in z around -inf 65.6%

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

   4. Taylor expanded in y around 0 95.2%

      \[\leadsto x + \left(-1 \cdot \color{blue}{\frac{y \cdot \left(36.52704169880642 + -1 \cdot \frac{457.9610022158428 + \left(t + -1 \cdot \frac{-1 \cdot a - \left(1112.0901850848957 + -15.234687407 \cdot \left(457.9610022158428 + t\right)\right)}{z}\right)}{z}\right)}{z}} + 3.13060547623 \cdot y\right) \]

   6. Simplified 95.2%

      \[\leadsto x + \left(-1 \cdot \color{blue}{\frac{y \cdot \left(36.52704169880642 + \left(-\frac{457.9610022158428 + \left(t + \left(-\frac{\left(-a\right) - \left(1112.0901850848957 + \left(-6976.8927133548 + -15.234687407 \cdot t\right)\right)}{z}\right)\right)}{z}\right)\right)}{z}} + 3.13060547623 \cdot y\right) \]

   7. Taylor expanded in a around inf 95.2%

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

      1. mul-1-neg 95.2%

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

      2. distribute-frac-neg 95.2%

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

   9. Simplified 95.2%

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

       1. associate-/l* 99.9%

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

       2. unsub-neg 99.9%

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

       3. unsub-neg 99.9%

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

   11. Applied egg-rr 99.9%

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

       1. distribute-frac-neg 99.9%

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

       2. mul-1-neg 99.9%

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

       3. cancel-sign-sub-inv 99.9%

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

       4. metadata-eval 99.9%

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

       5. *-lft-identity 99.9%

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

   13. Simplified 99.9%

       \[\leadsto x + \left(-1 \cdot \color{blue}{\left(y \cdot \frac{36.52704169880642 - \frac{457.9610022158428 + \left(t + \frac{a}{z}\right)}{z}}{z}\right)} + 3.13060547623 \cdot y\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 97.2%

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

Alternative 6: 98.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -250000:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 + y \cdot \frac{\frac{\left(t + 457.9610022158428\right) + \frac{\left(a - 5864.8025282699045\right) - t \cdot 15.234687407}{z}}{z} - 36.52704169880642}{z}\right)\\ \mathbf{elif}\;z \leq 1.05:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot 31.4690115749\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot \frac{\frac{457.9610022158428 + \left(t + \frac{a}{z}\right)}{z} - 36.52704169880642}{z} + y \cdot 3.13060547623\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -250000.0)
   (+
    x
    (+
     (* y 3.13060547623)
     (*
      y
      (/
       (-
        (/
         (+
          (+ t 457.9610022158428)
          (/ (- (- a 5864.8025282699045) (* t 15.234687407)) z))
         z)
        36.52704169880642)
       z))))
   (if (<= z 1.05)
     (+
      x
      (/
       (*
        y
        (+
         b
         (* z (+ a (* z (+ t (* z (+ 11.1667541262 (* z 3.13060547623)))))))))
       (+ 0.607771387771 (* z (+ 11.9400905721 (* z 31.4690115749))))))
     (+
      x
      (+
       (*
        y
        (/ (- (/ (+ 457.9610022158428 (+ t (/ a z))) z) 36.52704169880642) z))
       (* y 3.13060547623))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -250000.0) {
		tmp = x + ((y * 3.13060547623) + (y * (((((t + 457.9610022158428) + (((a - 5864.8025282699045) - (t * 15.234687407)) / z)) / z) - 36.52704169880642) / z)));
	} else if (z <= 1.05) {
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * (11.1667541262 + (z * 3.13060547623))))))))) / (0.607771387771 + (z * (11.9400905721 + (z * 31.4690115749)))));
	} else {
		tmp = x + ((y * ((((457.9610022158428 + (t + (a / z))) / z) - 36.52704169880642) / z)) + (y * 3.13060547623));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-250000.0d0)) then
        tmp = x + ((y * 3.13060547623d0) + (y * (((((t + 457.9610022158428d0) + (((a - 5864.8025282699045d0) - (t * 15.234687407d0)) / z)) / z) - 36.52704169880642d0) / z)))
    else if (z <= 1.05d0) then
        tmp = x + ((y * (b + (z * (a + (z * (t + (z * (11.1667541262d0 + (z * 3.13060547623d0))))))))) / (0.607771387771d0 + (z * (11.9400905721d0 + (z * 31.4690115749d0)))))
    else
        tmp = x + ((y * ((((457.9610022158428d0 + (t + (a / z))) / z) - 36.52704169880642d0) / z)) + (y * 3.13060547623d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -250000.0) {
		tmp = x + ((y * 3.13060547623) + (y * (((((t + 457.9610022158428) + (((a - 5864.8025282699045) - (t * 15.234687407)) / z)) / z) - 36.52704169880642) / z)));
	} else if (z <= 1.05) {
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * (11.1667541262 + (z * 3.13060547623))))))))) / (0.607771387771 + (z * (11.9400905721 + (z * 31.4690115749)))));
	} else {
		tmp = x + ((y * ((((457.9610022158428 + (t + (a / z))) / z) - 36.52704169880642) / z)) + (y * 3.13060547623));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -250000.0:
		tmp = x + ((y * 3.13060547623) + (y * (((((t + 457.9610022158428) + (((a - 5864.8025282699045) - (t * 15.234687407)) / z)) / z) - 36.52704169880642) / z)))
	elif z <= 1.05:
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * (11.1667541262 + (z * 3.13060547623))))))))) / (0.607771387771 + (z * (11.9400905721 + (z * 31.4690115749)))))
	else:
		tmp = x + ((y * ((((457.9610022158428 + (t + (a / z))) / z) - 36.52704169880642) / z)) + (y * 3.13060547623))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -250000.0)
		tmp = Float64(x + Float64(Float64(y * 3.13060547623) + Float64(y * Float64(Float64(Float64(Float64(Float64(t + 457.9610022158428) + Float64(Float64(Float64(a - 5864.8025282699045) - Float64(t * 15.234687407)) / z)) / z) - 36.52704169880642) / z))));
	elseif (z <= 1.05)
		tmp = Float64(x + Float64(Float64(y * Float64(b + Float64(z * Float64(a + Float64(z * Float64(t + Float64(z * Float64(11.1667541262 + Float64(z * 3.13060547623))))))))) / Float64(0.607771387771 + Float64(z * Float64(11.9400905721 + Float64(z * 31.4690115749))))));
	else
		tmp = Float64(x + Float64(Float64(y * Float64(Float64(Float64(Float64(457.9610022158428 + Float64(t + Float64(a / z))) / z) - 36.52704169880642) / z)) + Float64(y * 3.13060547623)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -250000.0)
		tmp = x + ((y * 3.13060547623) + (y * (((((t + 457.9610022158428) + (((a - 5864.8025282699045) - (t * 15.234687407)) / z)) / z) - 36.52704169880642) / z)));
	elseif (z <= 1.05)
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * (11.1667541262 + (z * 3.13060547623))))))))) / (0.607771387771 + (z * (11.9400905721 + (z * 31.4690115749)))));
	else
		tmp = x + ((y * ((((457.9610022158428 + (t + (a / z))) / z) - 36.52704169880642) / z)) + (y * 3.13060547623));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -250000.0], N[(x + N[(N[(y * 3.13060547623), $MachinePrecision] + N[(y * N[(N[(N[(N[(N[(t + 457.9610022158428), $MachinePrecision] + N[(N[(N[(a - 5864.8025282699045), $MachinePrecision] - N[(t * 15.234687407), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] - 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.05], N[(x + N[(N[(y * N[(b + N[(z * N[(a + N[(z * N[(t + N[(z * N[(11.1667541262 + N[(z * 3.13060547623), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(0.607771387771 + N[(z * N[(11.9400905721 + N[(z * 31.4690115749), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * N[(N[(N[(N[(457.9610022158428 + N[(t + N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] - 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.5e5

   1. Initial program 18.3%

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

   3. Taylor expanded in z around -inf 76.3%

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

   4. Taylor expanded in y around 0 97.8%

      \[\leadsto x + \left(-1 \cdot \color{blue}{\frac{y \cdot \left(36.52704169880642 + -1 \cdot \frac{457.9610022158428 + \left(t + -1 \cdot \frac{-1 \cdot a - \left(1112.0901850848957 + -15.234687407 \cdot \left(457.9610022158428 + t\right)\right)}{z}\right)}{z}\right)}{z}} + 3.13060547623 \cdot y\right) \]

   6. Simplified 97.8%

      \[\leadsto x + \left(-1 \cdot \color{blue}{\frac{y \cdot \left(36.52704169880642 + \left(-\frac{457.9610022158428 + \left(t + \left(-\frac{\left(-a\right) - \left(1112.0901850848957 + \left(-6976.8927133548 + -15.234687407 \cdot t\right)\right)}{z}\right)\right)}{z}\right)\right)}{z}} + 3.13060547623 \cdot y\right) \]

   8. Applied egg-rr 99.3%

      \[\leadsto x + \left(-1 \cdot \color{blue}{\left(y \cdot \frac{36.52704169880642 - \frac{457.9610022158428 + \left(t - \frac{\left(-a\right) - \left(-5864.8025282699045 + t \cdot -15.234687407\right)}{z}\right)}{z}}{z}\right)} + 3.13060547623 \cdot y\right) \]

   10. Simplified 99.3%

       \[\leadsto x + \left(-1 \cdot \color{blue}{\left(y \cdot \frac{36.52704169880642 - \frac{\left(t + 457.9610022158428\right) - \frac{\left(5864.8025282699045 - a\right) + 15.234687407 \cdot t}{z}}{z}}{z}\right)} + 3.13060547623 \cdot y\right) \]

   if -2.5e5 < z < 1.05000000000000004

   1. Initial program 99.0%

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

   3. Taylor expanded in z around 0 97.9%

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

      1. *-commutative 97.9%

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

   5. Simplified 97.9%

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

   if 1.05000000000000004 < z

   1. Initial program 14.3%

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

   3. Taylor expanded in z around -inf 63.3%

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

   4. Taylor expanded in y around 0 89.7%

      \[\leadsto x + \left(-1 \cdot \color{blue}{\frac{y \cdot \left(36.52704169880642 + -1 \cdot \frac{457.9610022158428 + \left(t + -1 \cdot \frac{-1 \cdot a - \left(1112.0901850848957 + -15.234687407 \cdot \left(457.9610022158428 + t\right)\right)}{z}\right)}{z}\right)}{z}} + 3.13060547623 \cdot y\right) \]

   6. Simplified 89.7%

      \[\leadsto x + \left(-1 \cdot \color{blue}{\frac{y \cdot \left(36.52704169880642 + \left(-\frac{457.9610022158428 + \left(t + \left(-\frac{\left(-a\right) - \left(1112.0901850848957 + \left(-6976.8927133548 + -15.234687407 \cdot t\right)\right)}{z}\right)\right)}{z}\right)\right)}{z}} + 3.13060547623 \cdot y\right) \]

   7. Taylor expanded in a around inf 89.7%

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

      1. mul-1-neg 89.7%

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

      2. distribute-frac-neg 89.7%

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

   9. Simplified 89.7%

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

       1. associate-/l* 95.7%

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

       2. unsub-neg 95.7%

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

       3. unsub-neg 95.7%

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

   11. Applied egg-rr 95.7%

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

       1. distribute-frac-neg 95.7%

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

       2. mul-1-neg 95.7%

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

       3. cancel-sign-sub-inv 95.7%

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

       4. metadata-eval 95.7%

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

       5. *-lft-identity 95.7%

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

   13. Simplified 95.7%

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

4. Final simplification 97.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -250000:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 + y \cdot \frac{\frac{\left(t + 457.9610022158428\right) + \frac{\left(a - 5864.8025282699045\right) - t \cdot 15.234687407}{z}}{z} - 36.52704169880642}{z}\right)\\ \mathbf{elif}\;z \leq 1.05:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot 31.4690115749\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot \frac{\frac{457.9610022158428 + \left(t + \frac{a}{z}\right)}{z} - 36.52704169880642}{z} + y \cdot 3.13060547623\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 97.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -13:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 + y \cdot \frac{\frac{\left(t + 457.9610022158428\right) + \frac{\left(a - 5864.8025282699045\right) - t \cdot 15.234687407}{z}}{z} - 36.52704169880642}{z}\right)\\ \mathbf{elif}\;z \leq 1.05:\\ \;\;\;\;x + \frac{y \cdot b + y \cdot \left(z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\right)\right)\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot \frac{\frac{457.9610022158428 + \left(t + \frac{a}{z}\right)}{z} - 36.52704169880642}{z} + y \cdot 3.13060547623\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -13.0)
   (+
    x
    (+
     (* y 3.13060547623)
     (*
      y
      (/
       (-
        (/
         (+
          (+ t 457.9610022158428)
          (/ (- (- a 5864.8025282699045) (* t 15.234687407)) z))
         z)
        36.52704169880642)
       z))))
   (if (<= z 1.05)
     (+
      x
      (/
       (+
        (* y b)
        (*
         y
         (* z (+ a (* z (+ t (* z (+ 11.1667541262 (* z 3.13060547623)))))))))
       (+ 0.607771387771 (* z 11.9400905721))))
     (+
      x
      (+
       (*
        y
        (/ (- (/ (+ 457.9610022158428 (+ t (/ a z))) z) 36.52704169880642) z))
       (* y 3.13060547623))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -13.0) {
		tmp = x + ((y * 3.13060547623) + (y * (((((t + 457.9610022158428) + (((a - 5864.8025282699045) - (t * 15.234687407)) / z)) / z) - 36.52704169880642) / z)));
	} else if (z <= 1.05) {
		tmp = x + (((y * b) + (y * (z * (a + (z * (t + (z * (11.1667541262 + (z * 3.13060547623))))))))) / (0.607771387771 + (z * 11.9400905721)));
	} else {
		tmp = x + ((y * ((((457.9610022158428 + (t + (a / z))) / z) - 36.52704169880642) / z)) + (y * 3.13060547623));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-13.0d0)) then
        tmp = x + ((y * 3.13060547623d0) + (y * (((((t + 457.9610022158428d0) + (((a - 5864.8025282699045d0) - (t * 15.234687407d0)) / z)) / z) - 36.52704169880642d0) / z)))
    else if (z <= 1.05d0) then
        tmp = x + (((y * b) + (y * (z * (a + (z * (t + (z * (11.1667541262d0 + (z * 3.13060547623d0))))))))) / (0.607771387771d0 + (z * 11.9400905721d0)))
    else
        tmp = x + ((y * ((((457.9610022158428d0 + (t + (a / z))) / z) - 36.52704169880642d0) / z)) + (y * 3.13060547623d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -13.0) {
		tmp = x + ((y * 3.13060547623) + (y * (((((t + 457.9610022158428) + (((a - 5864.8025282699045) - (t * 15.234687407)) / z)) / z) - 36.52704169880642) / z)));
	} else if (z <= 1.05) {
		tmp = x + (((y * b) + (y * (z * (a + (z * (t + (z * (11.1667541262 + (z * 3.13060547623))))))))) / (0.607771387771 + (z * 11.9400905721)));
	} else {
		tmp = x + ((y * ((((457.9610022158428 + (t + (a / z))) / z) - 36.52704169880642) / z)) + (y * 3.13060547623));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -13.0:
		tmp = x + ((y * 3.13060547623) + (y * (((((t + 457.9610022158428) + (((a - 5864.8025282699045) - (t * 15.234687407)) / z)) / z) - 36.52704169880642) / z)))
	elif z <= 1.05:
		tmp = x + (((y * b) + (y * (z * (a + (z * (t + (z * (11.1667541262 + (z * 3.13060547623))))))))) / (0.607771387771 + (z * 11.9400905721)))
	else:
		tmp = x + ((y * ((((457.9610022158428 + (t + (a / z))) / z) - 36.52704169880642) / z)) + (y * 3.13060547623))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -13.0)
		tmp = Float64(x + Float64(Float64(y * 3.13060547623) + Float64(y * Float64(Float64(Float64(Float64(Float64(t + 457.9610022158428) + Float64(Float64(Float64(a - 5864.8025282699045) - Float64(t * 15.234687407)) / z)) / z) - 36.52704169880642) / z))));
	elseif (z <= 1.05)
		tmp = Float64(x + Float64(Float64(Float64(y * b) + Float64(y * Float64(z * Float64(a + Float64(z * Float64(t + Float64(z * Float64(11.1667541262 + Float64(z * 3.13060547623))))))))) / Float64(0.607771387771 + Float64(z * 11.9400905721))));
	else
		tmp = Float64(x + Float64(Float64(y * Float64(Float64(Float64(Float64(457.9610022158428 + Float64(t + Float64(a / z))) / z) - 36.52704169880642) / z)) + Float64(y * 3.13060547623)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -13.0)
		tmp = x + ((y * 3.13060547623) + (y * (((((t + 457.9610022158428) + (((a - 5864.8025282699045) - (t * 15.234687407)) / z)) / z) - 36.52704169880642) / z)));
	elseif (z <= 1.05)
		tmp = x + (((y * b) + (y * (z * (a + (z * (t + (z * (11.1667541262 + (z * 3.13060547623))))))))) / (0.607771387771 + (z * 11.9400905721)));
	else
		tmp = x + ((y * ((((457.9610022158428 + (t + (a / z))) / z) - 36.52704169880642) / z)) + (y * 3.13060547623));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -13.0], N[(x + N[(N[(y * 3.13060547623), $MachinePrecision] + N[(y * N[(N[(N[(N[(N[(t + 457.9610022158428), $MachinePrecision] + N[(N[(N[(a - 5864.8025282699045), $MachinePrecision] - N[(t * 15.234687407), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] - 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.05], N[(x + N[(N[(N[(y * b), $MachinePrecision] + N[(y * N[(z * N[(a + N[(z * N[(t + N[(z * N[(11.1667541262 + N[(z * 3.13060547623), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(0.607771387771 + N[(z * 11.9400905721), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * N[(N[(N[(N[(457.9610022158428 + N[(t + N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] - 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -13

   1. Initial program 19.4%

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

   3. Taylor expanded in z around -inf 75.3%

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

   4. Taylor expanded in y around 0 96.5%

      \[\leadsto x + \left(-1 \cdot \color{blue}{\frac{y \cdot \left(36.52704169880642 + -1 \cdot \frac{457.9610022158428 + \left(t + -1 \cdot \frac{-1 \cdot a - \left(1112.0901850848957 + -15.234687407 \cdot \left(457.9610022158428 + t\right)\right)}{z}\right)}{z}\right)}{z}} + 3.13060547623 \cdot y\right) \]

   6. Simplified 96.5%

      \[\leadsto x + \left(-1 \cdot \color{blue}{\frac{y \cdot \left(36.52704169880642 + \left(-\frac{457.9610022158428 + \left(t + \left(-\frac{\left(-a\right) - \left(1112.0901850848957 + \left(-6976.8927133548 + -15.234687407 \cdot t\right)\right)}{z}\right)\right)}{z}\right)\right)}{z}} + 3.13060547623 \cdot y\right) \]

   8. Applied egg-rr 97.9%

      \[\leadsto x + \left(-1 \cdot \color{blue}{\left(y \cdot \frac{36.52704169880642 - \frac{457.9610022158428 + \left(t - \frac{\left(-a\right) - \left(-5864.8025282699045 + t \cdot -15.234687407\right)}{z}\right)}{z}}{z}\right)} + 3.13060547623 \cdot y\right) \]

   10. Simplified 97.9%

       \[\leadsto x + \left(-1 \cdot \color{blue}{\left(y \cdot \frac{36.52704169880642 - \frac{\left(t + 457.9610022158428\right) - \frac{\left(5864.8025282699045 - a\right) + 15.234687407 \cdot t}{z}}{z}}{z}\right)} + 3.13060547623 \cdot y\right) \]

   if -13 < z < 1.05000000000000004

   1. Initial program 99.0%

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

   3. Taylor expanded in b around 0 99.0%

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

   4. Taylor expanded in z around 0 98.4%

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

      1. *-commutative 98.4%

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

   6. Simplified 98.4%

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

   if 1.05000000000000004 < z

   1. Initial program 14.3%

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

   3. Taylor expanded in z around -inf 63.3%

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

   4. Taylor expanded in y around 0 89.7%

      \[\leadsto x + \left(-1 \cdot \color{blue}{\frac{y \cdot \left(36.52704169880642 + -1 \cdot \frac{457.9610022158428 + \left(t + -1 \cdot \frac{-1 \cdot a - \left(1112.0901850848957 + -15.234687407 \cdot \left(457.9610022158428 + t\right)\right)}{z}\right)}{z}\right)}{z}} + 3.13060547623 \cdot y\right) \]

   6. Simplified 89.7%

      \[\leadsto x + \left(-1 \cdot \color{blue}{\frac{y \cdot \left(36.52704169880642 + \left(-\frac{457.9610022158428 + \left(t + \left(-\frac{\left(-a\right) - \left(1112.0901850848957 + \left(-6976.8927133548 + -15.234687407 \cdot t\right)\right)}{z}\right)\right)}{z}\right)\right)}{z}} + 3.13060547623 \cdot y\right) \]

   7. Taylor expanded in a around inf 89.7%

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

      1. mul-1-neg 89.7%

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

      2. distribute-frac-neg 89.7%

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

   9. Simplified 89.7%

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

       1. associate-/l* 95.7%

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

       2. unsub-neg 95.7%

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

       3. unsub-neg 95.7%

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

   11. Applied egg-rr 95.7%

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

       1. distribute-frac-neg 95.7%

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

       2. mul-1-neg 95.7%

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

       3. cancel-sign-sub-inv 95.7%

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

       4. metadata-eval 95.7%

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

       5. *-lft-identity 95.7%

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

   13. Simplified 95.7%

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

4. Final simplification 97.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -13:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 + y \cdot \frac{\frac{\left(t + 457.9610022158428\right) + \frac{\left(a - 5864.8025282699045\right) - t \cdot 15.234687407}{z}}{z} - 36.52704169880642}{z}\right)\\ \mathbf{elif}\;z \leq 1.05:\\ \;\;\;\;x + \frac{y \cdot b + y \cdot \left(z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\right)\right)\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot \frac{\frac{457.9610022158428 + \left(t + \frac{a}{z}\right)}{z} - 36.52704169880642}{z} + y \cdot 3.13060547623\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 97.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -13 \lor \neg \left(z \leq 1.05\right):\\ \;\;\;\;x + \left(y \cdot \frac{\frac{457.9610022158428 + \left(t + \frac{a}{z}\right)}{z} - 36.52704169880642}{z} + y \cdot 3.13060547623\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\right)\right)\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -13.0) (not (<= z 1.05)))
   (+
    x
    (+
     (*
      y
      (/ (- (/ (+ 457.9610022158428 (+ t (/ a z))) z) 36.52704169880642) z))
     (* y 3.13060547623)))
   (+
    x
    (/
     (*
      y
      (+
       b
       (* z (+ a (* z (+ t (* z (+ 11.1667541262 (* z 3.13060547623)))))))))
     (+ 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 <= 1.05)) {
		tmp = x + ((y * ((((457.9610022158428 + (t + (a / z))) / z) - 36.52704169880642) / z)) + (y * 3.13060547623));
	} else {
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * (11.1667541262 + (z * 3.13060547623))))))))) / (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 <= 1.05d0))) then
        tmp = x + ((y * ((((457.9610022158428d0 + (t + (a / z))) / z) - 36.52704169880642d0) / z)) + (y * 3.13060547623d0))
    else
        tmp = x + ((y * (b + (z * (a + (z * (t + (z * (11.1667541262d0 + (z * 3.13060547623d0))))))))) / (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 <= 1.05)) {
		tmp = x + ((y * ((((457.9610022158428 + (t + (a / z))) / z) - 36.52704169880642) / z)) + (y * 3.13060547623));
	} else {
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * (11.1667541262 + (z * 3.13060547623))))))))) / (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 <= 1.05):
		tmp = x + ((y * ((((457.9610022158428 + (t + (a / z))) / z) - 36.52704169880642) / z)) + (y * 3.13060547623))
	else:
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * (11.1667541262 + (z * 3.13060547623))))))))) / (0.607771387771 + (z * 11.9400905721)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -13.0) || !(z <= 1.05))
		tmp = Float64(x + Float64(Float64(y * Float64(Float64(Float64(Float64(457.9610022158428 + Float64(t + Float64(a / z))) / z) - 36.52704169880642) / z)) + Float64(y * 3.13060547623)));
	else
		tmp = Float64(x + Float64(Float64(y * Float64(b + Float64(z * Float64(a + Float64(z * Float64(t + Float64(z * Float64(11.1667541262 + Float64(z * 3.13060547623))))))))) / 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 <= 1.05)))
		tmp = x + ((y * ((((457.9610022158428 + (t + (a / z))) / z) - 36.52704169880642) / z)) + (y * 3.13060547623));
	else
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * (11.1667541262 + (z * 3.13060547623))))))))) / (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, 1.05]], $MachinePrecision]], N[(x + N[(N[(y * N[(N[(N[(N[(457.9610022158428 + N[(t + N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] - 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * N[(b + N[(z * N[(a + N[(z * N[(t + N[(z * N[(11.1667541262 + N[(z * 3.13060547623), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(0.607771387771 + N[(z * 11.9400905721), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -13 or 1.05000000000000004 < z

   1. Initial program 16.9%

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

   3. Taylor expanded in z around -inf 69.4%

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

   4. Taylor expanded in y around 0 93.2%

      \[\leadsto x + \left(-1 \cdot \color{blue}{\frac{y \cdot \left(36.52704169880642 + -1 \cdot \frac{457.9610022158428 + \left(t + -1 \cdot \frac{-1 \cdot a - \left(1112.0901850848957 + -15.234687407 \cdot \left(457.9610022158428 + t\right)\right)}{z}\right)}{z}\right)}{z}} + 3.13060547623 \cdot y\right) \]

   6. Simplified 93.2%

      \[\leadsto x + \left(-1 \cdot \color{blue}{\frac{y \cdot \left(36.52704169880642 + \left(-\frac{457.9610022158428 + \left(t + \left(-\frac{\left(-a\right) - \left(1112.0901850848957 + \left(-6976.8927133548 + -15.234687407 \cdot t\right)\right)}{z}\right)\right)}{z}\right)\right)}{z}} + 3.13060547623 \cdot y\right) \]

   7. Taylor expanded in a around inf 93.0%

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

      1. mul-1-neg 93.0%

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

      2. distribute-frac-neg 93.0%

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

   9. Simplified 93.0%

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

       1. associate-/l* 96.7%

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

       2. unsub-neg 96.7%

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

       3. unsub-neg 96.7%

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

   11. Applied egg-rr 96.7%

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

       1. distribute-frac-neg 96.7%

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

       2. mul-1-neg 96.7%

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

       3. cancel-sign-sub-inv 96.7%

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

       4. metadata-eval 96.7%

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

       5. *-lft-identity 96.7%

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

   13. Simplified 96.7%

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

   if -13 < z < 1.05000000000000004

   1. Initial program 99.0%

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

   3. Taylor expanded in z around 0 98.4%

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

      1. *-commutative 98.4%

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

   5. Simplified 98.4%

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

4. Final simplification 97.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -13 \lor \neg \left(z \leq 1.05\right):\\ \;\;\;\;x + \left(y \cdot \frac{\frac{457.9610022158428 + \left(t + \frac{a}{z}\right)}{z} - 36.52704169880642}{z} + y \cdot 3.13060547623\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\right)\right)\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 97.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -13:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 + y \cdot \frac{\frac{\left(t + 457.9610022158428\right) + \frac{\left(a - 5864.8025282699045\right) - t \cdot 15.234687407}{z}}{z} - 36.52704169880642}{z}\right)\\ \mathbf{elif}\;z \leq 1.05:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\right)\right)\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot \frac{\frac{457.9610022158428 + \left(t + \frac{a}{z}\right)}{z} - 36.52704169880642}{z} + y \cdot 3.13060547623\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -13.0)
   (+
    x
    (+
     (* y 3.13060547623)
     (*
      y
      (/
       (-
        (/
         (+
          (+ t 457.9610022158428)
          (/ (- (- a 5864.8025282699045) (* t 15.234687407)) z))
         z)
        36.52704169880642)
       z))))
   (if (<= z 1.05)
     (+
      x
      (/
       (*
        y
        (+
         b
         (* z (+ a (* z (+ t (* z (+ 11.1667541262 (* z 3.13060547623)))))))))
       (+ 0.607771387771 (* z 11.9400905721))))
     (+
      x
      (+
       (*
        y
        (/ (- (/ (+ 457.9610022158428 (+ t (/ a z))) z) 36.52704169880642) z))
       (* y 3.13060547623))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -13.0) {
		tmp = x + ((y * 3.13060547623) + (y * (((((t + 457.9610022158428) + (((a - 5864.8025282699045) - (t * 15.234687407)) / z)) / z) - 36.52704169880642) / z)));
	} else if (z <= 1.05) {
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * (11.1667541262 + (z * 3.13060547623))))))))) / (0.607771387771 + (z * 11.9400905721)));
	} else {
		tmp = x + ((y * ((((457.9610022158428 + (t + (a / z))) / z) - 36.52704169880642) / z)) + (y * 3.13060547623));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-13.0d0)) then
        tmp = x + ((y * 3.13060547623d0) + (y * (((((t + 457.9610022158428d0) + (((a - 5864.8025282699045d0) - (t * 15.234687407d0)) / z)) / z) - 36.52704169880642d0) / z)))
    else if (z <= 1.05d0) then
        tmp = x + ((y * (b + (z * (a + (z * (t + (z * (11.1667541262d0 + (z * 3.13060547623d0))))))))) / (0.607771387771d0 + (z * 11.9400905721d0)))
    else
        tmp = x + ((y * ((((457.9610022158428d0 + (t + (a / z))) / z) - 36.52704169880642d0) / z)) + (y * 3.13060547623d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -13.0) {
		tmp = x + ((y * 3.13060547623) + (y * (((((t + 457.9610022158428) + (((a - 5864.8025282699045) - (t * 15.234687407)) / z)) / z) - 36.52704169880642) / z)));
	} else if (z <= 1.05) {
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * (11.1667541262 + (z * 3.13060547623))))))))) / (0.607771387771 + (z * 11.9400905721)));
	} else {
		tmp = x + ((y * ((((457.9610022158428 + (t + (a / z))) / z) - 36.52704169880642) / z)) + (y * 3.13060547623));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -13.0:
		tmp = x + ((y * 3.13060547623) + (y * (((((t + 457.9610022158428) + (((a - 5864.8025282699045) - (t * 15.234687407)) / z)) / z) - 36.52704169880642) / z)))
	elif z <= 1.05:
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * (11.1667541262 + (z * 3.13060547623))))))))) / (0.607771387771 + (z * 11.9400905721)))
	else:
		tmp = x + ((y * ((((457.9610022158428 + (t + (a / z))) / z) - 36.52704169880642) / z)) + (y * 3.13060547623))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -13.0)
		tmp = Float64(x + Float64(Float64(y * 3.13060547623) + Float64(y * Float64(Float64(Float64(Float64(Float64(t + 457.9610022158428) + Float64(Float64(Float64(a - 5864.8025282699045) - Float64(t * 15.234687407)) / z)) / z) - 36.52704169880642) / z))));
	elseif (z <= 1.05)
		tmp = Float64(x + Float64(Float64(y * Float64(b + Float64(z * Float64(a + Float64(z * Float64(t + Float64(z * Float64(11.1667541262 + Float64(z * 3.13060547623))))))))) / Float64(0.607771387771 + Float64(z * 11.9400905721))));
	else
		tmp = Float64(x + Float64(Float64(y * Float64(Float64(Float64(Float64(457.9610022158428 + Float64(t + Float64(a / z))) / z) - 36.52704169880642) / z)) + Float64(y * 3.13060547623)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -13.0)
		tmp = x + ((y * 3.13060547623) + (y * (((((t + 457.9610022158428) + (((a - 5864.8025282699045) - (t * 15.234687407)) / z)) / z) - 36.52704169880642) / z)));
	elseif (z <= 1.05)
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * (11.1667541262 + (z * 3.13060547623))))))))) / (0.607771387771 + (z * 11.9400905721)));
	else
		tmp = x + ((y * ((((457.9610022158428 + (t + (a / z))) / z) - 36.52704169880642) / z)) + (y * 3.13060547623));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -13.0], N[(x + N[(N[(y * 3.13060547623), $MachinePrecision] + N[(y * N[(N[(N[(N[(N[(t + 457.9610022158428), $MachinePrecision] + N[(N[(N[(a - 5864.8025282699045), $MachinePrecision] - N[(t * 15.234687407), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] - 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.05], N[(x + N[(N[(y * N[(b + N[(z * N[(a + N[(z * N[(t + N[(z * N[(11.1667541262 + N[(z * 3.13060547623), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(0.607771387771 + N[(z * 11.9400905721), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * N[(N[(N[(N[(457.9610022158428 + N[(t + N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] - 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -13

   1. Initial program 19.4%

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

   3. Taylor expanded in z around -inf 75.3%

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

   4. Taylor expanded in y around 0 96.5%

      \[\leadsto x + \left(-1 \cdot \color{blue}{\frac{y \cdot \left(36.52704169880642 + -1 \cdot \frac{457.9610022158428 + \left(t + -1 \cdot \frac{-1 \cdot a - \left(1112.0901850848957 + -15.234687407 \cdot \left(457.9610022158428 + t\right)\right)}{z}\right)}{z}\right)}{z}} + 3.13060547623 \cdot y\right) \]

   6. Simplified 96.5%

      \[\leadsto x + \left(-1 \cdot \color{blue}{\frac{y \cdot \left(36.52704169880642 + \left(-\frac{457.9610022158428 + \left(t + \left(-\frac{\left(-a\right) - \left(1112.0901850848957 + \left(-6976.8927133548 + -15.234687407 \cdot t\right)\right)}{z}\right)\right)}{z}\right)\right)}{z}} + 3.13060547623 \cdot y\right) \]

   8. Applied egg-rr 97.9%

      \[\leadsto x + \left(-1 \cdot \color{blue}{\left(y \cdot \frac{36.52704169880642 - \frac{457.9610022158428 + \left(t - \frac{\left(-a\right) - \left(-5864.8025282699045 + t \cdot -15.234687407\right)}{z}\right)}{z}}{z}\right)} + 3.13060547623 \cdot y\right) \]

   10. Simplified 97.9%

       \[\leadsto x + \left(-1 \cdot \color{blue}{\left(y \cdot \frac{36.52704169880642 - \frac{\left(t + 457.9610022158428\right) - \frac{\left(5864.8025282699045 - a\right) + 15.234687407 \cdot t}{z}}{z}}{z}\right)} + 3.13060547623 \cdot y\right) \]

   if -13 < z < 1.05000000000000004

   1. Initial program 99.0%

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

   3. Taylor expanded in z around 0 98.4%

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

      1. *-commutative 98.4%

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

   5. Simplified 98.4%

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

   if 1.05000000000000004 < z

   1. Initial program 14.3%

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

   3. Taylor expanded in z around -inf 63.3%

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

   4. Taylor expanded in y around 0 89.7%

      \[\leadsto x + \left(-1 \cdot \color{blue}{\frac{y \cdot \left(36.52704169880642 + -1 \cdot \frac{457.9610022158428 + \left(t + -1 \cdot \frac{-1 \cdot a - \left(1112.0901850848957 + -15.234687407 \cdot \left(457.9610022158428 + t\right)\right)}{z}\right)}{z}\right)}{z}} + 3.13060547623 \cdot y\right) \]

   6. Simplified 89.7%

      \[\leadsto x + \left(-1 \cdot \color{blue}{\frac{y \cdot \left(36.52704169880642 + \left(-\frac{457.9610022158428 + \left(t + \left(-\frac{\left(-a\right) - \left(1112.0901850848957 + \left(-6976.8927133548 + -15.234687407 \cdot t\right)\right)}{z}\right)\right)}{z}\right)\right)}{z}} + 3.13060547623 \cdot y\right) \]

   7. Taylor expanded in a around inf 89.7%

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

      1. mul-1-neg 89.7%

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

      2. distribute-frac-neg 89.7%

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

   9. Simplified 89.7%

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

       1. associate-/l* 95.7%

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

       2. unsub-neg 95.7%

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

       3. unsub-neg 95.7%

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

   11. Applied egg-rr 95.7%

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

       1. distribute-frac-neg 95.7%

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

       2. mul-1-neg 95.7%

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

       3. cancel-sign-sub-inv 95.7%

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

       4. metadata-eval 95.7%

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

       5. *-lft-identity 95.7%

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

   13. Simplified 95.7%

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

4. Final simplification 97.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -13:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 + y \cdot \frac{\frac{\left(t + 457.9610022158428\right) + \frac{\left(a - 5864.8025282699045\right) - t \cdot 15.234687407}{z}}{z} - 36.52704169880642}{z}\right)\\ \mathbf{elif}\;z \leq 1.05:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\right)\right)\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot \frac{\frac{457.9610022158428 + \left(t + \frac{a}{z}\right)}{z} - 36.52704169880642}{z} + y \cdot 3.13060547623\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 94.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -140000000 \lor \neg \left(z \leq 4.1 \cdot 10^{+36}\right):\\ \;\;\;\;x + \left(y \cdot \frac{\frac{457.9610022158428 + \left(t + \frac{a}{z}\right)}{z} - 36.52704169880642}{z} + y \cdot 3.13060547623\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot a\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -140000000.0) (not (<= z 4.1e+36)))
   (+
    x
    (+
     (*
      y
      (/ (- (/ (+ 457.9610022158428 (+ t (/ a z))) z) 36.52704169880642) z))
     (* y 3.13060547623)))
   (+
    x
    (/
     (* y (+ b (* z a)))
     (+
      (* z (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721))
      0.607771387771)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -140000000.0) || !(z <= 4.1e+36)) {
		tmp = x + ((y * ((((457.9610022158428 + (t + (a / z))) / z) - 36.52704169880642) / z)) + (y * 3.13060547623));
	} else {
		tmp = x + ((y * (b + (z * a))) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-140000000.0d0)) .or. (.not. (z <= 4.1d+36))) then
        tmp = x + ((y * ((((457.9610022158428d0 + (t + (a / z))) / z) - 36.52704169880642d0) / z)) + (y * 3.13060547623d0))
    else
        tmp = x + ((y * (b + (z * a))) / ((z * ((z * ((z * (z + 15.234687407d0)) + 31.4690115749d0)) + 11.9400905721d0)) + 0.607771387771d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -140000000.0) || !(z <= 4.1e+36)) {
		tmp = x + ((y * ((((457.9610022158428 + (t + (a / z))) / z) - 36.52704169880642) / z)) + (y * 3.13060547623));
	} else {
		tmp = x + ((y * (b + (z * a))) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -140000000.0) or not (z <= 4.1e+36):
		tmp = x + ((y * ((((457.9610022158428 + (t + (a / z))) / z) - 36.52704169880642) / z)) + (y * 3.13060547623))
	else:
		tmp = x + ((y * (b + (z * a))) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -140000000.0) || !(z <= 4.1e+36))
		tmp = Float64(x + Float64(Float64(y * Float64(Float64(Float64(Float64(457.9610022158428 + Float64(t + Float64(a / z))) / z) - 36.52704169880642) / z)) + Float64(y * 3.13060547623)));
	else
		tmp = Float64(x + Float64(Float64(y * Float64(b + Float64(z * a))) / Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -140000000.0) || ~((z <= 4.1e+36)))
		tmp = x + ((y * ((((457.9610022158428 + (t + (a / z))) / z) - 36.52704169880642) / z)) + (y * 3.13060547623));
	else
		tmp = x + ((y * (b + (z * a))) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -140000000.0], N[Not[LessEqual[z, 4.1e+36]], $MachinePrecision]], N[(x + N[(N[(y * N[(N[(N[(N[(457.9610022158428 + N[(t + N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] - 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * N[(b + N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(z * N[(N[(z * N[(N[(z * N[(z + 15.234687407), $MachinePrecision]), $MachinePrecision] + 31.4690115749), $MachinePrecision]), $MachinePrecision] + 11.9400905721), $MachinePrecision]), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.4e8 or 4.10000000000000013e36 < z

   1. Initial program 13.0%

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

   3. Taylor expanded in z around -inf 69.9%

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

   4. Taylor expanded in y around 0 95.0%

      \[\leadsto x + \left(-1 \cdot \color{blue}{\frac{y \cdot \left(36.52704169880642 + -1 \cdot \frac{457.9610022158428 + \left(t + -1 \cdot \frac{-1 \cdot a - \left(1112.0901850848957 + -15.234687407 \cdot \left(457.9610022158428 + t\right)\right)}{z}\right)}{z}\right)}{z}} + 3.13060547623 \cdot y\right) \]

   6. Simplified 95.0%

      \[\leadsto x + \left(-1 \cdot \color{blue}{\frac{y \cdot \left(36.52704169880642 + \left(-\frac{457.9610022158428 + \left(t + \left(-\frac{\left(-a\right) - \left(1112.0901850848957 + \left(-6976.8927133548 + -15.234687407 \cdot t\right)\right)}{z}\right)\right)}{z}\right)\right)}{z}} + 3.13060547623 \cdot y\right) \]

   7. Taylor expanded in a around inf 94.9%

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

      1. mul-1-neg 94.9%

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

      2. distribute-frac-neg 94.9%

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

   9. Simplified 94.9%

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

       1. associate-/l* 98.7%

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

       2. unsub-neg 98.7%

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

       3. unsub-neg 98.7%

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

   11. Applied egg-rr 98.7%

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

       1. distribute-frac-neg 98.7%

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

       2. mul-1-neg 98.7%

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

       3. cancel-sign-sub-inv 98.7%

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

       4. metadata-eval 98.7%

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

       5. *-lft-identity 98.7%

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

   13. Simplified 98.7%

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

   if -1.4e8 < z < 4.10000000000000013e36

   1. Initial program 98.3%

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

   3. Taylor expanded in b around 0 98.3%

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

   4. Taylor expanded in z around 0 90.4%

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

      1. associate-*r* 82.6%

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

      2. *-commutative 82.6%

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

      3. associate-*l* 90.5%

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

   6. Simplified 90.5%

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

   7. Taylor expanded in b around 0 90.4%

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

      1. +-commutative 90.4%

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

      2. *-commutative 90.4%

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

      3. associate-*r* 82.6%

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

      4. *-commutative 82.6%

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

      5. associate-*r* 90.5%

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

      6. distribute-lft-in 91.2%

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

   9. Simplified 91.2%

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

4. Final simplification 94.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -140000000 \lor \neg \left(z \leq 4.1 \cdot 10^{+36}\right):\\ \;\;\;\;x + \left(y \cdot \frac{\frac{457.9610022158428 + \left(t + \frac{a}{z}\right)}{z} - 36.52704169880642}{z} + y \cdot 3.13060547623\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot a\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 94.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -260000 \lor \neg \left(z \leq 0.0036\right):\\ \;\;\;\;x + \left(y \cdot \frac{\frac{457.9610022158428 + \left(t + \frac{a}{z}\right)}{z} - 36.52704169880642}{z} + y \cdot 3.13060547623\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998 + \left(z \cdot a\right) \cdot 1.6453555072203998\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -260000.0) (not (<= z 0.0036)))
   (+
    x
    (+
     (*
      y
      (/ (- (/ (+ 457.9610022158428 (+ t (/ a z))) z) 36.52704169880642) z))
     (* y 3.13060547623)))
   (+ x (* y (+ (* b 1.6453555072203998) (* (* z a) 1.6453555072203998))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -260000.0) || !(z <= 0.0036)) {
		tmp = x + ((y * ((((457.9610022158428 + (t + (a / z))) / z) - 36.52704169880642) / z)) + (y * 3.13060547623));
	} else {
		tmp = x + (y * ((b * 1.6453555072203998) + ((z * a) * 1.6453555072203998)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-260000.0d0)) .or. (.not. (z <= 0.0036d0))) then
        tmp = x + ((y * ((((457.9610022158428d0 + (t + (a / z))) / z) - 36.52704169880642d0) / z)) + (y * 3.13060547623d0))
    else
        tmp = x + (y * ((b * 1.6453555072203998d0) + ((z * a) * 1.6453555072203998d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -260000.0) || !(z <= 0.0036)) {
		tmp = x + ((y * ((((457.9610022158428 + (t + (a / z))) / z) - 36.52704169880642) / z)) + (y * 3.13060547623));
	} else {
		tmp = x + (y * ((b * 1.6453555072203998) + ((z * a) * 1.6453555072203998)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -260000.0) or not (z <= 0.0036):
		tmp = x + ((y * ((((457.9610022158428 + (t + (a / z))) / z) - 36.52704169880642) / z)) + (y * 3.13060547623))
	else:
		tmp = x + (y * ((b * 1.6453555072203998) + ((z * a) * 1.6453555072203998)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -260000.0) || !(z <= 0.0036))
		tmp = Float64(x + Float64(Float64(y * Float64(Float64(Float64(Float64(457.9610022158428 + Float64(t + Float64(a / z))) / z) - 36.52704169880642) / z)) + Float64(y * 3.13060547623)));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(b * 1.6453555072203998) + Float64(Float64(z * a) * 1.6453555072203998))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -260000.0) || ~((z <= 0.0036)))
		tmp = x + ((y * ((((457.9610022158428 + (t + (a / z))) / z) - 36.52704169880642) / z)) + (y * 3.13060547623));
	else
		tmp = x + (y * ((b * 1.6453555072203998) + ((z * a) * 1.6453555072203998)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -260000.0], N[Not[LessEqual[z, 0.0036]], $MachinePrecision]], N[(x + N[(N[(y * N[(N[(N[(N[(457.9610022158428 + N[(t + N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] - 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(b * 1.6453555072203998), $MachinePrecision] + N[(N[(z * a), $MachinePrecision] * 1.6453555072203998), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.6e5 or 0.0035999999999999999 < z

   1. Initial program 16.3%

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

   3. Taylor expanded in z around -inf 69.9%

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

   4. Taylor expanded in y around 0 93.8%

      \[\leadsto x + \left(-1 \cdot \color{blue}{\frac{y \cdot \left(36.52704169880642 + -1 \cdot \frac{457.9610022158428 + \left(t + -1 \cdot \frac{-1 \cdot a - \left(1112.0901850848957 + -15.234687407 \cdot \left(457.9610022158428 + t\right)\right)}{z}\right)}{z}\right)}{z}} + 3.13060547623 \cdot y\right) \]

   6. Simplified 93.8%

      \[\leadsto x + \left(-1 \cdot \color{blue}{\frac{y \cdot \left(36.52704169880642 + \left(-\frac{457.9610022158428 + \left(t + \left(-\frac{\left(-a\right) - \left(1112.0901850848957 + \left(-6976.8927133548 + -15.234687407 \cdot t\right)\right)}{z}\right)\right)}{z}\right)\right)}{z}} + 3.13060547623 \cdot y\right) \]

   7. Taylor expanded in a around inf 93.7%

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

      1. mul-1-neg 93.7%

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

      2. distribute-frac-neg 93.7%

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

   9. Simplified 93.7%

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

       1. associate-/l* 97.4%

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

       2. unsub-neg 97.4%

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

       3. unsub-neg 97.4%

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

   11. Applied egg-rr 97.4%

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

       1. distribute-frac-neg 97.4%

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

       2. mul-1-neg 97.4%

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

       3. cancel-sign-sub-inv 97.4%

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

       4. metadata-eval 97.4%

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

       5. *-lft-identity 97.4%

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

   13. Simplified 97.4%

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

   if -2.6e5 < z < 0.0035999999999999999

   1. Initial program 99.0%

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

   3. Taylor expanded in z around 0 76.1%

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

   4. Taylor expanded in a around inf 81.1%

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

      1. *-commutative 81.1%

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

      2. associate-*r* 81.1%

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

      3. *-commutative 81.1%

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

   6. Simplified 81.1%

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

   7. Taylor expanded in y around 0 90.1%

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

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -260000 \lor \neg \left(z \leq 0.0036\right):\\ \;\;\;\;x + \left(y \cdot \frac{\frac{457.9610022158428 + \left(t + \frac{a}{z}\right)}{z} - 36.52704169880642}{z} + y \cdot 3.13060547623\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998 + \left(z \cdot a\right) \cdot 1.6453555072203998\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 91.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2800000:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 + \frac{y \cdot \frac{t + 457.9610022158428}{z} - y \cdot 36.52704169880642}{z}\right)\\ \mathbf{elif}\;z \leq 1.05:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998 + \left(z \cdot a\right) \cdot 1.6453555072203998\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 - \frac{y \cdot \left(36.52704169880642 - \frac{457.9610022158428 + \frac{a}{z}}{z}\right)}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -2800000.0)
   (+
    x
    (+
     (* y 3.13060547623)
     (/ (- (* y (/ (+ t 457.9610022158428) z)) (* y 36.52704169880642)) z)))
   (if (<= z 1.05)
     (+ x (* y (+ (* b 1.6453555072203998) (* (* z a) 1.6453555072203998))))
     (+
      x
      (-
       (* y 3.13060547623)
       (/
        (* y (- 36.52704169880642 (/ (+ 457.9610022158428 (/ a z)) z)))
        z))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2800000.0) {
		tmp = x + ((y * 3.13060547623) + (((y * ((t + 457.9610022158428) / z)) - (y * 36.52704169880642)) / z));
	} else if (z <= 1.05) {
		tmp = x + (y * ((b * 1.6453555072203998) + ((z * a) * 1.6453555072203998)));
	} else {
		tmp = x + ((y * 3.13060547623) - ((y * (36.52704169880642 - ((457.9610022158428 + (a / z)) / z))) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-2800000.0d0)) then
        tmp = x + ((y * 3.13060547623d0) + (((y * ((t + 457.9610022158428d0) / z)) - (y * 36.52704169880642d0)) / z))
    else if (z <= 1.05d0) then
        tmp = x + (y * ((b * 1.6453555072203998d0) + ((z * a) * 1.6453555072203998d0)))
    else
        tmp = x + ((y * 3.13060547623d0) - ((y * (36.52704169880642d0 - ((457.9610022158428d0 + (a / z)) / z))) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2800000.0) {
		tmp = x + ((y * 3.13060547623) + (((y * ((t + 457.9610022158428) / z)) - (y * 36.52704169880642)) / z));
	} else if (z <= 1.05) {
		tmp = x + (y * ((b * 1.6453555072203998) + ((z * a) * 1.6453555072203998)));
	} else {
		tmp = x + ((y * 3.13060547623) - ((y * (36.52704169880642 - ((457.9610022158428 + (a / z)) / z))) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -2800000.0:
		tmp = x + ((y * 3.13060547623) + (((y * ((t + 457.9610022158428) / z)) - (y * 36.52704169880642)) / z))
	elif z <= 1.05:
		tmp = x + (y * ((b * 1.6453555072203998) + ((z * a) * 1.6453555072203998)))
	else:
		tmp = x + ((y * 3.13060547623) - ((y * (36.52704169880642 - ((457.9610022158428 + (a / z)) / z))) / z))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -2800000.0)
		tmp = Float64(x + Float64(Float64(y * 3.13060547623) + Float64(Float64(Float64(y * Float64(Float64(t + 457.9610022158428) / z)) - Float64(y * 36.52704169880642)) / z)));
	elseif (z <= 1.05)
		tmp = Float64(x + Float64(y * Float64(Float64(b * 1.6453555072203998) + Float64(Float64(z * a) * 1.6453555072203998))));
	else
		tmp = Float64(x + Float64(Float64(y * 3.13060547623) - Float64(Float64(y * Float64(36.52704169880642 - Float64(Float64(457.9610022158428 + Float64(a / z)) / z))) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -2800000.0)
		tmp = x + ((y * 3.13060547623) + (((y * ((t + 457.9610022158428) / z)) - (y * 36.52704169880642)) / z));
	elseif (z <= 1.05)
		tmp = x + (y * ((b * 1.6453555072203998) + ((z * a) * 1.6453555072203998)));
	else
		tmp = x + ((y * 3.13060547623) - ((y * (36.52704169880642 - ((457.9610022158428 + (a / z)) / z))) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -2800000.0], N[(x + N[(N[(y * 3.13060547623), $MachinePrecision] + N[(N[(N[(y * N[(N[(t + 457.9610022158428), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] - N[(y * 36.52704169880642), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.05], N[(x + N[(y * N[(N[(b * 1.6453555072203998), $MachinePrecision] + N[(N[(z * a), $MachinePrecision] * 1.6453555072203998), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * 3.13060547623), $MachinePrecision] - N[(N[(y * N[(36.52704169880642 - N[(N[(457.9610022158428 + N[(a / z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.8e6

   1. Initial program 18.3%

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

   3. Taylor expanded in z around -inf 76.3%

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

   4. Taylor expanded in y around 0 97.8%

      \[\leadsto x + \left(-1 \cdot \color{blue}{\frac{y \cdot \left(36.52704169880642 + -1 \cdot \frac{457.9610022158428 + \left(t + -1 \cdot \frac{-1 \cdot a - \left(1112.0901850848957 + -15.234687407 \cdot \left(457.9610022158428 + t\right)\right)}{z}\right)}{z}\right)}{z}} + 3.13060547623 \cdot y\right) \]

   6. Simplified 97.8%

      \[\leadsto x + \left(-1 \cdot \color{blue}{\frac{y \cdot \left(36.52704169880642 + \left(-\frac{457.9610022158428 + \left(t + \left(-\frac{\left(-a\right) - \left(1112.0901850848957 + \left(-6976.8927133548 + -15.234687407 \cdot t\right)\right)}{z}\right)\right)}{z}\right)\right)}{z}} + 3.13060547623 \cdot y\right) \]

   7. Taylor expanded in z around inf 83.3%

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

      1. +-commutative 83.3%

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

      2. mul-1-neg 83.3%

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

      3. unsub-neg 83.3%

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

      4. *-commutative 83.3%

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

      5. associate-/l* 97.5%

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

      6. +-commutative 97.5%

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

   9. Simplified 97.5%

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

   if -2.8e6 < z < 1.05000000000000004

   1. Initial program 99.0%

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

   3. Taylor expanded in z around 0 76.1%

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

   4. Taylor expanded in a around inf 81.1%

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

      1. *-commutative 81.1%

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

      2. associate-*r* 81.1%

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

      3. *-commutative 81.1%

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

   6. Simplified 81.1%

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

   7. Taylor expanded in y around 0 90.1%

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

   if 1.05000000000000004 < z

   1. Initial program 14.3%

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

   3. Taylor expanded in z around -inf 63.3%

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

   4. Taylor expanded in y around 0 89.7%

      \[\leadsto x + \left(-1 \cdot \color{blue}{\frac{y \cdot \left(36.52704169880642 + -1 \cdot \frac{457.9610022158428 + \left(t + -1 \cdot \frac{-1 \cdot a - \left(1112.0901850848957 + -15.234687407 \cdot \left(457.9610022158428 + t\right)\right)}{z}\right)}{z}\right)}{z}} + 3.13060547623 \cdot y\right) \]

   6. Simplified 89.7%

      \[\leadsto x + \left(-1 \cdot \color{blue}{\frac{y \cdot \left(36.52704169880642 + \left(-\frac{457.9610022158428 + \left(t + \left(-\frac{\left(-a\right) - \left(1112.0901850848957 + \left(-6976.8927133548 + -15.234687407 \cdot t\right)\right)}{z}\right)\right)}{z}\right)\right)}{z}} + 3.13060547623 \cdot y\right) \]

   7. Taylor expanded in a around inf 89.7%

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

      1. mul-1-neg 89.7%

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

      2. distribute-frac-neg 89.7%

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

   9. Simplified 89.7%

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

   10. Taylor expanded in t around 0 89.8%

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

       1. sub-neg 89.8%

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

       2. mul-1-neg 89.8%

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

       3. remove-double-neg 89.8%

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

   12. Simplified 89.8%

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

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2800000:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 + \frac{y \cdot \frac{t + 457.9610022158428}{z} - y \cdot 36.52704169880642}{z}\right)\\ \mathbf{elif}\;z \leq 1.05:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998 + \left(z \cdot a\right) \cdot 1.6453555072203998\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 - \frac{y \cdot \left(36.52704169880642 - \frac{457.9610022158428 + \frac{a}{z}}{z}\right)}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 92.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -300000:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 + \frac{y \cdot \frac{t + 457.9610022158428}{z} - y \cdot 36.52704169880642}{z}\right)\\ \mathbf{elif}\;z \leq 0.115:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998 + \left(z \cdot a\right) \cdot 1.6453555072203998\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 + \frac{t \cdot \frac{y}{z}}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -300000.0)
   (+
    x
    (+
     (* y 3.13060547623)
     (/ (- (* y (/ (+ t 457.9610022158428) z)) (* y 36.52704169880642)) z)))
   (if (<= z 0.115)
     (+ x (* y (+ (* b 1.6453555072203998) (* (* z a) 1.6453555072203998))))
     (+ x (+ (* y 3.13060547623) (/ (* t (/ y z)) z))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -300000.0) {
		tmp = x + ((y * 3.13060547623) + (((y * ((t + 457.9610022158428) / z)) - (y * 36.52704169880642)) / z));
	} else if (z <= 0.115) {
		tmp = x + (y * ((b * 1.6453555072203998) + ((z * a) * 1.6453555072203998)));
	} else {
		tmp = x + ((y * 3.13060547623) + ((t * (y / z)) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-300000.0d0)) then
        tmp = x + ((y * 3.13060547623d0) + (((y * ((t + 457.9610022158428d0) / z)) - (y * 36.52704169880642d0)) / z))
    else if (z <= 0.115d0) then
        tmp = x + (y * ((b * 1.6453555072203998d0) + ((z * a) * 1.6453555072203998d0)))
    else
        tmp = x + ((y * 3.13060547623d0) + ((t * (y / z)) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -300000.0) {
		tmp = x + ((y * 3.13060547623) + (((y * ((t + 457.9610022158428) / z)) - (y * 36.52704169880642)) / z));
	} else if (z <= 0.115) {
		tmp = x + (y * ((b * 1.6453555072203998) + ((z * a) * 1.6453555072203998)));
	} else {
		tmp = x + ((y * 3.13060547623) + ((t * (y / z)) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -300000.0:
		tmp = x + ((y * 3.13060547623) + (((y * ((t + 457.9610022158428) / z)) - (y * 36.52704169880642)) / z))
	elif z <= 0.115:
		tmp = x + (y * ((b * 1.6453555072203998) + ((z * a) * 1.6453555072203998)))
	else:
		tmp = x + ((y * 3.13060547623) + ((t * (y / z)) / z))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -300000.0)
		tmp = Float64(x + Float64(Float64(y * 3.13060547623) + Float64(Float64(Float64(y * Float64(Float64(t + 457.9610022158428) / z)) - Float64(y * 36.52704169880642)) / z)));
	elseif (z <= 0.115)
		tmp = Float64(x + Float64(y * Float64(Float64(b * 1.6453555072203998) + Float64(Float64(z * a) * 1.6453555072203998))));
	else
		tmp = Float64(x + Float64(Float64(y * 3.13060547623) + Float64(Float64(t * Float64(y / z)) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -300000.0)
		tmp = x + ((y * 3.13060547623) + (((y * ((t + 457.9610022158428) / z)) - (y * 36.52704169880642)) / z));
	elseif (z <= 0.115)
		tmp = x + (y * ((b * 1.6453555072203998) + ((z * a) * 1.6453555072203998)));
	else
		tmp = x + ((y * 3.13060547623) + ((t * (y / z)) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -300000.0], N[(x + N[(N[(y * 3.13060547623), $MachinePrecision] + N[(N[(N[(y * N[(N[(t + 457.9610022158428), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] - N[(y * 36.52704169880642), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.115], N[(x + N[(y * N[(N[(b * 1.6453555072203998), $MachinePrecision] + N[(N[(z * a), $MachinePrecision] * 1.6453555072203998), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * 3.13060547623), $MachinePrecision] + N[(N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3e5

   1. Initial program 18.3%

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

   3. Taylor expanded in z around -inf 76.3%

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

   4. Taylor expanded in y around 0 97.8%

      \[\leadsto x + \left(-1 \cdot \color{blue}{\frac{y \cdot \left(36.52704169880642 + -1 \cdot \frac{457.9610022158428 + \left(t + -1 \cdot \frac{-1 \cdot a - \left(1112.0901850848957 + -15.234687407 \cdot \left(457.9610022158428 + t\right)\right)}{z}\right)}{z}\right)}{z}} + 3.13060547623 \cdot y\right) \]

   6. Simplified 97.8%

      \[\leadsto x + \left(-1 \cdot \color{blue}{\frac{y \cdot \left(36.52704169880642 + \left(-\frac{457.9610022158428 + \left(t + \left(-\frac{\left(-a\right) - \left(1112.0901850848957 + \left(-6976.8927133548 + -15.234687407 \cdot t\right)\right)}{z}\right)\right)}{z}\right)\right)}{z}} + 3.13060547623 \cdot y\right) \]

   7. Taylor expanded in z around inf 83.3%

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

      1. +-commutative 83.3%

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

      2. mul-1-neg 83.3%

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

      3. unsub-neg 83.3%

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

      4. *-commutative 83.3%

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

      5. associate-/l* 97.5%

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

      6. +-commutative 97.5%

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

   9. Simplified 97.5%

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

   if -3e5 < z < 0.115000000000000005

   1. Initial program 99.0%

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

   3. Taylor expanded in z around 0 76.1%

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

   4. Taylor expanded in a around inf 81.1%

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

      1. *-commutative 81.1%

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

      2. associate-*r* 81.1%

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

      3. *-commutative 81.1%

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

   6. Simplified 81.1%

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

   7. Taylor expanded in y around 0 90.1%

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

   if 0.115000000000000005 < z

   1. Initial program 14.3%

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

   3. Taylor expanded in z around -inf 63.3%

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

   4. Taylor expanded in y around 0 89.7%

      \[\leadsto x + \left(-1 \cdot \color{blue}{\frac{y \cdot \left(36.52704169880642 + -1 \cdot \frac{457.9610022158428 + \left(t + -1 \cdot \frac{-1 \cdot a - \left(1112.0901850848957 + -15.234687407 \cdot \left(457.9610022158428 + t\right)\right)}{z}\right)}{z}\right)}{z}} + 3.13060547623 \cdot y\right) \]

   6. Simplified 89.7%

      \[\leadsto x + \left(-1 \cdot \color{blue}{\frac{y \cdot \left(36.52704169880642 + \left(-\frac{457.9610022158428 + \left(t + \left(-\frac{\left(-a\right) - \left(1112.0901850848957 + \left(-6976.8927133548 + -15.234687407 \cdot t\right)\right)}{z}\right)\right)}{z}\right)\right)}{z}} + 3.13060547623 \cdot y\right) \]

   7. Taylor expanded in a around inf 89.7%

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

      1. mul-1-neg 89.7%

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

      2. distribute-frac-neg 89.7%

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

   9. Simplified 89.7%

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

   10. Taylor expanded in t around inf 75.9%

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

       1. mul-1-neg 75.9%

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

       2. associate-/l* 88.1%

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

       3. distribute-rgt-neg-in 88.1%

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

       4. mul-1-neg 88.1%

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

       5. associate-*r/ 88.1%

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

       6. mul-1-neg 88.1%

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

   12. Simplified 88.1%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -300000:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 + \frac{y \cdot \frac{t + 457.9610022158428}{z} - y \cdot 36.52704169880642}{z}\right)\\ \mathbf{elif}\;z \leq 0.115:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998 + \left(z \cdot a\right) \cdot 1.6453555072203998\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 + \frac{t \cdot \frac{y}{z}}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 89.6% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+55} \lor \neg \left(z \leq 1.05\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998 + \left(z \cdot a\right) \cdot 1.6453555072203998\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.4e+55) (not (<= z 1.05)))
   (+ x (* y 3.13060547623))
   (+ x (* y (+ (* b 1.6453555072203998) (* (* z a) 1.6453555072203998))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.4e+55) || !(z <= 1.05)) {
		tmp = x + (y * 3.13060547623);
	} else {
		tmp = x + (y * ((b * 1.6453555072203998) + ((z * a) * 1.6453555072203998)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-1.4d+55)) .or. (.not. (z <= 1.05d0))) then
        tmp = x + (y * 3.13060547623d0)
    else
        tmp = x + (y * ((b * 1.6453555072203998d0) + ((z * a) * 1.6453555072203998d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.4e+55) || !(z <= 1.05)) {
		tmp = x + (y * 3.13060547623);
	} else {
		tmp = x + (y * ((b * 1.6453555072203998) + ((z * a) * 1.6453555072203998)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.4e+55) or not (z <= 1.05):
		tmp = x + (y * 3.13060547623)
	else:
		tmp = x + (y * ((b * 1.6453555072203998) + ((z * a) * 1.6453555072203998)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.4e+55) || !(z <= 1.05))
		tmp = Float64(x + Float64(y * 3.13060547623));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(b * 1.6453555072203998) + Float64(Float64(z * a) * 1.6453555072203998))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.4e+55) || ~((z <= 1.05)))
		tmp = x + (y * 3.13060547623);
	else
		tmp = x + (y * ((b * 1.6453555072203998) + ((z * a) * 1.6453555072203998)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.4e+55], N[Not[LessEqual[z, 1.05]], $MachinePrecision]], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(b * 1.6453555072203998), $MachinePrecision] + N[(N[(z * a), $MachinePrecision] * 1.6453555072203998), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.4e55 or 1.05000000000000004 < z

   1. Initial program 10.1%

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

   3. Simplified 11.6%

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

   5. Taylor expanded in z around inf 90.3%

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

      1. +-commutative 90.3%

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

      2. *-commutative 90.3%

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

   7. Simplified 90.3%

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

   if -1.4e55 < z < 1.05000000000000004

   1. Initial program 99.0%

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

   3. Taylor expanded in z around 0 75.6%

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

   4. Taylor expanded in a around inf 80.3%

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

      1. *-commutative 80.3%

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

      2. associate-*r* 80.3%

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

      3. *-commutative 80.3%

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

   6. Simplified 80.3%

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

   7. Taylor expanded in y around 0 88.7%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+55} \lor \neg \left(z \leq 1.05\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998 + \left(z \cdot a\right) \cdot 1.6453555072203998\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 92.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2700000000 \lor \neg \left(z \leq 0.34\right):\\ \;\;\;\;x + \left(y \cdot 3.13060547623 + \frac{t \cdot \frac{y}{z}}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998 + \left(z \cdot a\right) \cdot 1.6453555072203998\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2700000000.0) (not (<= z 0.34)))
   (+ x (+ (* y 3.13060547623) (/ (* t (/ y z)) z)))
   (+ x (* y (+ (* b 1.6453555072203998) (* (* z a) 1.6453555072203998))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2700000000.0) || !(z <= 0.34)) {
		tmp = x + ((y * 3.13060547623) + ((t * (y / z)) / z));
	} else {
		tmp = x + (y * ((b * 1.6453555072203998) + ((z * a) * 1.6453555072203998)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-2700000000.0d0)) .or. (.not. (z <= 0.34d0))) then
        tmp = x + ((y * 3.13060547623d0) + ((t * (y / z)) / z))
    else
        tmp = x + (y * ((b * 1.6453555072203998d0) + ((z * a) * 1.6453555072203998d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2700000000.0) || !(z <= 0.34)) {
		tmp = x + ((y * 3.13060547623) + ((t * (y / z)) / z));
	} else {
		tmp = x + (y * ((b * 1.6453555072203998) + ((z * a) * 1.6453555072203998)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -2700000000.0) or not (z <= 0.34):
		tmp = x + ((y * 3.13060547623) + ((t * (y / z)) / z))
	else:
		tmp = x + (y * ((b * 1.6453555072203998) + ((z * a) * 1.6453555072203998)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2700000000.0) || !(z <= 0.34))
		tmp = Float64(x + Float64(Float64(y * 3.13060547623) + Float64(Float64(t * Float64(y / z)) / z)));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(b * 1.6453555072203998) + Float64(Float64(z * a) * 1.6453555072203998))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -2700000000.0) || ~((z <= 0.34)))
		tmp = x + ((y * 3.13060547623) + ((t * (y / z)) / z));
	else
		tmp = x + (y * ((b * 1.6453555072203998) + ((z * a) * 1.6453555072203998)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2700000000.0], N[Not[LessEqual[z, 0.34]], $MachinePrecision]], N[(x + N[(N[(y * 3.13060547623), $MachinePrecision] + N[(N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(b * 1.6453555072203998), $MachinePrecision] + N[(N[(z * a), $MachinePrecision] * 1.6453555072203998), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.7e9 or 0.340000000000000024 < z

   1. Initial program 16.3%

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

   3. Taylor expanded in z around -inf 69.9%

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

   4. Taylor expanded in y around 0 93.8%

      \[\leadsto x + \left(-1 \cdot \color{blue}{\frac{y \cdot \left(36.52704169880642 + -1 \cdot \frac{457.9610022158428 + \left(t + -1 \cdot \frac{-1 \cdot a - \left(1112.0901850848957 + -15.234687407 \cdot \left(457.9610022158428 + t\right)\right)}{z}\right)}{z}\right)}{z}} + 3.13060547623 \cdot y\right) \]

   6. Simplified 93.8%

      \[\leadsto x + \left(-1 \cdot \color{blue}{\frac{y \cdot \left(36.52704169880642 + \left(-\frac{457.9610022158428 + \left(t + \left(-\frac{\left(-a\right) - \left(1112.0901850848957 + \left(-6976.8927133548 + -15.234687407 \cdot t\right)\right)}{z}\right)\right)}{z}\right)\right)}{z}} + 3.13060547623 \cdot y\right) \]

   7. Taylor expanded in a around inf 93.7%

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

      1. mul-1-neg 93.7%

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

      2. distribute-frac-neg 93.7%

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

   9. Simplified 93.7%

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

   10. Taylor expanded in t around inf 79.6%

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

       1. mul-1-neg 79.6%

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

       2. associate-/l* 92.9%

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

       3. distribute-rgt-neg-in 92.9%

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

       4. mul-1-neg 92.9%

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

       5. associate-*r/ 92.9%

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

       6. mul-1-neg 92.9%

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

   12. Simplified 92.9%

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

   if -2.7e9 < z < 0.340000000000000024

   1. Initial program 99.0%

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

   3. Taylor expanded in z around 0 76.1%

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

   4. Taylor expanded in a around inf 81.1%

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

      1. *-commutative 81.1%

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

      2. associate-*r* 81.1%

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

      3. *-commutative 81.1%

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

   6. Simplified 81.1%

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

   7. Taylor expanded in y around 0 90.1%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2700000000 \lor \neg \left(z \leq 0.34\right):\\ \;\;\;\;x + \left(y \cdot 3.13060547623 + \frac{t \cdot \frac{y}{z}}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998 + \left(z \cdot a\right) \cdot 1.6453555072203998\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 89.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+55} \lor \neg \left(z \leq 1.05\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(\left(b + z \cdot a\right) \cdot 1.6453555072203998\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.4e+55) (not (<= z 1.05)))
   (+ x (* y 3.13060547623))
   (+ x (* y (* (+ b (* z a)) 1.6453555072203998)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.4e+55) || !(z <= 1.05)) {
		tmp = x + (y * 3.13060547623);
	} else {
		tmp = x + (y * ((b + (z * a)) * 1.6453555072203998));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-1.4d+55)) .or. (.not. (z <= 1.05d0))) then
        tmp = x + (y * 3.13060547623d0)
    else
        tmp = x + (y * ((b + (z * a)) * 1.6453555072203998d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.4e+55) || !(z <= 1.05)) {
		tmp = x + (y * 3.13060547623);
	} else {
		tmp = x + (y * ((b + (z * a)) * 1.6453555072203998));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.4e+55) or not (z <= 1.05):
		tmp = x + (y * 3.13060547623)
	else:
		tmp = x + (y * ((b + (z * a)) * 1.6453555072203998))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.4e+55) || !(z <= 1.05))
		tmp = Float64(x + Float64(y * 3.13060547623));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(b + Float64(z * a)) * 1.6453555072203998)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.4e+55) || ~((z <= 1.05)))
		tmp = x + (y * 3.13060547623);
	else
		tmp = x + (y * ((b + (z * a)) * 1.6453555072203998));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.4e+55], N[Not[LessEqual[z, 1.05]], $MachinePrecision]], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(b + N[(z * a), $MachinePrecision]), $MachinePrecision] * 1.6453555072203998), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.4e55 or 1.05000000000000004 < z

   1. Initial program 10.1%

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

   3. Simplified 11.6%

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

   5. Taylor expanded in z around inf 90.3%

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

      1. +-commutative 90.3%

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

      2. *-commutative 90.3%

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

   7. Simplified 90.3%

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

   if -1.4e55 < z < 1.05000000000000004

   1. Initial program 99.0%

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

   3. Taylor expanded in z around 0 75.6%

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

   4. Taylor expanded in a around inf 80.3%

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

      1. *-commutative 80.3%

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

      2. associate-*r* 80.3%

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

      3. *-commutative 80.3%

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

   6. Simplified 80.3%

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

   7. Taylor expanded in y around 0 88.7%

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

      1. distribute-lft-out 88.7%

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

      2. *-commutative 88.7%

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

   9. Simplified 88.7%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+55} \lor \neg \left(z \leq 1.05\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(\left(b + z \cdot a\right) \cdot 1.6453555072203998\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 82.7% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+55} \lor \neg \left(z \leq 0.108\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(y \cdot 1.6453555072203998\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.4e+55) (not (<= z 0.108)))
   (+ x (* y 3.13060547623))
   (+ x (* b (* y 1.6453555072203998)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.4e+55) || !(z <= 0.108)) {
		tmp = x + (y * 3.13060547623);
	} else {
		tmp = x + (b * (y * 1.6453555072203998));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-1.4d+55)) .or. (.not. (z <= 0.108d0))) then
        tmp = x + (y * 3.13060547623d0)
    else
        tmp = x + (b * (y * 1.6453555072203998d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.4e+55) || !(z <= 0.108)) {
		tmp = x + (y * 3.13060547623);
	} else {
		tmp = x + (b * (y * 1.6453555072203998));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.4e+55) or not (z <= 0.108):
		tmp = x + (y * 3.13060547623)
	else:
		tmp = x + (b * (y * 1.6453555072203998))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.4e+55) || !(z <= 0.108))
		tmp = Float64(x + Float64(y * 3.13060547623));
	else
		tmp = Float64(x + Float64(b * Float64(y * 1.6453555072203998)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.4e+55) || ~((z <= 0.108)))
		tmp = x + (y * 3.13060547623);
	else
		tmp = x + (b * (y * 1.6453555072203998));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.4e+55], N[Not[LessEqual[z, 0.108]], $MachinePrecision]], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision], N[(x + N[(b * N[(y * 1.6453555072203998), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.4e55 or 0.107999999999999999 < z

   1. Initial program 10.1%

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

   3. Simplified 11.6%

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

   5. Taylor expanded in z around inf 90.3%

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

      1. +-commutative 90.3%

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

      2. *-commutative 90.3%

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

   7. Simplified 90.3%

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

   if -1.4e55 < z < 0.107999999999999999

   1. Initial program 99.0%

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

   3. Taylor expanded in b around 0 99.1%

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

   4. Taylor expanded in z around 0 89.2%

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

      1. associate-*r* 81.6%

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

      2. *-commutative 81.6%

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

      3. associate-*l* 89.3%

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

   6. Simplified 89.3%

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

   7. Taylor expanded in z around 0 76.1%

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

      1. associate-*r* 76.1%

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

      2. *-commutative 76.1%

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

      3. associate-*r* 76.1%

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

      4. *-commutative 76.1%

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

   9. Simplified 76.1%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+55} \lor \neg \left(z \leq 0.108\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(y \cdot 1.6453555072203998\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 65.2% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.3 \cdot 10^{-123} \lor \neg \left(z \leq 4.8 \cdot 10^{-100}\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -5.3e-123) (not (<= z 4.8e-100))) (+ x (* y 3.13060547623)) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -5.3e-123) || !(z <= 4.8e-100)) {
		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 <= (-5.3d-123)) .or. (.not. (z <= 4.8d-100))) 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 <= -5.3e-123) || !(z <= 4.8e-100)) {
		tmp = x + (y * 3.13060547623);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -5.3e-123) or not (z <= 4.8e-100):
		tmp = x + (y * 3.13060547623)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -5.3e-123) || !(z <= 4.8e-100))
		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 <= -5.3e-123) || ~((z <= 4.8e-100)))
		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, -5.3e-123], N[Not[LessEqual[z, 4.8e-100]], $MachinePrecision]], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -5.29999999999999971e-123 or 4.8000000000000005e-100 < z

   1. Initial program 36.8%

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

   3. Simplified 38.4%

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

   5. Taylor expanded in z around inf 72.0%

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

      1. +-commutative 72.0%

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

      2. *-commutative 72.0%

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

   7. Simplified 72.0%

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

   if -5.29999999999999971e-123 < z < 4.8000000000000005e-100

   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 y around 0 49.2%

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

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.3 \cdot 10^{-123} \lor \neg \left(z \leq 4.8 \cdot 10^{-100}\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 45.5% 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 57.0%

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

3. Simplified 58.1%

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

5. Taylor expanded in y around 0 41.3%

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

6. Final simplification 41.3%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 98.4% 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 2024076 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, D"
  :precision binary64

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

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