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

Percentage Accurate: 59.4% → 96.9%

Time: 19.7s

Alternatives: 15

Speedup: 7.4×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 59.4% 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: 96.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+16} \lor \neg \left(z \leq 4.1 \cdot 10^{+51}\right):\\ \;\;\;\;x + \left(y \cdot 3.13060547623 + y \cdot \frac{\frac{t}{z} + -36.52704169880642}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot 11.1667541262\right)\right)\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.5e+16) (not (<= z 4.1e+51)))
   (+ x (+ (* y 3.13060547623) (* y (/ (+ (/ t z) -36.52704169880642) z))))
   (+
    x
    (/
     (* y (+ b (* z (+ a (* z (+ t (* z 11.1667541262)))))))
     (+
      (* z (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721))
      0.607771387771)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.5e+16) || !(z <= 4.1e+51)) {
		tmp = x + ((y * 3.13060547623) + (y * (((t / z) + -36.52704169880642) / z)));
	} else {
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-1.5d+16)) .or. (.not. (z <= 4.1d+51))) then
        tmp = x + ((y * 3.13060547623d0) + (y * (((t / z) + (-36.52704169880642d0)) / z)))
    else
        tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262d0))))))) / ((z * ((z * ((z * (z + 15.234687407d0)) + 31.4690115749d0)) + 11.9400905721d0)) + 0.607771387771d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.5e+16) || !(z <= 4.1e+51)) {
		tmp = x + ((y * 3.13060547623) + (y * (((t / z) + -36.52704169880642) / z)));
	} else {
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.5e+16) or not (z <= 4.1e+51):
		tmp = x + ((y * 3.13060547623) + (y * (((t / z) + -36.52704169880642) / z)))
	else:
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.5e+16) || !(z <= 4.1e+51))
		tmp = Float64(x + Float64(Float64(y * 3.13060547623) + Float64(y * Float64(Float64(Float64(t / z) + -36.52704169880642) / z))));
	else
		tmp = Float64(x + Float64(Float64(y * Float64(b + Float64(z * Float64(a + Float64(z * Float64(t + Float64(z * 11.1667541262))))))) / Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.5e+16) || ~((z <= 4.1e+51)))
		tmp = x + ((y * 3.13060547623) + (y * (((t / z) + -36.52704169880642) / z)));
	else
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.5e+16], N[Not[LessEqual[z, 4.1e+51]], $MachinePrecision]], N[(x + N[(N[(y * 3.13060547623), $MachinePrecision] + N[(y * N[(N[(N[(t / z), $MachinePrecision] + -36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * N[(b + N[(z * N[(a + N[(z * N[(t + N[(z * 11.1667541262), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(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 < -1.5e16 or 4.10000000000000011e51 < z

   1. Initial program 4.5%

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

      1. remove-double-neg 4.5%

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

      2. distribute-lft-neg-out 4.5%

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

   3. Simplified 4.5%

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

   5. Taylor expanded in z around -inf 82.4%

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

   6. Taylor expanded in t around inf 82.4%

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

      1. *-commutative 82.4%

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

   8. Simplified 82.4%

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

   9. Taylor expanded in y around -inf 95.8%

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

       1. associate-/l* 99.1%

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

       2. sub-neg 99.1%

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

       3. metadata-eval 99.1%

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

   11. Simplified 99.1%

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

   if -1.5e16 < z < 4.10000000000000011e51

   1. Initial program 98.5%

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

   3. Taylor expanded in z around 0 98.5%

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

      1. *-commutative 98.5%

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

   5. Simplified 98.5%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+16} \lor \neg \left(z \leq 4.1 \cdot 10^{+51}\right):\\ \;\;\;\;x + \left(y \cdot 3.13060547623 + y \cdot \frac{\frac{t}{z} + -36.52704169880642}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot 11.1667541262\right)\right)\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 97.7% accurate, 0.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(N[(y * N[(N[(z * N[(N[(z * N[(N[(z * N[(N[(z * 3.13060547623), $MachinePrecision] + 11.1667541262), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(N[(z * N[(N[(z * N[(N[(z * N[(z + 15.234687407), $MachinePrecision]), $MachinePrecision] + 31.4690115749), $MachinePrecision]), $MachinePrecision] + 11.9400905721), $MachinePrecision]), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision], Infinity], N[(y * N[(N[(z * N[(z * N[(z * N[(z * 3.13060547623 + 11.1667541262), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision] + b), $MachinePrecision] / N[(z * N[(z * N[(z * N[(z + 15.234687407), $MachinePrecision] + 31.4690115749), $MachinePrecision] + 11.9400905721), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(x + N[(N[(t * N[(y / N[Power[z, 2.0], $MachinePrecision]), $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 95.3%

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

   3. Simplified 96.5%

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

   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. Step-by-step derivation

      1. remove-double-neg 0.0%

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

      2. distribute-lft-neg-out 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in z around -inf 81.6%

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

   6. Taylor expanded in t around inf 81.4%

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

      1. mul-1-neg 81.4%

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

      2. associate-/l* 100.0%

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

      3. distribute-rgt-neg-in 100.0%

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

      4. mul-1-neg 100.0%

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

      5. associate-*r/ 100.0%

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

      6. neg-mul-1 100.0%

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

   8. Simplified 100.0%

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

4. Final simplification 97.9%

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

Alternative 3: 97.2% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z * N[(N[(z * N[(N[(z * N[(z + 15.234687407), $MachinePrecision]), $MachinePrecision] + 31.4690115749), $MachinePrecision]), $MachinePrecision] + 11.9400905721), $MachinePrecision]), $MachinePrecision] + 0.607771387771), $MachinePrecision]}, If[LessEqual[N[(N[(y * N[(N[(z * N[(N[(z * N[(N[(z * N[(N[(z * 3.13060547623), $MachinePrecision] + 11.1667541262), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], Infinity], N[(N[(z * N[(z * N[(z * N[(z * 3.13060547623 + 11.1667541262), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision] + b), $MachinePrecision] * N[(y / t$95$1), $MachinePrecision] + x), $MachinePrecision], N[(x + N[(N[(t * N[(y / N[Power[z, 2.0], $MachinePrecision]), $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 95.3%

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

   3. Simplified 96.4%

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

   5. Taylor expanded in y around 0 96.4%

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

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

   1. Initial program 0.0%

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

      1. remove-double-neg 0.0%

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

      2. distribute-lft-neg-out 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in z around -inf 81.6%

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

   6. Taylor expanded in t around inf 81.4%

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

      1. mul-1-neg 81.4%

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

      2. associate-/l* 100.0%

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

      3. distribute-rgt-neg-in 100.0%

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

      4. mul-1-neg 100.0%

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

      5. associate-*r/ 100.0%

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

      6. neg-mul-1 100.0%

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

   8. Simplified 100.0%

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

4. Final simplification 97.9%

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

Alternative 4: 95.4% accurate, 0.2× speedup

Math

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

FPCore

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

C

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

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771);
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1 + x;
	} else {
		tmp = x + ((t * (y / Math.pow(z, 2.0))) + (y * 3.13060547623));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1 + x
	else:
		tmp = x + ((t * (y / math.pow(z, 2.0))) + (y * 3.13060547623))
	return tmp

Julia

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

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771);
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1 + x;
	else
		tmp = x + ((t * (y / (z ^ 2.0))) + (y * 3.13060547623));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y * N[(N[(z * N[(N[(z * N[(N[(z * N[(N[(z * 3.13060547623), $MachinePrecision] + 11.1667541262), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(N[(z * N[(N[(z * N[(N[(z * N[(z + 15.234687407), $MachinePrecision]), $MachinePrecision] + 31.4690115749), $MachinePrecision]), $MachinePrecision] + 11.9400905721), $MachinePrecision]), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], N[(t$95$1 + x), $MachinePrecision], N[(x + N[(N[(t * N[(y / N[Power[z, 2.0], $MachinePrecision]), $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 95.3%

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

   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. Step-by-step derivation

      1. remove-double-neg 0.0%

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

      2. distribute-lft-neg-out 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in z around -inf 81.6%

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

   6. Taylor expanded in t around inf 81.4%

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

      1. mul-1-neg 81.4%

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

      2. associate-/l* 100.0%

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

      3. distribute-rgt-neg-in 100.0%

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

      4. mul-1-neg 100.0%

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

      5. associate-*r/ 100.0%

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

      6. neg-mul-1 100.0%

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

   8. Simplified 100.0%

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

4. Final simplification 97.3%

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

Alternative 5: 95.6% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z #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 95.3%

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

   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. Step-by-step derivation

      1. remove-double-neg 0.0%

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

      2. distribute-lft-neg-out 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in z around -inf 81.6%

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

   6. Taylor expanded in t around inf 81.6%

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

      1. *-commutative 81.6%

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

   8. Simplified 81.6%

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

   9. Taylor expanded in y around -inf 96.4%

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

       1. associate-/l* 100.0%

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

       2. sub-neg 100.0%

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

       3. metadata-eval 100.0%

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

   11. Simplified 100.0%

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

4. Final simplification 97.3%

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

Alternative 6: 95.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -110000000 \lor \neg \left(z \leq 4.1 \cdot 10^{+51}\right):\\ \;\;\;\;x + \left(y \cdot 3.13060547623 + y \cdot \frac{\frac{t}{z} + -36.52704169880642}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot 31.4690115749\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -110000000.0) (not (<= z 4.1e+51)))
   (+ x (+ (* y 3.13060547623) (* y (/ (+ (/ t z) -36.52704169880642) z))))
   (+
    x
    (/
     (*
      y
      (+
       (* z (+ (* z (+ (* z (+ (* z 3.13060547623) 11.1667541262)) t)) a))
       b))
     (+ 0.607771387771 (* z (+ 11.9400905721 (* z 31.4690115749))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -110000000.0) || !(z <= 4.1e+51)) {
		tmp = x + ((y * 3.13060547623) + (y * (((t / z) + -36.52704169880642) / z)));
	} else {
		tmp = x + ((y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / (0.607771387771 + (z * (11.9400905721 + (z * 31.4690115749)))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-110000000.0d0)) .or. (.not. (z <= 4.1d+51))) then
        tmp = x + ((y * 3.13060547623d0) + (y * (((t / z) + (-36.52704169880642d0)) / z)))
    else
        tmp = x + ((y * ((z * ((z * ((z * ((z * 3.13060547623d0) + 11.1667541262d0)) + t)) + a)) + b)) / (0.607771387771d0 + (z * (11.9400905721d0 + (z * 31.4690115749d0)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -110000000.0) || !(z <= 4.1e+51)) {
		tmp = x + ((y * 3.13060547623) + (y * (((t / z) + -36.52704169880642) / z)));
	} else {
		tmp = x + ((y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / (0.607771387771 + (z * (11.9400905721 + (z * 31.4690115749)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -110000000.0) or not (z <= 4.1e+51):
		tmp = x + ((y * 3.13060547623) + (y * (((t / z) + -36.52704169880642) / z)))
	else:
		tmp = x + ((y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / (0.607771387771 + (z * (11.9400905721 + (z * 31.4690115749)))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -110000000.0) || !(z <= 4.1e+51))
		tmp = Float64(x + Float64(Float64(y * 3.13060547623) + Float64(y * Float64(Float64(Float64(t / z) + -36.52704169880642) / z))));
	else
		tmp = Float64(x + Float64(Float64(y * Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / Float64(0.607771387771 + Float64(z * Float64(11.9400905721 + Float64(z * 31.4690115749))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -110000000.0) || ~((z <= 4.1e+51)))
		tmp = x + ((y * 3.13060547623) + (y * (((t / z) + -36.52704169880642) / z)));
	else
		tmp = x + ((y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / (0.607771387771 + (z * (11.9400905721 + (z * 31.4690115749)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -110000000.0], N[Not[LessEqual[z, 4.1e+51]], $MachinePrecision]], N[(x + N[(N[(y * 3.13060547623), $MachinePrecision] + N[(y * N[(N[(N[(t / z), $MachinePrecision] + -36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * N[(N[(z * N[(N[(z * N[(N[(z * N[(N[(z * 3.13060547623), $MachinePrecision] + 11.1667541262), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(0.607771387771 + N[(z * N[(11.9400905721 + N[(z * 31.4690115749), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.1e8 or 4.10000000000000011e51 < z

   1. Initial program 5.3%

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

      1. remove-double-neg 5.3%

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

      2. distribute-lft-neg-out 5.3%

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

   3. Simplified 5.3%

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

   5. Taylor expanded in z around -inf 82.1%

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

   6. Taylor expanded in t around inf 82.1%

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

      1. *-commutative 82.1%

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

   8. Simplified 82.1%

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

   9. Taylor expanded in y around -inf 95.4%

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

       1. associate-/l* 98.7%

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

       2. sub-neg 98.7%

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

       3. metadata-eval 98.7%

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

   11. Simplified 98.7%

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

   if -1.1e8 < z < 4.10000000000000011e51

   1. Initial program 98.5%

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

   3. Taylor expanded in z around 0 97.6%

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

      1. *-commutative 97.6%

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

   5. Simplified 97.6%

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

4. Final simplification 98.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -110000000 \lor \neg \left(z \leq 4.1 \cdot 10^{+51}\right):\\ \;\;\;\;x + \left(y \cdot 3.13060547623 + y \cdot \frac{\frac{t}{z} + -36.52704169880642}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot 31.4690115749\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 95.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -12.8 \lor \neg \left(z \leq 4.1 \cdot 10^{+51}\right):\\ \;\;\;\;x + \left(y \cdot 3.13060547623 + y \cdot \frac{\frac{t}{z} + -36.52704169880642}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -12.8) (not (<= z 4.1e+51)))
   (+ x (+ (* y 3.13060547623) (* y (/ (+ (/ t z) -36.52704169880642) z))))
   (+
    x
    (/
     (*
      y
      (+
       (* z (+ (* z (+ (* z (+ (* z 3.13060547623) 11.1667541262)) t)) a))
       b))
     (+ 0.607771387771 (* z 11.9400905721))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -12.8) || !(z <= 4.1e+51)) {
		tmp = x + ((y * 3.13060547623) + (y * (((t / z) + -36.52704169880642) / z)));
	} else {
		tmp = x + ((y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / (0.607771387771 + (z * 11.9400905721)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-12.8d0)) .or. (.not. (z <= 4.1d+51))) then
        tmp = x + ((y * 3.13060547623d0) + (y * (((t / z) + (-36.52704169880642d0)) / z)))
    else
        tmp = x + ((y * ((z * ((z * ((z * ((z * 3.13060547623d0) + 11.1667541262d0)) + t)) + a)) + b)) / (0.607771387771d0 + (z * 11.9400905721d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -12.8) || !(z <= 4.1e+51)) {
		tmp = x + ((y * 3.13060547623) + (y * (((t / z) + -36.52704169880642) / z)));
	} else {
		tmp = x + ((y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / (0.607771387771 + (z * 11.9400905721)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -12.8) or not (z <= 4.1e+51):
		tmp = x + ((y * 3.13060547623) + (y * (((t / z) + -36.52704169880642) / z)))
	else:
		tmp = x + ((y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / (0.607771387771 + (z * 11.9400905721)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -12.8) || !(z <= 4.1e+51))
		tmp = Float64(x + Float64(Float64(y * 3.13060547623) + Float64(y * Float64(Float64(Float64(t / z) + -36.52704169880642) / z))));
	else
		tmp = Float64(x + Float64(Float64(y * Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / Float64(0.607771387771 + Float64(z * 11.9400905721))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -12.8) || ~((z <= 4.1e+51)))
		tmp = x + ((y * 3.13060547623) + (y * (((t / z) + -36.52704169880642) / z)));
	else
		tmp = x + ((y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / (0.607771387771 + (z * 11.9400905721)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -12.8], N[Not[LessEqual[z, 4.1e+51]], $MachinePrecision]], N[(x + N[(N[(y * 3.13060547623), $MachinePrecision] + N[(y * N[(N[(N[(t / z), $MachinePrecision] + -36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * N[(N[(z * N[(N[(z * N[(N[(z * N[(N[(z * 3.13060547623), $MachinePrecision] + 11.1667541262), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(0.607771387771 + N[(z * 11.9400905721), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -12.800000000000001 or 4.10000000000000011e51 < z

   1. Initial program 6.1%

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

      1. remove-double-neg 6.1%

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

      2. distribute-lft-neg-out 6.1%

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

   3. Simplified 6.1%

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

   5. Taylor expanded in z around -inf 81.4%

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

   6. Taylor expanded in t around inf 81.4%

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

      1. *-commutative 81.4%

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

   8. Simplified 81.4%

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

   9. Taylor expanded in y around -inf 94.6%

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

       1. associate-/l* 97.9%

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

       2. sub-neg 97.9%

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

       3. metadata-eval 97.9%

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

   11. Simplified 97.9%

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

   if -12.800000000000001 < z < 4.10000000000000011e51

   1. Initial program 98.4%

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

   3. Taylor expanded in z around 0 97.4%

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

      1. *-commutative 97.4%

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

   5. Simplified 97.4%

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

4. Final simplification 97.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -12.8 \lor \neg \left(z \leq 4.1 \cdot 10^{+51}\right):\\ \;\;\;\;x + \left(y \cdot 3.13060547623 + y \cdot \frac{\frac{t}{z} + -36.52704169880642}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 93.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -17500000 \lor \neg \left(z \leq 0.00018\right):\\ \;\;\;\;x + \left(y \cdot 3.13060547623 + y \cdot \frac{\frac{t}{z} + -36.52704169880642}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(1.6453555072203998 \cdot \left(b + z \cdot a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -17500000.0) (not (<= z 0.00018)))
   (+ x (+ (* y 3.13060547623) (* y (/ (+ (/ t z) -36.52704169880642) z))))
   (+ x (* y (* 1.6453555072203998 (+ b (* z a)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -17500000.0) || !(z <= 0.00018)) {
		tmp = x + ((y * 3.13060547623) + (y * (((t / z) + -36.52704169880642) / z)));
	} else {
		tmp = x + (y * (1.6453555072203998 * (b + (z * a))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-17500000.0d0)) .or. (.not. (z <= 0.00018d0))) then
        tmp = x + ((y * 3.13060547623d0) + (y * (((t / z) + (-36.52704169880642d0)) / z)))
    else
        tmp = x + (y * (1.6453555072203998d0 * (b + (z * a))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -17500000.0) || !(z <= 0.00018)) {
		tmp = x + ((y * 3.13060547623) + (y * (((t / z) + -36.52704169880642) / z)));
	} else {
		tmp = x + (y * (1.6453555072203998 * (b + (z * a))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -17500000.0) or not (z <= 0.00018):
		tmp = x + ((y * 3.13060547623) + (y * (((t / z) + -36.52704169880642) / z)))
	else:
		tmp = x + (y * (1.6453555072203998 * (b + (z * a))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -17500000.0) || !(z <= 0.00018))
		tmp = Float64(x + Float64(Float64(y * 3.13060547623) + Float64(y * Float64(Float64(Float64(t / z) + -36.52704169880642) / z))));
	else
		tmp = Float64(x + Float64(y * Float64(1.6453555072203998 * Float64(b + Float64(z * a)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -17500000.0) || ~((z <= 0.00018)))
		tmp = x + ((y * 3.13060547623) + (y * (((t / z) + -36.52704169880642) / z)));
	else
		tmp = x + (y * (1.6453555072203998 * (b + (z * a))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -17500000.0], N[Not[LessEqual[z, 0.00018]], $MachinePrecision]], N[(x + N[(N[(y * 3.13060547623), $MachinePrecision] + N[(y * N[(N[(N[(t / z), $MachinePrecision] + -36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(1.6453555072203998 * N[(b + N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.75e7 or 1.80000000000000011e-4 < z

   1. Initial program 9.9%

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

      1. remove-double-neg 9.9%

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

      2. distribute-lft-neg-out 9.9%

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

   3. Simplified 9.9%

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

   5. Taylor expanded in z around -inf 80.8%

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

   6. Taylor expanded in t around inf 80.8%

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

      1. *-commutative 80.8%

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

   8. Simplified 80.8%

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

   9. Taylor expanded in y around -inf 93.2%

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

       1. associate-/l* 96.3%

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

       2. sub-neg 96.3%

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

       3. metadata-eval 96.3%

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

   11. Simplified 96.3%

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

   if -1.75e7 < z < 1.80000000000000011e-4

   1. Initial program 99.8%

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

      1. remove-double-neg 99.8%

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

      2. distribute-lft-neg-out 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 83.3%

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

   6. Taylor expanded in a around inf 91.0%

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

      1. *-commutative 91.0%

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

      2. *-commutative 91.0%

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

   8. Simplified 91.0%

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

   9. Taylor expanded in y around 0 93.7%

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

       1. distribute-lft-out 93.7%

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

       2. *-commutative 93.7%

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

   11. Simplified 93.7%

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

4. Final simplification 95.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -17500000 \lor \neg \left(z \leq 0.00018\right):\\ \;\;\;\;x + \left(y \cdot 3.13060547623 + y \cdot \frac{\frac{t}{z} + -36.52704169880642}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(1.6453555072203998 \cdot \left(b + z \cdot a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 89.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{+15}:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 - \frac{y \cdot 36.52704169880642}{z}\right)\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+51}:\\ \;\;\;\;x + y \cdot \left(1.6453555072203998 \cdot \left(b + z \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.02e+15)
   (+ x (- (* y 3.13060547623) (/ (* y 36.52704169880642) z)))
   (if (<= z 4.6e+51)
     (+ x (* y (* 1.6453555072203998 (+ b (* z a)))))
     (+ x (* y 3.13060547623)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.02e+15) {
		tmp = x + ((y * 3.13060547623) - ((y * 36.52704169880642) / z));
	} else if (z <= 4.6e+51) {
		tmp = x + (y * (1.6453555072203998 * (b + (z * a))));
	} else {
		tmp = x + (y * 3.13060547623);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-1.02d+15)) then
        tmp = x + ((y * 3.13060547623d0) - ((y * 36.52704169880642d0) / z))
    else if (z <= 4.6d+51) then
        tmp = x + (y * (1.6453555072203998d0 * (b + (z * a))))
    else
        tmp = x + (y * 3.13060547623d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.02e+15) {
		tmp = x + ((y * 3.13060547623) - ((y * 36.52704169880642) / z));
	} else if (z <= 4.6e+51) {
		tmp = x + (y * (1.6453555072203998 * (b + (z * a))));
	} else {
		tmp = x + (y * 3.13060547623);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.02e+15:
		tmp = x + ((y * 3.13060547623) - ((y * 36.52704169880642) / z))
	elif z <= 4.6e+51:
		tmp = x + (y * (1.6453555072203998 * (b + (z * a))))
	else:
		tmp = x + (y * 3.13060547623)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.02e+15)
		tmp = Float64(x + Float64(Float64(y * 3.13060547623) - Float64(Float64(y * 36.52704169880642) / z)));
	elseif (z <= 4.6e+51)
		tmp = Float64(x + Float64(y * Float64(1.6453555072203998 * Float64(b + Float64(z * a)))));
	else
		tmp = Float64(x + Float64(y * 3.13060547623));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1.02e+15)
		tmp = x + ((y * 3.13060547623) - ((y * 36.52704169880642) / z));
	elseif (z <= 4.6e+51)
		tmp = x + (y * (1.6453555072203998 * (b + (z * a))));
	else
		tmp = x + (y * 3.13060547623);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.02e+15], N[(x + N[(N[(y * 3.13060547623), $MachinePrecision] - N[(N[(y * 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.6e+51], N[(x + N[(y * N[(1.6453555072203998 * N[(b + N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.02e15

   1. Initial program 8.1%

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

   3. Simplified 8.1%

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

   5. Taylor expanded in z around -inf 90.2%

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

      1. +-commutative 90.2%

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

      2. +-commutative 90.2%

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

      3. mul-1-neg 90.2%

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

      4. unsub-neg 90.2%

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

      5. distribute-rgt-out-- 90.2%

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

      6. metadata-eval 90.2%

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

   7. Simplified 90.2%

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

   if -1.02e15 < z < 4.6000000000000001e51

   1. Initial program 98.5%

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

      1. remove-double-neg 98.5%

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

      2. distribute-lft-neg-out 98.5%

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

   3. Simplified 98.4%

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

   5. Taylor expanded in z around 0 79.5%

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

   6. Taylor expanded in a around inf 88.1%

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

      1. *-commutative 88.1%

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

      2. *-commutative 88.1%

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

   8. Simplified 88.1%

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

   9. Taylor expanded in y around 0 90.6%

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

       1. distribute-lft-out 90.6%

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

       2. *-commutative 90.6%

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

   11. Simplified 90.6%

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

   if 4.6000000000000001e51 < z

   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 98.1%

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

      1. +-commutative 98.1%

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

   7. Simplified 98.1%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{+15}:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 - \frac{y \cdot 36.52704169880642}{z}\right)\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+51}:\\ \;\;\;\;x + y \cdot \left(1.6453555072203998 \cdot \left(b + z \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 89.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1000000000000:\\ \;\;\;\;x + y \cdot \left(3.13060547623 - \frac{36.52704169880642}{z}\right)\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+51}:\\ \;\;\;\;x + y \cdot \left(1.6453555072203998 \cdot \left(b + z \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1000000000000.0)
   (+ x (* y (- 3.13060547623 (/ 36.52704169880642 z))))
   (if (<= z 4.1e+51)
     (+ x (* y (* 1.6453555072203998 (+ b (* z a)))))
     (+ x (* y 3.13060547623)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1000000000000.0) {
		tmp = x + (y * (3.13060547623 - (36.52704169880642 / z)));
	} else if (z <= 4.1e+51) {
		tmp = x + (y * (1.6453555072203998 * (b + (z * a))));
	} else {
		tmp = x + (y * 3.13060547623);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-1000000000000.0d0)) then
        tmp = x + (y * (3.13060547623d0 - (36.52704169880642d0 / z)))
    else if (z <= 4.1d+51) then
        tmp = x + (y * (1.6453555072203998d0 * (b + (z * a))))
    else
        tmp = x + (y * 3.13060547623d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1000000000000.0) {
		tmp = x + (y * (3.13060547623 - (36.52704169880642 / z)));
	} else if (z <= 4.1e+51) {
		tmp = x + (y * (1.6453555072203998 * (b + (z * a))));
	} else {
		tmp = x + (y * 3.13060547623);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1000000000000.0:
		tmp = x + (y * (3.13060547623 - (36.52704169880642 / z)))
	elif z <= 4.1e+51:
		tmp = x + (y * (1.6453555072203998 * (b + (z * a))))
	else:
		tmp = x + (y * 3.13060547623)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1000000000000.0)
		tmp = Float64(x + Float64(y * Float64(3.13060547623 - Float64(36.52704169880642 / z))));
	elseif (z <= 4.1e+51)
		tmp = Float64(x + Float64(y * Float64(1.6453555072203998 * Float64(b + Float64(z * a)))));
	else
		tmp = Float64(x + Float64(y * 3.13060547623));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1000000000000.0)
		tmp = x + (y * (3.13060547623 - (36.52704169880642 / z)));
	elseif (z <= 4.1e+51)
		tmp = x + (y * (1.6453555072203998 * (b + (z * a))));
	else
		tmp = x + (y * 3.13060547623);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1000000000000.0], N[(x + N[(y * N[(3.13060547623 - N[(36.52704169880642 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.1e+51], N[(x + N[(y * N[(1.6453555072203998 * N[(b + N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1e12

   1. Initial program 8.1%

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

      1. remove-double-neg 8.1%

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

      2. distribute-lft-neg-out 8.1%

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

   3. Simplified 8.1%

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

   5. Taylor expanded in t around inf 9.5%

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

   6. Taylor expanded in z around -inf 80.8%

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

      1. +-commutative 80.8%

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

      2. mul-1-neg 80.8%

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

      3. unsub-neg 80.8%

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

      4. *-commutative 80.8%

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

      5. associate-/l* 80.8%

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

      6. associate-*r/ 80.8%

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

      7. associate-*r/ 80.8%

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

      8. div-sub 81.5%

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

      9. distribute-rgt-out-- 81.5%

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

      10. metadata-eval 81.5%

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

      11. associate-/r* 87.3%

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

      12. *-commutative 87.3%

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

      13. times-frac 87.3%

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

   8. Simplified 87.3%

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

   9. Taylor expanded in y around 0 90.2%

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

       1. associate-*r/ 90.2%

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

       2. metadata-eval 90.2%

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

   11. Simplified 90.2%

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

   if -1e12 < z < 4.10000000000000011e51

   1. Initial program 98.5%

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

      1. remove-double-neg 98.5%

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

      2. distribute-lft-neg-out 98.5%

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

   3. Simplified 98.4%

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

   5. Taylor expanded in z around 0 79.5%

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

   6. Taylor expanded in a around inf 88.1%

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

      1. *-commutative 88.1%

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

      2. *-commutative 88.1%

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

   8. Simplified 88.1%

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

   9. Taylor expanded in y around 0 90.6%

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

       1. distribute-lft-out 90.6%

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

       2. *-commutative 90.6%

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

   11. Simplified 90.6%

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

   if 4.10000000000000011e51 < z

   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 98.1%

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

      1. +-commutative 98.1%

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

   7. Simplified 98.1%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1000000000000:\\ \;\;\;\;x + y \cdot \left(3.13060547623 - \frac{36.52704169880642}{z}\right)\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+51}:\\ \;\;\;\;x + y \cdot \left(1.6453555072203998 \cdot \left(b + z \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 82.6% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.075 \lor \neg \left(z \leq 6.5 \cdot 10^{+29}\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -0.075) (not (<= z 6.5e+29)))
   (+ x (* y 3.13060547623))
   (+ x (* y (* b 1.6453555072203998)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -0.075) || !(z <= 6.5e+29)) {
		tmp = x + (y * 3.13060547623);
	} else {
		tmp = x + (y * (b * 1.6453555072203998));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-0.075d0)) .or. (.not. (z <= 6.5d+29))) then
        tmp = x + (y * 3.13060547623d0)
    else
        tmp = x + (y * (b * 1.6453555072203998d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -0.075) || !(z <= 6.5e+29)) {
		tmp = x + (y * 3.13060547623);
	} else {
		tmp = x + (y * (b * 1.6453555072203998));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -0.075) or not (z <= 6.5e+29):
		tmp = x + (y * 3.13060547623)
	else:
		tmp = x + (y * (b * 1.6453555072203998))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -0.075) || !(z <= 6.5e+29))
		tmp = Float64(x + Float64(y * 3.13060547623));
	else
		tmp = Float64(x + Float64(y * Float64(b * 1.6453555072203998)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -0.075) || ~((z <= 6.5e+29)))
		tmp = x + (y * 3.13060547623);
	else
		tmp = x + (y * (b * 1.6453555072203998));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -0.075], N[Not[LessEqual[z, 6.5e+29]], $MachinePrecision]], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(b * 1.6453555072203998), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.0749999999999999972 or 6.49999999999999971e29 < z

   1. Initial program 6.9%

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

   3. Simplified 7.6%

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

   5. Taylor expanded in z around inf 91.5%

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

      1. +-commutative 91.5%

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

   7. Simplified 91.5%

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

   if -0.0749999999999999972 < z < 6.49999999999999971e29

   1. Initial program 99.1%

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

      1. remove-double-neg 99.1%

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

      2. distribute-lft-neg-out 99.1%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in b around inf 78.6%

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

   6. Taylor expanded in z around 0 78.6%

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

      1. *-commutative 78.6%

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

   8. Simplified 78.6%

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

   9. Taylor expanded in z around 0 78.5%

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

   10. Taylor expanded in b around 0 78.4%

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

       1. *-commutative 78.4%

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

       2. associate-*r* 78.4%

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

       3. *-commutative 78.4%

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

       4. associate-*l* 78.5%

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

   12. Simplified 78.5%

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

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.075 \lor \neg \left(z \leq 6.5 \cdot 10^{+29}\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 82.6% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.1:\\ \;\;\;\;x + y \cdot \left(3.13060547623 - \frac{36.52704169880642}{z}\right)\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+29}:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -0.1)
   (+ x (* y (- 3.13060547623 (/ 36.52704169880642 z))))
   (if (<= z 6e+29)
     (+ x (* y (* b 1.6453555072203998)))
     (+ x (* y 3.13060547623)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -0.1) {
		tmp = x + (y * (3.13060547623 - (36.52704169880642 / z)));
	} else if (z <= 6e+29) {
		tmp = x + (y * (b * 1.6453555072203998));
	} else {
		tmp = x + (y * 3.13060547623);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-0.1d0)) then
        tmp = x + (y * (3.13060547623d0 - (36.52704169880642d0 / z)))
    else if (z <= 6d+29) then
        tmp = x + (y * (b * 1.6453555072203998d0))
    else
        tmp = x + (y * 3.13060547623d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -0.1) {
		tmp = x + (y * (3.13060547623 - (36.52704169880642 / z)));
	} else if (z <= 6e+29) {
		tmp = x + (y * (b * 1.6453555072203998));
	} else {
		tmp = x + (y * 3.13060547623);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -0.1:
		tmp = x + (y * (3.13060547623 - (36.52704169880642 / z)))
	elif z <= 6e+29:
		tmp = x + (y * (b * 1.6453555072203998))
	else:
		tmp = x + (y * 3.13060547623)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -0.1)
		tmp = Float64(x + Float64(y * Float64(3.13060547623 - Float64(36.52704169880642 / z))));
	elseif (z <= 6e+29)
		tmp = Float64(x + Float64(y * Float64(b * 1.6453555072203998)));
	else
		tmp = Float64(x + Float64(y * 3.13060547623));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -0.1)
		tmp = x + (y * (3.13060547623 - (36.52704169880642 / z)));
	elseif (z <= 6e+29)
		tmp = x + (y * (b * 1.6453555072203998));
	else
		tmp = x + (y * 3.13060547623);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -0.1], N[(x + N[(y * N[(3.13060547623 - N[(36.52704169880642 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6e+29], N[(x + N[(y * N[(b * 1.6453555072203998), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.10000000000000001

   1. Initial program 10.8%

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

      1. remove-double-neg 10.8%

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

      2. distribute-lft-neg-out 10.8%

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

   3. Simplified 10.8%

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

   5. Taylor expanded in t around inf 12.2%

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

   6. Taylor expanded in z around -inf 78.4%

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

      1. +-commutative 78.4%

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

      2. mul-1-neg 78.4%

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

      3. unsub-neg 78.4%

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

      4. *-commutative 78.4%

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

      5. associate-/l* 78.4%

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

      6. associate-*r/ 78.4%

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

      7. associate-*r/ 78.4%

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

      8. div-sub 79.0%

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

      9. distribute-rgt-out-- 79.0%

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

      10. metadata-eval 79.0%

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

      11. associate-/r* 84.6%

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

      12. *-commutative 84.6%

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

      13. times-frac 84.6%

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

   8. Simplified 84.6%

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

   9. Taylor expanded in y around 0 87.4%

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

       1. associate-*r/ 87.4%

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

       2. metadata-eval 87.4%

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

   11. Simplified 87.4%

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

   if -0.10000000000000001 < z < 5.9999999999999998e29

   1. Initial program 99.1%

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

      1. remove-double-neg 99.1%

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

      2. distribute-lft-neg-out 99.1%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in b around inf 78.6%

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

   6. Taylor expanded in z around 0 78.6%

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

      1. *-commutative 78.6%

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

   8. Simplified 78.6%

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

   9. Taylor expanded in z around 0 78.5%

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

   10. Taylor expanded in b around 0 78.4%

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

       1. *-commutative 78.4%

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

       2. associate-*r* 78.4%

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

       3. *-commutative 78.4%

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

       4. associate-*l* 78.5%

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

   12. Simplified 78.5%

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

   if 5.9999999999999998e29 < z

   1. Initial program 2.1%

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

   3. Simplified 3.7%

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

   5. Taylor expanded in z around inf 96.4%

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

      1. +-commutative 96.4%

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

   7. Simplified 96.4%

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

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.1:\\ \;\;\;\;x + y \cdot \left(3.13060547623 - \frac{36.52704169880642}{z}\right)\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+29}:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 51.0% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+59} \lor \neg \left(y \leq 2.4 \cdot 10^{+154}\right):\\ \;\;\;\;y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2.3e+59) (not (<= y 2.4e+154))) (* y 3.13060547623) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.3e+59) || !(y <= 2.4e+154)) {
		tmp = y * 3.13060547623;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-2.3d+59)) .or. (.not. (y <= 2.4d+154))) then
        tmp = y * 3.13060547623d0
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.3e+59) || !(y <= 2.4e+154)) {
		tmp = y * 3.13060547623;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -2.3e+59) or not (y <= 2.4e+154):
		tmp = y * 3.13060547623
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -2.3e+59) || !(y <= 2.4e+154))
		tmp = Float64(y * 3.13060547623);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -2.3e+59) || ~((y <= 2.4e+154)))
		tmp = y * 3.13060547623;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -2.3e+59], N[Not[LessEqual[y, 2.4e+154]], $MachinePrecision]], N[(y * 3.13060547623), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -2.30000000000000008e59 or 2.40000000000000015e154 < y

   1. Initial program 55.0%

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

   3. Simplified 57.6%

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

   5. Taylor expanded in z around inf 43.8%

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

      1. +-commutative 43.8%

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

   7. Simplified 43.8%

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

   8. Taylor expanded in y around inf 34.4%

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

      1. *-commutative 34.4%

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

   10. Simplified 34.4%

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

   if -2.30000000000000008e59 < y < 2.40000000000000015e154

   1. Initial program 56.2%

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

   3. Simplified 56.1%

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

   5. Taylor expanded in y around 0 64.2%

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

4. Final simplification 55.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+59} \lor \neg \left(y \leq 2.4 \cdot 10^{+154}\right):\\ \;\;\;\;y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 61.3% accurate, 7.4× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = x + (y * 3.13060547623d0)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 55.9%

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

3. Simplified 56.5%

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

5. Taylor expanded in z around inf 63.4%

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

   1. +-commutative 63.4%

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

7. Simplified 63.4%

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

8. Final simplification 63.4%

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

Alternative 15: 45.1% 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 55.9%

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

3. Simplified 56.5%

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

5. Taylor expanded in y around 0 50.3%

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

Developer Target 1: 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 2024137 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, D"
  :precision binary64

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

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