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

Percentage Accurate: 58.9% → 97.0%

Time: 17.1s

Alternatives: 15

Speedup: 2.5×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 58.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)\\ t_2 := z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right)\\ \mathbf{if}\;\frac{y \cdot \left(t\_2 + b\right)}{t\_1} \leq \infty:\\ \;\;\;\;x + y \cdot \left(\frac{b}{t\_1} + \frac{t\_2}{t\_1}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+
          0.607771387771
          (*
           z
           (+
            11.9400905721
            (* z (+ 31.4690115749 (* z (+ z 15.234687407))))))))
        (t_2
         (* z (+ (* z (+ (* z (+ (* z 3.13060547623) 11.1667541262)) t)) a))))
   (if (<= (/ (* y (+ t_2 b)) t_1) INFINITY)
     (+ x (* y (+ (/ b t_1) (/ t_2 t_1))))
     (+ x (* y 3.13060547623)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * (z + 15.234687407))))));
	double t_2 = z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a);
	double tmp;
	if (((y * (t_2 + b)) / t_1) <= ((double) INFINITY)) {
		tmp = x + (y * ((b / t_1) + (t_2 / t_1)));
	} else {
		tmp = x + (y * 3.13060547623);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * (z + 15.234687407))))));
	double t_2 = z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a);
	double tmp;
	if (((y * (t_2 + b)) / t_1) <= Double.POSITIVE_INFINITY) {
		tmp = x + (y * ((b / t_1) + (t_2 / t_1)));
	} else {
		tmp = x + (y * 3.13060547623);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = 0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * (z + 15.234687407))))))
	t_2 = z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)
	tmp = 0
	if ((y * (t_2 + b)) / t_1) <= math.inf:
		tmp = x + (y * ((b / t_1) + (t_2 / t_1)))
	else:
		tmp = x + (y * 3.13060547623)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(0.607771387771 + Float64(z * Float64(11.9400905721 + Float64(z * Float64(31.4690115749 + Float64(z * Float64(z + 15.234687407)))))))
	t_2 = Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * 3.13060547623) + 11.1667541262)) + t)) + a))
	tmp = 0.0
	if (Float64(Float64(y * Float64(t_2 + b)) / t_1) <= Inf)
		tmp = Float64(x + Float64(y * Float64(Float64(b / t_1) + Float64(t_2 / t_1))));
	else
		tmp = Float64(x + Float64(y * 3.13060547623));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * (z + 15.234687407))))));
	t_2 = z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a);
	tmp = 0.0;
	if (((y * (t_2 + b)) / t_1) <= Inf)
		tmp = x + (y * ((b / t_1) + (t_2 / t_1)));
	else
		tmp = x + (y * 3.13060547623);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(0.607771387771 + N[(z * N[(11.9400905721 + N[(z * N[(31.4690115749 + N[(z * N[(z + 15.234687407), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(z * N[(N[(z * N[(N[(z * 3.13060547623), $MachinePrecision] + 11.1667541262), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(y * N[(t$95$2 + b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], Infinity], N[(x + N[(y * N[(N[(b / t$95$1), $MachinePrecision] + N[(t$95$2 / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 92.3%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x + y \cdot \left(\frac{b}{\frac{607771387771}{1000000000000} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)} + \frac{z \cdot \left(a + z \cdot \left(t + z \cdot \left(\frac{55833770631}{5000000000} + \frac{313060547623}{100000000000} \cdot z\right)\right)\right)}{\frac{607771387771}{1000000000000} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)}\right)} \]

   5. Simplified 97.4%

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

   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. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{x + \frac{313060547623}{100000000000} \cdot y} \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{313060547623}{100000000000} \cdot y\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{313060547623}{100000000000}}\right)\right) \]

      3. *-lowering-*.f64 99.9%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\frac{313060547623}{100000000000}}\right)\right) \]

   5. Simplified 99.9%

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

4. Final simplification 98.3%

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

Alternative 2: 95.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)\\ t_2 := z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\\ t_3 := \frac{y \cdot t\_2}{t\_1}\\ \mathbf{if}\;t\_3 \leq 10^{+221}:\\ \;\;\;\;t\_3 + x\\ \mathbf{elif}\;t\_3 \leq \infty:\\ \;\;\;\;t\_2 \cdot \frac{y}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+
          0.607771387771
          (*
           z
           (+
            11.9400905721
            (* z (+ 31.4690115749 (* z (+ z 15.234687407))))))))
        (t_2
         (+
          (* z (+ (* z (+ (* z (+ (* z 3.13060547623) 11.1667541262)) t)) a))
          b))
        (t_3 (/ (* y t_2) t_1)))
   (if (<= t_3 1e+221)
     (+ t_3 x)
     (if (<= t_3 INFINITY) (* t_2 (/ y t_1)) (+ x (* y 3.13060547623))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * (z + 15.234687407))))));
	double t_2 = (z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b;
	double t_3 = (y * t_2) / t_1;
	double tmp;
	if (t_3 <= 1e+221) {
		tmp = t_3 + x;
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = t_2 * (y / t_1);
	} else {
		tmp = x + (y * 3.13060547623);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * (z + 15.234687407))))));
	double t_2 = (z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b;
	double t_3 = (y * t_2) / t_1;
	double tmp;
	if (t_3 <= 1e+221) {
		tmp = t_3 + x;
	} else if (t_3 <= Double.POSITIVE_INFINITY) {
		tmp = t_2 * (y / t_1);
	} else {
		tmp = x + (y * 3.13060547623);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = 0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * (z + 15.234687407))))))
	t_2 = (z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b
	t_3 = (y * t_2) / t_1
	tmp = 0
	if t_3 <= 1e+221:
		tmp = t_3 + x
	elif t_3 <= math.inf:
		tmp = t_2 * (y / t_1)
	else:
		tmp = x + (y * 3.13060547623)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(0.607771387771 + Float64(z * Float64(11.9400905721 + Float64(z * Float64(31.4690115749 + Float64(z * Float64(z + 15.234687407)))))))
	t_2 = Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)
	t_3 = Float64(Float64(y * t_2) / t_1)
	tmp = 0.0
	if (t_3 <= 1e+221)
		tmp = Float64(t_3 + x);
	elseif (t_3 <= Inf)
		tmp = Float64(t_2 * Float64(y / t_1));
	else
		tmp = Float64(x + Float64(y * 3.13060547623));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * (z + 15.234687407))))));
	t_2 = (z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b;
	t_3 = (y * t_2) / t_1;
	tmp = 0.0;
	if (t_3 <= 1e+221)
		tmp = t_3 + x;
	elseif (t_3 <= Inf)
		tmp = t_2 * (y / t_1);
	else
		tmp = x + (y * 3.13060547623);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(0.607771387771 + N[(z * N[(11.9400905721 + N[(z * N[(31.4690115749 + N[(z * N[(z + 15.234687407), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = 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]}, Block[{t$95$3 = N[(N[(y * t$95$2), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$3, 1e+221], N[(t$95$3 + x), $MachinePrecision], If[LessEqual[t$95$3, Infinity], N[(t$95$2 * N[(y / t$95$1), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 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))) < 1e221

   1. Initial program 96.9%

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

   if 1e221 < (/.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 73.7%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(\frac{55833770631}{5000000000} + \frac{313060547623}{100000000000} \cdot z\right)\right)\right)\right)}{\frac{607771387771}{1000000000000} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)}} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{\left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(\frac{55833770631}{5000000000} + \frac{313060547623}{100000000000} \cdot z\right)\right)\right)\right) \cdot y}{\color{blue}{\frac{607771387771}{1000000000000}} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)} \]

      2. associate-/l* N/A

         \[\leadsto \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(\frac{55833770631}{5000000000} + \frac{313060547623}{100000000000} \cdot z\right)\right)\right)\right) \cdot \color{blue}{\frac{y}{\frac{607771387771}{1000000000000} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)}} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(\frac{55833770631}{5000000000} + \frac{313060547623}{100000000000} \cdot z\right)\right)\right)\right), \color{blue}{\left(\frac{y}{\frac{607771387771}{1000000000000} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)}\right)}\right) \]

   5. Simplified 90.3%

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

   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. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{x + \frac{313060547623}{100000000000} \cdot y} \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{313060547623}{100000000000} \cdot y\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{313060547623}{100000000000}}\right)\right) \]

      3. *-lowering-*.f64 99.9%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\frac{313060547623}{100000000000}}\right)\right) \]

   5. Simplified 99.9%

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

4. Final simplification 97.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)} \leq 10^{+221}:\\ \;\;\;\;\frac{y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)} + x\\ \mathbf{elif}\;\frac{y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)} \leq \infty:\\ \;\;\;\;\left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right) \cdot \frac{y}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 97.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)\\ t_2 := z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\\ \mathbf{if}\;\frac{y \cdot t\_2}{t\_1} \leq \infty:\\ \;\;\;\;x + y \cdot \frac{t\_2}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+
          0.607771387771
          (*
           z
           (+
            11.9400905721
            (* z (+ 31.4690115749 (* z (+ z 15.234687407))))))))
        (t_2
         (+
          (* z (+ (* z (+ (* z (+ (* z 3.13060547623) 11.1667541262)) t)) a))
          b)))
   (if (<= (/ (* y t_2) t_1) INFINITY)
     (+ x (* y (/ t_2 t_1)))
     (+ x (* y 3.13060547623)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * (z + 15.234687407))))));
	double t_2 = (z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b;
	double tmp;
	if (((y * t_2) / t_1) <= ((double) INFINITY)) {
		tmp = x + (y * (t_2 / t_1));
	} else {
		tmp = x + (y * 3.13060547623);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * (z + 15.234687407))))));
	double t_2 = (z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b;
	double tmp;
	if (((y * t_2) / t_1) <= Double.POSITIVE_INFINITY) {
		tmp = x + (y * (t_2 / t_1));
	} else {
		tmp = x + (y * 3.13060547623);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = 0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * (z + 15.234687407))))))
	t_2 = (z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b
	tmp = 0
	if ((y * t_2) / t_1) <= math.inf:
		tmp = x + (y * (t_2 / t_1))
	else:
		tmp = x + (y * 3.13060547623)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(0.607771387771 + Float64(z * Float64(11.9400905721 + Float64(z * Float64(31.4690115749 + Float64(z * Float64(z + 15.234687407)))))))
	t_2 = Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)
	tmp = 0.0
	if (Float64(Float64(y * t_2) / t_1) <= Inf)
		tmp = Float64(x + Float64(y * Float64(t_2 / t_1)));
	else
		tmp = Float64(x + Float64(y * 3.13060547623));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * (z + 15.234687407))))));
	t_2 = (z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b;
	tmp = 0.0;
	if (((y * t_2) / t_1) <= Inf)
		tmp = x + (y * (t_2 / t_1));
	else
		tmp = x + (y * 3.13060547623);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(0.607771387771 + N[(z * N[(11.9400905721 + N[(z * N[(31.4690115749 + N[(z * N[(z + 15.234687407), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = 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]}, If[LessEqual[N[(N[(y * t$95$2), $MachinePrecision] / t$95$1), $MachinePrecision], Infinity], N[(x + N[(y * N[(t$95$2 / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 92.3%

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

      1. +-commutative N/A

         \[\leadsto \frac{y \cdot \left(\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} + \color{blue}{x} \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{y \cdot \left(\left(\left(\left(z \cdot \frac{313060547623}{100000000000} + \frac{55833770631}{5000000000}\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}}\right), \color{blue}{x}\right) \]

   4. Applied egg-rr 97.4%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{x + \frac{313060547623}{100000000000} \cdot y} \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{313060547623}{100000000000} \cdot y\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{313060547623}{100000000000}}\right)\right) \]

      3. *-lowering-*.f64 99.9%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\frac{313060547623}{100000000000}}\right)\right) \]

   5. Simplified 99.9%

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

4. Final simplification 98.3%

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

Alternative 4: 91.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot 3.13060547623\\ \mathbf{if}\;z \leq -2.4 \cdot 10^{+42}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+36}:\\ \;\;\;\;x + y \cdot \frac{b + z \cdot a}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1 + \frac{y}{z} \cdot -36.52704169880642\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* y 3.13060547623))))
   (if (<= z -2.4e+42)
     t_1
     (if (<= z 1.3e+36)
       (+
        x
        (*
         y
         (/
          (+ b (* z a))
          (+
           0.607771387771
           (*
            z
            (+
             11.9400905721
             (* z (+ 31.4690115749 (* z (+ z 15.234687407))))))))))
       (+ t_1 (* (/ y z) -36.52704169880642))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * 3.13060547623);
	double tmp;
	if (z <= -2.4e+42) {
		tmp = t_1;
	} else if (z <= 1.3e+36) {
		tmp = x + (y * ((b + (z * a)) / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * (z + 15.234687407)))))))));
	} else {
		tmp = t_1 + ((y / z) * -36.52704169880642);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * 3.13060547623d0)
    if (z <= (-2.4d+42)) then
        tmp = t_1
    else if (z <= 1.3d+36) then
        tmp = x + (y * ((b + (z * a)) / (0.607771387771d0 + (z * (11.9400905721d0 + (z * (31.4690115749d0 + (z * (z + 15.234687407d0)))))))))
    else
        tmp = t_1 + ((y / z) * (-36.52704169880642d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * 3.13060547623);
	double tmp;
	if (z <= -2.4e+42) {
		tmp = t_1;
	} else if (z <= 1.3e+36) {
		tmp = x + (y * ((b + (z * a)) / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * (z + 15.234687407)))))))));
	} else {
		tmp = t_1 + ((y / z) * -36.52704169880642);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y * 3.13060547623)
	tmp = 0
	if z <= -2.4e+42:
		tmp = t_1
	elif z <= 1.3e+36:
		tmp = x + (y * ((b + (z * a)) / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * (z + 15.234687407)))))))))
	else:
		tmp = t_1 + ((y / z) * -36.52704169880642)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y * 3.13060547623))
	tmp = 0.0
	if (z <= -2.4e+42)
		tmp = t_1;
	elseif (z <= 1.3e+36)
		tmp = Float64(x + Float64(y * Float64(Float64(b + Float64(z * a)) / Float64(0.607771387771 + Float64(z * Float64(11.9400905721 + Float64(z * Float64(31.4690115749 + Float64(z * Float64(z + 15.234687407))))))))));
	else
		tmp = Float64(t_1 + Float64(Float64(y / z) * -36.52704169880642));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (y * 3.13060547623);
	tmp = 0.0;
	if (z <= -2.4e+42)
		tmp = t_1;
	elseif (z <= 1.3e+36)
		tmp = x + (y * ((b + (z * a)) / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * (z + 15.234687407)))))))));
	else
		tmp = t_1 + ((y / z) * -36.52704169880642);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.4e+42], t$95$1, If[LessEqual[z, 1.3e+36], N[(x + N[(y * N[(N[(b + N[(z * a), $MachinePrecision]), $MachinePrecision] / N[(0.607771387771 + N[(z * N[(11.9400905721 + N[(z * N[(31.4690115749 + N[(z * N[(z + 15.234687407), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(N[(y / z), $MachinePrecision] * -36.52704169880642), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.3999999999999999e42

   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. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{x + \frac{313060547623}{100000000000} \cdot y} \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{313060547623}{100000000000} \cdot y\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{313060547623}{100000000000}}\right)\right) \]

      3. *-lowering-*.f64 95.2%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\frac{313060547623}{100000000000}}\right)\right) \]

   5. Simplified 95.2%

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

   if -2.3999999999999999e42 < z < 1.3000000000000001e36

   1. Initial program 97.8%

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

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \color{blue}{\left(b + a \cdot z\right)}\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right), z\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \left(a \cdot z\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right), \color{blue}{z}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \left(z \cdot a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right), z\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      3. *-lowering-*.f64 93.8%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \mathsf{*.f64}\left(z, a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right), z\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

   5. Simplified 93.8%

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

      1. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{b + z \cdot a}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}}}\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{b + z \cdot a}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \cdot \color{blue}{y}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{b + z \cdot a}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}}\right), \color{blue}{y}\right)\right) \]

   7. Applied egg-rr 94.4%

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

   if 1.3000000000000001e36 < z

   1. Initial program 9.4%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\left(x + \left(\frac{313060547623}{100000000000} \cdot y + \frac{55833770631}{5000000000} \cdot \frac{y}{z}\right)\right) - \frac{4769379582500641883561}{100000000000000000000} \cdot \frac{y}{z}} \]
   4. Step-by-step derivation

      1. associate-+r+ N/A

         \[\leadsto \left(\left(x + \frac{313060547623}{100000000000} \cdot y\right) + \frac{55833770631}{5000000000} \cdot \frac{y}{z}\right) - \color{blue}{\frac{4769379582500641883561}{100000000000000000000}} \cdot \frac{y}{z} \]

      2. associate--l+ N/A

         \[\leadsto \left(x + \frac{313060547623}{100000000000} \cdot y\right) + \color{blue}{\left(\frac{55833770631}{5000000000} \cdot \frac{y}{z} - \frac{4769379582500641883561}{100000000000000000000} \cdot \frac{y}{z}\right)} \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x + \frac{313060547623}{100000000000} \cdot y\right), \color{blue}{\left(\frac{55833770631}{5000000000} \cdot \frac{y}{z} - \frac{4769379582500641883561}{100000000000000000000} \cdot \frac{y}{z}\right)}\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \left(\frac{313060547623}{100000000000} \cdot y\right)\right), \left(\color{blue}{\frac{55833770631}{5000000000} \cdot \frac{y}{z}} - \frac{4769379582500641883561}{100000000000000000000} \cdot \frac{y}{z}\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \left(y \cdot \frac{313060547623}{100000000000}\right)\right), \left(\frac{55833770631}{5000000000} \cdot \color{blue}{\frac{y}{z}} - \frac{4769379582500641883561}{100000000000000000000} \cdot \frac{y}{z}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \left(\frac{55833770631}{5000000000} \cdot \color{blue}{\frac{y}{z}} - \frac{4769379582500641883561}{100000000000000000000} \cdot \frac{y}{z}\right)\right) \]

      7. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \left(\frac{y}{z} \cdot \color{blue}{\left(\frac{55833770631}{5000000000} - \frac{4769379582500641883561}{100000000000000000000}\right)}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{*.f64}\left(\left(\frac{y}{z}\right), \color{blue}{\left(\frac{55833770631}{5000000000} - \frac{4769379582500641883561}{100000000000000000000}\right)}\right)\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, z\right), \left(\color{blue}{\frac{55833770631}{5000000000}} - \frac{4769379582500641883561}{100000000000000000000}\right)\right)\right) \]

      10. metadata-eval 93.6%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, z\right), \frac{-3652704169880641883561}{100000000000000000000}\right)\right) \]

   5. Simplified 93.6%

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

4. Final simplification 94.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+42}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+36}:\\ \;\;\;\;x + y \cdot \frac{b + z \cdot a}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y \cdot 3.13060547623\right) + \frac{y}{z} \cdot -36.52704169880642\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 91.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot 3.13060547623\\ \mathbf{if}\;z \leq -2.5 \cdot 10^{+42}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+34}:\\ \;\;\;\;x + y \cdot \frac{b + z \cdot a}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(z \cdot z\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1 + \frac{y}{z} \cdot -36.52704169880642\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* y 3.13060547623))))
   (if (<= z -2.5e+42)
     t_1
     (if (<= z 6.8e+34)
       (+
        x
        (*
         y
         (/
          (+ b (* z a))
          (+ 0.607771387771 (* z (+ 11.9400905721 (* z (* z z))))))))
       (+ t_1 (* (/ y z) -36.52704169880642))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * 3.13060547623);
	double tmp;
	if (z <= -2.5e+42) {
		tmp = t_1;
	} else if (z <= 6.8e+34) {
		tmp = x + (y * ((b + (z * a)) / (0.607771387771 + (z * (11.9400905721 + (z * (z * z)))))));
	} else {
		tmp = t_1 + ((y / z) * -36.52704169880642);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * 3.13060547623d0)
    if (z <= (-2.5d+42)) then
        tmp = t_1
    else if (z <= 6.8d+34) then
        tmp = x + (y * ((b + (z * a)) / (0.607771387771d0 + (z * (11.9400905721d0 + (z * (z * z)))))))
    else
        tmp = t_1 + ((y / z) * (-36.52704169880642d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * 3.13060547623);
	double tmp;
	if (z <= -2.5e+42) {
		tmp = t_1;
	} else if (z <= 6.8e+34) {
		tmp = x + (y * ((b + (z * a)) / (0.607771387771 + (z * (11.9400905721 + (z * (z * z)))))));
	} else {
		tmp = t_1 + ((y / z) * -36.52704169880642);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y * 3.13060547623)
	tmp = 0
	if z <= -2.5e+42:
		tmp = t_1
	elif z <= 6.8e+34:
		tmp = x + (y * ((b + (z * a)) / (0.607771387771 + (z * (11.9400905721 + (z * (z * z)))))))
	else:
		tmp = t_1 + ((y / z) * -36.52704169880642)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y * 3.13060547623))
	tmp = 0.0
	if (z <= -2.5e+42)
		tmp = t_1;
	elseif (z <= 6.8e+34)
		tmp = Float64(x + Float64(y * Float64(Float64(b + Float64(z * a)) / Float64(0.607771387771 + Float64(z * Float64(11.9400905721 + Float64(z * Float64(z * z))))))));
	else
		tmp = Float64(t_1 + Float64(Float64(y / z) * -36.52704169880642));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (y * 3.13060547623);
	tmp = 0.0;
	if (z <= -2.5e+42)
		tmp = t_1;
	elseif (z <= 6.8e+34)
		tmp = x + (y * ((b + (z * a)) / (0.607771387771 + (z * (11.9400905721 + (z * (z * z)))))));
	else
		tmp = t_1 + ((y / z) * -36.52704169880642);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.5e+42], t$95$1, If[LessEqual[z, 6.8e+34], N[(x + N[(y * N[(N[(b + N[(z * a), $MachinePrecision]), $MachinePrecision] / N[(0.607771387771 + N[(z * N[(11.9400905721 + N[(z * N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(N[(y / z), $MachinePrecision] * -36.52704169880642), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.50000000000000003e42

   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. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{x + \frac{313060547623}{100000000000} \cdot y} \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{313060547623}{100000000000} \cdot y\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{313060547623}{100000000000}}\right)\right) \]

      3. *-lowering-*.f64 95.2%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\frac{313060547623}{100000000000}}\right)\right) \]

   5. Simplified 95.2%

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

   if -2.50000000000000003e42 < z < 6.7999999999999999e34

   1. Initial program 97.8%

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

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \color{blue}{\left(b + a \cdot z\right)}\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right), z\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \left(a \cdot z\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right), \color{blue}{z}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \left(z \cdot a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right), z\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      3. *-lowering-*.f64 93.8%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \mathsf{*.f64}\left(z, a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right), z\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

   5. Simplified 93.8%

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

      1. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{b + z \cdot a}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}}}\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{b + z \cdot a}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \cdot \color{blue}{y}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{b + z \cdot a}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}}\right), \color{blue}{y}\right)\right) \]

   7. Applied egg-rr 94.4%

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

   8. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \mathsf{*.f64}\left(z, a\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{119400905721}{10000000000}, \color{blue}{\left({z}^{3}\right)}\right)\right), \frac{607771387771}{1000000000000}\right)\right), y\right)\right) \]
   9. Step-by-step derivation

      1. cube-mult N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \mathsf{*.f64}\left(z, a\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{119400905721}{10000000000}, \left(z \cdot \left(z \cdot z\right)\right)\right)\right), \frac{607771387771}{1000000000000}\right)\right), y\right)\right) \]

      2. unpow2 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \mathsf{*.f64}\left(z, a\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{119400905721}{10000000000}, \left(z \cdot {z}^{2}\right)\right)\right), \frac{607771387771}{1000000000000}\right)\right), y\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \mathsf{*.f64}\left(z, a\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{119400905721}{10000000000}, \mathsf{*.f64}\left(z, \left({z}^{2}\right)\right)\right)\right), \frac{607771387771}{1000000000000}\right)\right), y\right)\right) \]

      4. unpow2 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \mathsf{*.f64}\left(z, a\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{119400905721}{10000000000}, \mathsf{*.f64}\left(z, \left(z \cdot z\right)\right)\right)\right), \frac{607771387771}{1000000000000}\right)\right), y\right)\right) \]

      5. *-lowering-*.f64 93.4%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \mathsf{*.f64}\left(z, a\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{119400905721}{10000000000}, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, z\right)\right)\right)\right), \frac{607771387771}{1000000000000}\right)\right), y\right)\right) \]

   10. Simplified 93.4%

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

   if 6.7999999999999999e34 < z

   1. Initial program 9.4%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\left(x + \left(\frac{313060547623}{100000000000} \cdot y + \frac{55833770631}{5000000000} \cdot \frac{y}{z}\right)\right) - \frac{4769379582500641883561}{100000000000000000000} \cdot \frac{y}{z}} \]
   4. Step-by-step derivation

      1. associate-+r+ N/A

         \[\leadsto \left(\left(x + \frac{313060547623}{100000000000} \cdot y\right) + \frac{55833770631}{5000000000} \cdot \frac{y}{z}\right) - \color{blue}{\frac{4769379582500641883561}{100000000000000000000}} \cdot \frac{y}{z} \]

      2. associate--l+ N/A

         \[\leadsto \left(x + \frac{313060547623}{100000000000} \cdot y\right) + \color{blue}{\left(\frac{55833770631}{5000000000} \cdot \frac{y}{z} - \frac{4769379582500641883561}{100000000000000000000} \cdot \frac{y}{z}\right)} \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x + \frac{313060547623}{100000000000} \cdot y\right), \color{blue}{\left(\frac{55833770631}{5000000000} \cdot \frac{y}{z} - \frac{4769379582500641883561}{100000000000000000000} \cdot \frac{y}{z}\right)}\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \left(\frac{313060547623}{100000000000} \cdot y\right)\right), \left(\color{blue}{\frac{55833770631}{5000000000} \cdot \frac{y}{z}} - \frac{4769379582500641883561}{100000000000000000000} \cdot \frac{y}{z}\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \left(y \cdot \frac{313060547623}{100000000000}\right)\right), \left(\frac{55833770631}{5000000000} \cdot \color{blue}{\frac{y}{z}} - \frac{4769379582500641883561}{100000000000000000000} \cdot \frac{y}{z}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \left(\frac{55833770631}{5000000000} \cdot \color{blue}{\frac{y}{z}} - \frac{4769379582500641883561}{100000000000000000000} \cdot \frac{y}{z}\right)\right) \]

      7. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \left(\frac{y}{z} \cdot \color{blue}{\left(\frac{55833770631}{5000000000} - \frac{4769379582500641883561}{100000000000000000000}\right)}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{*.f64}\left(\left(\frac{y}{z}\right), \color{blue}{\left(\frac{55833770631}{5000000000} - \frac{4769379582500641883561}{100000000000000000000}\right)}\right)\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, z\right), \left(\color{blue}{\frac{55833770631}{5000000000}} - \frac{4769379582500641883561}{100000000000000000000}\right)\right)\right) \]

      10. metadata-eval 93.6%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, z\right), \frac{-3652704169880641883561}{100000000000000000000}\right)\right) \]

   5. Simplified 93.6%

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

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+42}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+34}:\\ \;\;\;\;x + y \cdot \frac{b + z \cdot a}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(z \cdot z\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y \cdot 3.13060547623\right) + \frac{y}{z} \cdot -36.52704169880642\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 84.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot 3.13060547623\\ \mathbf{if}\;z \leq -2.2 \cdot 10^{+42}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-26}:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998\right)\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+35}:\\ \;\;\;\;x + y \cdot \frac{a + \frac{b}{z}}{z \cdot \left(z \cdot z\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1 + \frac{y}{z} \cdot -36.52704169880642\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* y 3.13060547623))))
   (if (<= z -2.2e+42)
     t_1
     (if (<= z 6e-26)
       (+ x (* y (* b 1.6453555072203998)))
       (if (<= z 4.1e+35)
         (+ x (* y (/ (+ a (/ b z)) (* z (* z z)))))
         (+ t_1 (* (/ y z) -36.52704169880642)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * 3.13060547623);
	double tmp;
	if (z <= -2.2e+42) {
		tmp = t_1;
	} else if (z <= 6e-26) {
		tmp = x + (y * (b * 1.6453555072203998));
	} else if (z <= 4.1e+35) {
		tmp = x + (y * ((a + (b / z)) / (z * (z * z))));
	} else {
		tmp = t_1 + ((y / z) * -36.52704169880642);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * 3.13060547623d0)
    if (z <= (-2.2d+42)) then
        tmp = t_1
    else if (z <= 6d-26) then
        tmp = x + (y * (b * 1.6453555072203998d0))
    else if (z <= 4.1d+35) then
        tmp = x + (y * ((a + (b / z)) / (z * (z * z))))
    else
        tmp = t_1 + ((y / z) * (-36.52704169880642d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * 3.13060547623);
	double tmp;
	if (z <= -2.2e+42) {
		tmp = t_1;
	} else if (z <= 6e-26) {
		tmp = x + (y * (b * 1.6453555072203998));
	} else if (z <= 4.1e+35) {
		tmp = x + (y * ((a + (b / z)) / (z * (z * z))));
	} else {
		tmp = t_1 + ((y / z) * -36.52704169880642);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y * 3.13060547623)
	tmp = 0
	if z <= -2.2e+42:
		tmp = t_1
	elif z <= 6e-26:
		tmp = x + (y * (b * 1.6453555072203998))
	elif z <= 4.1e+35:
		tmp = x + (y * ((a + (b / z)) / (z * (z * z))))
	else:
		tmp = t_1 + ((y / z) * -36.52704169880642)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y * 3.13060547623))
	tmp = 0.0
	if (z <= -2.2e+42)
		tmp = t_1;
	elseif (z <= 6e-26)
		tmp = Float64(x + Float64(y * Float64(b * 1.6453555072203998)));
	elseif (z <= 4.1e+35)
		tmp = Float64(x + Float64(y * Float64(Float64(a + Float64(b / z)) / Float64(z * Float64(z * z)))));
	else
		tmp = Float64(t_1 + Float64(Float64(y / z) * -36.52704169880642));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (y * 3.13060547623);
	tmp = 0.0;
	if (z <= -2.2e+42)
		tmp = t_1;
	elseif (z <= 6e-26)
		tmp = x + (y * (b * 1.6453555072203998));
	elseif (z <= 4.1e+35)
		tmp = x + (y * ((a + (b / z)) / (z * (z * z))));
	else
		tmp = t_1 + ((y / z) * -36.52704169880642);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.2e+42], t$95$1, If[LessEqual[z, 6e-26], N[(x + N[(y * N[(b * 1.6453555072203998), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.1e+35], N[(x + N[(y * N[(N[(a + N[(b / z), $MachinePrecision]), $MachinePrecision] / N[(z * N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(N[(y / z), $MachinePrecision] * -36.52704169880642), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.2000000000000001e42

   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. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{x + \frac{313060547623}{100000000000} \cdot y} \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{313060547623}{100000000000} \cdot y\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{313060547623}{100000000000}}\right)\right) \]

      3. *-lowering-*.f64 95.2%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\frac{313060547623}{100000000000}}\right)\right) \]

   5. Simplified 95.2%

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

   if -2.2000000000000001e42 < z < 6.00000000000000023e-26

   1. Initial program 98.9%

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

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \color{blue}{\left(b + a \cdot z\right)}\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right), z\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \left(a \cdot z\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right), \color{blue}{z}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \left(z \cdot a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right), z\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      3. *-lowering-*.f64 95.2%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \mathsf{*.f64}\left(z, a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right), z\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

   5. Simplified 95.2%

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

      1. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{b + z \cdot a}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}}}\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{b + z \cdot a}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \cdot \color{blue}{y}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{b + z \cdot a}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}}\right), \color{blue}{y}\right)\right) \]

   7. Applied egg-rr 95.3%

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

   8. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\color{blue}{\left(\frac{1000000000000}{607771387771} \cdot b\right)}, y\right)\right) \]
   9. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(b \cdot \frac{1000000000000}{607771387771}\right), y\right)\right) \]

      2. *-lowering-*.f64 81.4%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \frac{1000000000000}{607771387771}\right), y\right)\right) \]

   10. Simplified 81.4%

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

   if 6.00000000000000023e-26 < z < 4.0999999999999998e35

   1. Initial program 86.8%

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

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \color{blue}{\left(b + a \cdot z\right)}\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right), z\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \left(a \cdot z\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right), \color{blue}{z}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \left(z \cdot a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right), z\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      3. *-lowering-*.f64 79.6%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \mathsf{*.f64}\left(z, a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right), z\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

   5. Simplified 79.6%

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

      1. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{b + z \cdot a}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}}}\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{b + z \cdot a}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \cdot \color{blue}{y}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{b + z \cdot a}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}}\right), \color{blue}{y}\right)\right) \]

   7. Applied egg-rr 86.0%

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

   8. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \mathsf{*.f64}\left(z, a\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{119400905721}{10000000000}, \color{blue}{\left({z}^{3}\right)}\right)\right), \frac{607771387771}{1000000000000}\right)\right), y\right)\right) \]
   9. Step-by-step derivation

      1. cube-mult N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \mathsf{*.f64}\left(z, a\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{119400905721}{10000000000}, \left(z \cdot \left(z \cdot z\right)\right)\right)\right), \frac{607771387771}{1000000000000}\right)\right), y\right)\right) \]

      2. unpow2 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \mathsf{*.f64}\left(z, a\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{119400905721}{10000000000}, \left(z \cdot {z}^{2}\right)\right)\right), \frac{607771387771}{1000000000000}\right)\right), y\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \mathsf{*.f64}\left(z, a\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{119400905721}{10000000000}, \mathsf{*.f64}\left(z, \left({z}^{2}\right)\right)\right)\right), \frac{607771387771}{1000000000000}\right)\right), y\right)\right) \]

      4. unpow2 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \mathsf{*.f64}\left(z, a\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{119400905721}{10000000000}, \mathsf{*.f64}\left(z, \left(z \cdot z\right)\right)\right)\right), \frac{607771387771}{1000000000000}\right)\right), y\right)\right) \]

      5. *-lowering-*.f64 80.2%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \mathsf{*.f64}\left(z, a\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{119400905721}{10000000000}, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, z\right)\right)\right)\right), \frac{607771387771}{1000000000000}\right)\right), y\right)\right) \]

   10. Simplified 80.2%

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

   11. Taylor expanded in z around inf

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\color{blue}{\left(\frac{a + \frac{b}{z}}{{z}^{3}}\right)}, y\right)\right) \]
   12. Step-by-step derivation

       1. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(a + \frac{b}{z}\right), \left({z}^{3}\right)\right), y\right)\right) \]

       2. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(a, \left(\frac{b}{z}\right)\right), \left({z}^{3}\right)\right), y\right)\right) \]

       3. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(a, \mathsf{/.f64}\left(b, z\right)\right), \left({z}^{3}\right)\right), y\right)\right) \]

       4. cube-mult N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(a, \mathsf{/.f64}\left(b, z\right)\right), \left(z \cdot \left(z \cdot z\right)\right)\right), y\right)\right) \]

       5. unpow2 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(a, \mathsf{/.f64}\left(b, z\right)\right), \left(z \cdot {z}^{2}\right)\right), y\right)\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(a, \mathsf{/.f64}\left(b, z\right)\right), \mathsf{*.f64}\left(z, \left({z}^{2}\right)\right)\right), y\right)\right) \]

       7. unpow2 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(a, \mathsf{/.f64}\left(b, z\right)\right), \mathsf{*.f64}\left(z, \left(z \cdot z\right)\right)\right), y\right)\right) \]

       8. *-lowering-*.f64 80.0%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(a, \mathsf{/.f64}\left(b, z\right)\right), \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, z\right)\right)\right), y\right)\right) \]

   13. Simplified 80.0%

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

   if 4.0999999999999998e35 < z

   1. Initial program 9.4%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\left(x + \left(\frac{313060547623}{100000000000} \cdot y + \frac{55833770631}{5000000000} \cdot \frac{y}{z}\right)\right) - \frac{4769379582500641883561}{100000000000000000000} \cdot \frac{y}{z}} \]
   4. Step-by-step derivation

      1. associate-+r+ N/A

         \[\leadsto \left(\left(x + \frac{313060547623}{100000000000} \cdot y\right) + \frac{55833770631}{5000000000} \cdot \frac{y}{z}\right) - \color{blue}{\frac{4769379582500641883561}{100000000000000000000}} \cdot \frac{y}{z} \]

      2. associate--l+ N/A

         \[\leadsto \left(x + \frac{313060547623}{100000000000} \cdot y\right) + \color{blue}{\left(\frac{55833770631}{5000000000} \cdot \frac{y}{z} - \frac{4769379582500641883561}{100000000000000000000} \cdot \frac{y}{z}\right)} \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x + \frac{313060547623}{100000000000} \cdot y\right), \color{blue}{\left(\frac{55833770631}{5000000000} \cdot \frac{y}{z} - \frac{4769379582500641883561}{100000000000000000000} \cdot \frac{y}{z}\right)}\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \left(\frac{313060547623}{100000000000} \cdot y\right)\right), \left(\color{blue}{\frac{55833770631}{5000000000} \cdot \frac{y}{z}} - \frac{4769379582500641883561}{100000000000000000000} \cdot \frac{y}{z}\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \left(y \cdot \frac{313060547623}{100000000000}\right)\right), \left(\frac{55833770631}{5000000000} \cdot \color{blue}{\frac{y}{z}} - \frac{4769379582500641883561}{100000000000000000000} \cdot \frac{y}{z}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \left(\frac{55833770631}{5000000000} \cdot \color{blue}{\frac{y}{z}} - \frac{4769379582500641883561}{100000000000000000000} \cdot \frac{y}{z}\right)\right) \]

      7. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \left(\frac{y}{z} \cdot \color{blue}{\left(\frac{55833770631}{5000000000} - \frac{4769379582500641883561}{100000000000000000000}\right)}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{*.f64}\left(\left(\frac{y}{z}\right), \color{blue}{\left(\frac{55833770631}{5000000000} - \frac{4769379582500641883561}{100000000000000000000}\right)}\right)\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, z\right), \left(\color{blue}{\frac{55833770631}{5000000000}} - \frac{4769379582500641883561}{100000000000000000000}\right)\right)\right) \]

      10. metadata-eval 93.6%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, z\right), \frac{-3652704169880641883561}{100000000000000000000}\right)\right) \]

   5. Simplified 93.6%

      \[\leadsto \color{blue}{\left(x + y \cdot 3.13060547623\right) + \frac{y}{z} \cdot -36.52704169880642} \]
3. Recombined 4 regimes into one program.

4. Final simplification 86.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+42}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-26}:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998\right)\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+35}:\\ \;\;\;\;x + y \cdot \frac{a + \frac{b}{z}}{z \cdot \left(z \cdot z\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y \cdot 3.13060547623\right) + \frac{y}{z} \cdot -36.52704169880642\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 91.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot 3.13060547623\\ \mathbf{if}\;z \leq -2.2 \cdot 10^{+42}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+36}:\\ \;\;\;\;x + y \cdot \frac{b + z \cdot a}{0.607771387771 + z \cdot \left(z \cdot \left(z \cdot z\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1 + \frac{y}{z} \cdot -36.52704169880642\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* y 3.13060547623))))
   (if (<= z -2.2e+42)
     t_1
     (if (<= z 1.3e+36)
       (+ x (* y (/ (+ b (* z a)) (+ 0.607771387771 (* z (* z (* z z)))))))
       (+ t_1 (* (/ y z) -36.52704169880642))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * 3.13060547623);
	double tmp;
	if (z <= -2.2e+42) {
		tmp = t_1;
	} else if (z <= 1.3e+36) {
		tmp = x + (y * ((b + (z * a)) / (0.607771387771 + (z * (z * (z * z))))));
	} else {
		tmp = t_1 + ((y / z) * -36.52704169880642);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * 3.13060547623d0)
    if (z <= (-2.2d+42)) then
        tmp = t_1
    else if (z <= 1.3d+36) then
        tmp = x + (y * ((b + (z * a)) / (0.607771387771d0 + (z * (z * (z * z))))))
    else
        tmp = t_1 + ((y / z) * (-36.52704169880642d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * 3.13060547623);
	double tmp;
	if (z <= -2.2e+42) {
		tmp = t_1;
	} else if (z <= 1.3e+36) {
		tmp = x + (y * ((b + (z * a)) / (0.607771387771 + (z * (z * (z * z))))));
	} else {
		tmp = t_1 + ((y / z) * -36.52704169880642);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y * 3.13060547623)
	tmp = 0
	if z <= -2.2e+42:
		tmp = t_1
	elif z <= 1.3e+36:
		tmp = x + (y * ((b + (z * a)) / (0.607771387771 + (z * (z * (z * z))))))
	else:
		tmp = t_1 + ((y / z) * -36.52704169880642)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y * 3.13060547623))
	tmp = 0.0
	if (z <= -2.2e+42)
		tmp = t_1;
	elseif (z <= 1.3e+36)
		tmp = Float64(x + Float64(y * Float64(Float64(b + Float64(z * a)) / Float64(0.607771387771 + Float64(z * Float64(z * Float64(z * z)))))));
	else
		tmp = Float64(t_1 + Float64(Float64(y / z) * -36.52704169880642));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (y * 3.13060547623);
	tmp = 0.0;
	if (z <= -2.2e+42)
		tmp = t_1;
	elseif (z <= 1.3e+36)
		tmp = x + (y * ((b + (z * a)) / (0.607771387771 + (z * (z * (z * z))))));
	else
		tmp = t_1 + ((y / z) * -36.52704169880642);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.2e+42], t$95$1, If[LessEqual[z, 1.3e+36], N[(x + N[(y * N[(N[(b + N[(z * a), $MachinePrecision]), $MachinePrecision] / N[(0.607771387771 + N[(z * N[(z * N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(N[(y / z), $MachinePrecision] * -36.52704169880642), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.2000000000000001e42

   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. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{x + \frac{313060547623}{100000000000} \cdot y} \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{313060547623}{100000000000} \cdot y\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{313060547623}{100000000000}}\right)\right) \]

      3. *-lowering-*.f64 95.2%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\frac{313060547623}{100000000000}}\right)\right) \]

   5. Simplified 95.2%

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

   if -2.2000000000000001e42 < z < 1.3000000000000001e36

   1. Initial program 97.8%

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

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \color{blue}{\left(b + a \cdot z\right)}\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right), z\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \left(a \cdot z\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right), \color{blue}{z}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \left(z \cdot a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right), z\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      3. *-lowering-*.f64 93.8%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \mathsf{*.f64}\left(z, a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right), z\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

   5. Simplified 93.8%

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

      1. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{b + z \cdot a}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}}}\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{b + z \cdot a}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \cdot \color{blue}{y}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{b + z \cdot a}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}}\right), \color{blue}{y}\right)\right) \]

   7. Applied egg-rr 94.4%

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

   8. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \mathsf{*.f64}\left(z, a\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{119400905721}{10000000000}, \color{blue}{\left({z}^{3}\right)}\right)\right), \frac{607771387771}{1000000000000}\right)\right), y\right)\right) \]
   9. Step-by-step derivation

      1. cube-mult N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \mathsf{*.f64}\left(z, a\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{119400905721}{10000000000}, \left(z \cdot \left(z \cdot z\right)\right)\right)\right), \frac{607771387771}{1000000000000}\right)\right), y\right)\right) \]

      2. unpow2 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \mathsf{*.f64}\left(z, a\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{119400905721}{10000000000}, \left(z \cdot {z}^{2}\right)\right)\right), \frac{607771387771}{1000000000000}\right)\right), y\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \mathsf{*.f64}\left(z, a\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{119400905721}{10000000000}, \mathsf{*.f64}\left(z, \left({z}^{2}\right)\right)\right)\right), \frac{607771387771}{1000000000000}\right)\right), y\right)\right) \]

      4. unpow2 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \mathsf{*.f64}\left(z, a\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{119400905721}{10000000000}, \mathsf{*.f64}\left(z, \left(z \cdot z\right)\right)\right)\right), \frac{607771387771}{1000000000000}\right)\right), y\right)\right) \]

      5. *-lowering-*.f64 93.4%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \mathsf{*.f64}\left(z, a\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{119400905721}{10000000000}, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, z\right)\right)\right)\right), \frac{607771387771}{1000000000000}\right)\right), y\right)\right) \]

   10. Simplified 93.4%

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

   11. Taylor expanded in z around inf

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \mathsf{*.f64}\left(z, a\right)\right), \mathsf{+.f64}\left(\color{blue}{\left({z}^{4}\right)}, \frac{607771387771}{1000000000000}\right)\right), y\right)\right) \]
   12. Step-by-step derivation

       1. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \mathsf{*.f64}\left(z, a\right)\right), \mathsf{+.f64}\left(\left({z}^{\left(3 + 1\right)}\right), \frac{607771387771}{1000000000000}\right)\right), y\right)\right) \]

       2. pow-plus N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \mathsf{*.f64}\left(z, a\right)\right), \mathsf{+.f64}\left(\left({z}^{3} \cdot z\right), \frac{607771387771}{1000000000000}\right)\right), y\right)\right) \]

       3. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \mathsf{*.f64}\left(z, a\right)\right), \mathsf{+.f64}\left(\left(z \cdot {z}^{3}\right), \frac{607771387771}{1000000000000}\right)\right), y\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \mathsf{*.f64}\left(z, a\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left({z}^{3}\right)\right), \frac{607771387771}{1000000000000}\right)\right), y\right)\right) \]

       5. cube-mult N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \mathsf{*.f64}\left(z, a\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(z \cdot \left(z \cdot z\right)\right)\right), \frac{607771387771}{1000000000000}\right)\right), y\right)\right) \]

       6. unpow2 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \mathsf{*.f64}\left(z, a\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \left(z \cdot {z}^{2}\right)\right), \frac{607771387771}{1000000000000}\right)\right), y\right)\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \mathsf{*.f64}\left(z, a\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, \left({z}^{2}\right)\right)\right), \frac{607771387771}{1000000000000}\right)\right), y\right)\right) \]

       8. unpow2 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \mathsf{*.f64}\left(z, a\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, \left(z \cdot z\right)\right)\right), \frac{607771387771}{1000000000000}\right)\right), y\right)\right) \]

       9. *-lowering-*.f64 93.4%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \mathsf{*.f64}\left(z, a\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(z, z\right)\right)\right), \frac{607771387771}{1000000000000}\right)\right), y\right)\right) \]

   13. Simplified 93.4%

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

   if 1.3000000000000001e36 < z

   1. Initial program 9.4%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\left(x + \left(\frac{313060547623}{100000000000} \cdot y + \frac{55833770631}{5000000000} \cdot \frac{y}{z}\right)\right) - \frac{4769379582500641883561}{100000000000000000000} \cdot \frac{y}{z}} \]
   4. Step-by-step derivation

      1. associate-+r+ N/A

         \[\leadsto \left(\left(x + \frac{313060547623}{100000000000} \cdot y\right) + \frac{55833770631}{5000000000} \cdot \frac{y}{z}\right) - \color{blue}{\frac{4769379582500641883561}{100000000000000000000}} \cdot \frac{y}{z} \]

      2. associate--l+ N/A

         \[\leadsto \left(x + \frac{313060547623}{100000000000} \cdot y\right) + \color{blue}{\left(\frac{55833770631}{5000000000} \cdot \frac{y}{z} - \frac{4769379582500641883561}{100000000000000000000} \cdot \frac{y}{z}\right)} \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x + \frac{313060547623}{100000000000} \cdot y\right), \color{blue}{\left(\frac{55833770631}{5000000000} \cdot \frac{y}{z} - \frac{4769379582500641883561}{100000000000000000000} \cdot \frac{y}{z}\right)}\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \left(\frac{313060547623}{100000000000} \cdot y\right)\right), \left(\color{blue}{\frac{55833770631}{5000000000} \cdot \frac{y}{z}} - \frac{4769379582500641883561}{100000000000000000000} \cdot \frac{y}{z}\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \left(y \cdot \frac{313060547623}{100000000000}\right)\right), \left(\frac{55833770631}{5000000000} \cdot \color{blue}{\frac{y}{z}} - \frac{4769379582500641883561}{100000000000000000000} \cdot \frac{y}{z}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \left(\frac{55833770631}{5000000000} \cdot \color{blue}{\frac{y}{z}} - \frac{4769379582500641883561}{100000000000000000000} \cdot \frac{y}{z}\right)\right) \]

      7. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \left(\frac{y}{z} \cdot \color{blue}{\left(\frac{55833770631}{5000000000} - \frac{4769379582500641883561}{100000000000000000000}\right)}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{*.f64}\left(\left(\frac{y}{z}\right), \color{blue}{\left(\frac{55833770631}{5000000000} - \frac{4769379582500641883561}{100000000000000000000}\right)}\right)\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, z\right), \left(\color{blue}{\frac{55833770631}{5000000000}} - \frac{4769379582500641883561}{100000000000000000000}\right)\right)\right) \]

      10. metadata-eval 93.6%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, z\right), \frac{-3652704169880641883561}{100000000000000000000}\right)\right) \]

   5. Simplified 93.6%

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

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+42}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+36}:\\ \;\;\;\;x + y \cdot \frac{b + z \cdot a}{0.607771387771 + z \cdot \left(z \cdot \left(z \cdot z\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y \cdot 3.13060547623\right) + \frac{y}{z} \cdot -36.52704169880642\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 90.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -12.8:\\ \;\;\;\;y \cdot 3.13060547623 + \left(x - \frac{y \cdot 36.52704169880642}{z}\right)\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+33}:\\ \;\;\;\;x + y \cdot \frac{b + z \cdot a}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y \cdot 3.13060547623\right) + \frac{y}{z} \cdot -36.52704169880642\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -12.8)
   (+ (* y 3.13060547623) (- x (/ (* y 36.52704169880642) z)))
   (if (<= z 1.9e+33)
     (+ x (* y (/ (+ b (* z a)) (+ 0.607771387771 (* z 11.9400905721)))))
     (+ (+ x (* y 3.13060547623)) (* (/ y z) -36.52704169880642)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -12.8) {
		tmp = (y * 3.13060547623) + (x - ((y * 36.52704169880642) / z));
	} else if (z <= 1.9e+33) {
		tmp = x + (y * ((b + (z * a)) / (0.607771387771 + (z * 11.9400905721))));
	} else {
		tmp = (x + (y * 3.13060547623)) + ((y / z) * -36.52704169880642);
	}
	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)) then
        tmp = (y * 3.13060547623d0) + (x - ((y * 36.52704169880642d0) / z))
    else if (z <= 1.9d+33) then
        tmp = x + (y * ((b + (z * a)) / (0.607771387771d0 + (z * 11.9400905721d0))))
    else
        tmp = (x + (y * 3.13060547623d0)) + ((y / z) * (-36.52704169880642d0))
    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) {
		tmp = (y * 3.13060547623) + (x - ((y * 36.52704169880642) / z));
	} else if (z <= 1.9e+33) {
		tmp = x + (y * ((b + (z * a)) / (0.607771387771 + (z * 11.9400905721))));
	} else {
		tmp = (x + (y * 3.13060547623)) + ((y / z) * -36.52704169880642);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -12.8:
		tmp = (y * 3.13060547623) + (x - ((y * 36.52704169880642) / z))
	elif z <= 1.9e+33:
		tmp = x + (y * ((b + (z * a)) / (0.607771387771 + (z * 11.9400905721))))
	else:
		tmp = (x + (y * 3.13060547623)) + ((y / z) * -36.52704169880642)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -12.8)
		tmp = Float64(Float64(y * 3.13060547623) + Float64(x - Float64(Float64(y * 36.52704169880642) / z)));
	elseif (z <= 1.9e+33)
		tmp = Float64(x + Float64(y * Float64(Float64(b + Float64(z * a)) / Float64(0.607771387771 + Float64(z * 11.9400905721)))));
	else
		tmp = Float64(Float64(x + Float64(y * 3.13060547623)) + Float64(Float64(y / z) * -36.52704169880642));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -12.8)
		tmp = (y * 3.13060547623) + (x - ((y * 36.52704169880642) / z));
	elseif (z <= 1.9e+33)
		tmp = x + (y * ((b + (z * a)) / (0.607771387771 + (z * 11.9400905721))));
	else
		tmp = (x + (y * 3.13060547623)) + ((y / z) * -36.52704169880642);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -12.8], N[(N[(y * 3.13060547623), $MachinePrecision] + N[(x - N[(N[(y * 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.9e+33], N[(x + N[(y * N[(N[(b + N[(z * a), $MachinePrecision]), $MachinePrecision] / N[(0.607771387771 + N[(z * 11.9400905721), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision] + N[(N[(y / z), $MachinePrecision] * -36.52704169880642), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -12.800000000000001

   1. Initial program 19.0%

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

   3. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{x + \left(-1 \cdot \frac{\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y}{z} + \frac{313060547623}{100000000000} \cdot y\right)} \]
   4. Step-by-step derivation

      1. associate-+r+ N/A

         \[\leadsto \left(x + -1 \cdot \frac{\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y}{z}\right) + \color{blue}{\frac{313060547623}{100000000000} \cdot y} \]

      2. +-commutative N/A

         \[\leadsto \frac{313060547623}{100000000000} \cdot y + \color{blue}{\left(x + -1 \cdot \frac{\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y}{z}\right)} \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\frac{313060547623}{100000000000} \cdot y\right), \color{blue}{\left(x + -1 \cdot \frac{\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y}{z}\right)}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\left(y \cdot \frac{313060547623}{100000000000}\right), \left(\color{blue}{x} + -1 \cdot \frac{\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y}{z}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right), \left(\color{blue}{x} + -1 \cdot \frac{\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y}{z}\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right), \left(x + \left(\mathsf{neg}\left(\frac{\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y}{z}\right)\right)\right)\right) \]

      7. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right), \left(x - \color{blue}{\frac{\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y}{z}}\right)\right) \]

      8. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right), \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y}{z}\right)}\right)\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right), \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y\right), \color{blue}{z}\right)\right)\right) \]

      10. distribute-rgt-out-- N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right), \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(y \cdot \left(\frac{-55833770631}{5000000000} - \frac{-4769379582500641883561}{100000000000000000000}\right)\right), z\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right), \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \left(\frac{-55833770631}{5000000000} - \frac{-4769379582500641883561}{100000000000000000000}\right)\right), z\right)\right)\right) \]

      12. metadata-eval 85.3%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right), \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \frac{3652704169880641883561}{100000000000000000000}\right), z\right)\right)\right) \]

   5. Simplified 85.3%

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

   if -12.800000000000001 < z < 1.90000000000000001e33

   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

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \color{blue}{\left(b + a \cdot z\right)}\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right), z\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \left(a \cdot z\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right), \color{blue}{z}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \left(z \cdot a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right), z\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      3. *-lowering-*.f64 95.4%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \mathsf{*.f64}\left(z, a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right), z\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

   5. Simplified 95.4%

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

      1. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{b + z \cdot a}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}}}\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{b + z \cdot a}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \cdot \color{blue}{y}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{b + z \cdot a}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}}\right), \color{blue}{y}\right)\right) \]

   7. Applied egg-rr 96.1%

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

   8. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \mathsf{*.f64}\left(z, a\right)\right), \mathsf{+.f64}\left(\color{blue}{\left(\frac{119400905721}{10000000000} \cdot z\right)}, \frac{607771387771}{1000000000000}\right)\right), y\right)\right) \]
   9. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \mathsf{*.f64}\left(z, a\right)\right), \mathsf{+.f64}\left(\left(z \cdot \frac{119400905721}{10000000000}\right), \frac{607771387771}{1000000000000}\right)\right), y\right)\right) \]

      2. *-lowering-*.f64 94.9%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{+.f64}\left(b, \mathsf{*.f64}\left(z, a\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{119400905721}{10000000000}\right), \frac{607771387771}{1000000000000}\right)\right), y\right)\right) \]

   10. Simplified 94.9%

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

   if 1.90000000000000001e33 < z

   1. Initial program 9.4%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\left(x + \left(\frac{313060547623}{100000000000} \cdot y + \frac{55833770631}{5000000000} \cdot \frac{y}{z}\right)\right) - \frac{4769379582500641883561}{100000000000000000000} \cdot \frac{y}{z}} \]
   4. Step-by-step derivation

      1. associate-+r+ N/A

         \[\leadsto \left(\left(x + \frac{313060547623}{100000000000} \cdot y\right) + \frac{55833770631}{5000000000} \cdot \frac{y}{z}\right) - \color{blue}{\frac{4769379582500641883561}{100000000000000000000}} \cdot \frac{y}{z} \]

      2. associate--l+ N/A

         \[\leadsto \left(x + \frac{313060547623}{100000000000} \cdot y\right) + \color{blue}{\left(\frac{55833770631}{5000000000} \cdot \frac{y}{z} - \frac{4769379582500641883561}{100000000000000000000} \cdot \frac{y}{z}\right)} \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x + \frac{313060547623}{100000000000} \cdot y\right), \color{blue}{\left(\frac{55833770631}{5000000000} \cdot \frac{y}{z} - \frac{4769379582500641883561}{100000000000000000000} \cdot \frac{y}{z}\right)}\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \left(\frac{313060547623}{100000000000} \cdot y\right)\right), \left(\color{blue}{\frac{55833770631}{5000000000} \cdot \frac{y}{z}} - \frac{4769379582500641883561}{100000000000000000000} \cdot \frac{y}{z}\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \left(y \cdot \frac{313060547623}{100000000000}\right)\right), \left(\frac{55833770631}{5000000000} \cdot \color{blue}{\frac{y}{z}} - \frac{4769379582500641883561}{100000000000000000000} \cdot \frac{y}{z}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \left(\frac{55833770631}{5000000000} \cdot \color{blue}{\frac{y}{z}} - \frac{4769379582500641883561}{100000000000000000000} \cdot \frac{y}{z}\right)\right) \]

      7. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \left(\frac{y}{z} \cdot \color{blue}{\left(\frac{55833770631}{5000000000} - \frac{4769379582500641883561}{100000000000000000000}\right)}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{*.f64}\left(\left(\frac{y}{z}\right), \color{blue}{\left(\frac{55833770631}{5000000000} - \frac{4769379582500641883561}{100000000000000000000}\right)}\right)\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, z\right), \left(\color{blue}{\frac{55833770631}{5000000000}} - \frac{4769379582500641883561}{100000000000000000000}\right)\right)\right) \]

      10. metadata-eval 93.6%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, z\right), \frac{-3652704169880641883561}{100000000000000000000}\right)\right) \]

   5. Simplified 93.6%

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

4. Final simplification 92.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -12.8:\\ \;\;\;\;y \cdot 3.13060547623 + \left(x - \frac{y \cdot 36.52704169880642}{z}\right)\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+33}:\\ \;\;\;\;x + y \cdot \frac{b + z \cdot a}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y \cdot 3.13060547623\right) + \frac{y}{z} \cdot -36.52704169880642\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 83.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot 3.13060547623\\ \mathbf{if}\;z \leq -2.2 \cdot 10^{+42}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+31}:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 + \frac{y}{z} \cdot -36.52704169880642\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* y 3.13060547623))))
   (if (<= z -2.2e+42)
     t_1
     (if (<= z 9e+31)
       (+ x (* y (* b 1.6453555072203998)))
       (+ t_1 (* (/ y z) -36.52704169880642))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * 3.13060547623);
	double tmp;
	if (z <= -2.2e+42) {
		tmp = t_1;
	} else if (z <= 9e+31) {
		tmp = x + (y * (b * 1.6453555072203998));
	} else {
		tmp = t_1 + ((y / z) * -36.52704169880642);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * 3.13060547623d0)
    if (z <= (-2.2d+42)) then
        tmp = t_1
    else if (z <= 9d+31) then
        tmp = x + (y * (b * 1.6453555072203998d0))
    else
        tmp = t_1 + ((y / z) * (-36.52704169880642d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * 3.13060547623);
	double tmp;
	if (z <= -2.2e+42) {
		tmp = t_1;
	} else if (z <= 9e+31) {
		tmp = x + (y * (b * 1.6453555072203998));
	} else {
		tmp = t_1 + ((y / z) * -36.52704169880642);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y * 3.13060547623)
	tmp = 0
	if z <= -2.2e+42:
		tmp = t_1
	elif z <= 9e+31:
		tmp = x + (y * (b * 1.6453555072203998))
	else:
		tmp = t_1 + ((y / z) * -36.52704169880642)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y * 3.13060547623))
	tmp = 0.0
	if (z <= -2.2e+42)
		tmp = t_1;
	elseif (z <= 9e+31)
		tmp = Float64(x + Float64(y * Float64(b * 1.6453555072203998)));
	else
		tmp = Float64(t_1 + Float64(Float64(y / z) * -36.52704169880642));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (y * 3.13060547623);
	tmp = 0.0;
	if (z <= -2.2e+42)
		tmp = t_1;
	elseif (z <= 9e+31)
		tmp = x + (y * (b * 1.6453555072203998));
	else
		tmp = t_1 + ((y / z) * -36.52704169880642);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.2e+42], t$95$1, If[LessEqual[z, 9e+31], N[(x + N[(y * N[(b * 1.6453555072203998), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(N[(y / z), $MachinePrecision] * -36.52704169880642), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.2000000000000001e42

   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. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{x + \frac{313060547623}{100000000000} \cdot y} \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{313060547623}{100000000000} \cdot y\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{313060547623}{100000000000}}\right)\right) \]

      3. *-lowering-*.f64 95.2%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\frac{313060547623}{100000000000}}\right)\right) \]

   5. Simplified 95.2%

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

   if -2.2000000000000001e42 < z < 8.9999999999999992e31

   1. Initial program 97.8%

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

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \color{blue}{\left(b + a \cdot z\right)}\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right), z\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \left(a \cdot z\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right), \color{blue}{z}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \left(z \cdot a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right), z\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      3. *-lowering-*.f64 93.8%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \mathsf{*.f64}\left(z, a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right), z\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

   5. Simplified 93.8%

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

      1. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{b + z \cdot a}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}}}\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{b + z \cdot a}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \cdot \color{blue}{y}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{b + z \cdot a}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}}\right), \color{blue}{y}\right)\right) \]

   7. Applied egg-rr 94.4%

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

   8. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\color{blue}{\left(\frac{1000000000000}{607771387771} \cdot b\right)}, y\right)\right) \]
   9. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(b \cdot \frac{1000000000000}{607771387771}\right), y\right)\right) \]

      2. *-lowering-*.f64 78.6%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \frac{1000000000000}{607771387771}\right), y\right)\right) \]

   10. Simplified 78.6%

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

   if 8.9999999999999992e31 < z

   1. Initial program 9.4%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\left(x + \left(\frac{313060547623}{100000000000} \cdot y + \frac{55833770631}{5000000000} \cdot \frac{y}{z}\right)\right) - \frac{4769379582500641883561}{100000000000000000000} \cdot \frac{y}{z}} \]
   4. Step-by-step derivation

      1. associate-+r+ N/A

         \[\leadsto \left(\left(x + \frac{313060547623}{100000000000} \cdot y\right) + \frac{55833770631}{5000000000} \cdot \frac{y}{z}\right) - \color{blue}{\frac{4769379582500641883561}{100000000000000000000}} \cdot \frac{y}{z} \]

      2. associate--l+ N/A

         \[\leadsto \left(x + \frac{313060547623}{100000000000} \cdot y\right) + \color{blue}{\left(\frac{55833770631}{5000000000} \cdot \frac{y}{z} - \frac{4769379582500641883561}{100000000000000000000} \cdot \frac{y}{z}\right)} \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(x + \frac{313060547623}{100000000000} \cdot y\right), \color{blue}{\left(\frac{55833770631}{5000000000} \cdot \frac{y}{z} - \frac{4769379582500641883561}{100000000000000000000} \cdot \frac{y}{z}\right)}\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \left(\frac{313060547623}{100000000000} \cdot y\right)\right), \left(\color{blue}{\frac{55833770631}{5000000000} \cdot \frac{y}{z}} - \frac{4769379582500641883561}{100000000000000000000} \cdot \frac{y}{z}\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \left(y \cdot \frac{313060547623}{100000000000}\right)\right), \left(\frac{55833770631}{5000000000} \cdot \color{blue}{\frac{y}{z}} - \frac{4769379582500641883561}{100000000000000000000} \cdot \frac{y}{z}\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \left(\frac{55833770631}{5000000000} \cdot \color{blue}{\frac{y}{z}} - \frac{4769379582500641883561}{100000000000000000000} \cdot \frac{y}{z}\right)\right) \]

      7. distribute-rgt-out-- N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \left(\frac{y}{z} \cdot \color{blue}{\left(\frac{55833770631}{5000000000} - \frac{4769379582500641883561}{100000000000000000000}\right)}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{*.f64}\left(\left(\frac{y}{z}\right), \color{blue}{\left(\frac{55833770631}{5000000000} - \frac{4769379582500641883561}{100000000000000000000}\right)}\right)\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, z\right), \left(\color{blue}{\frac{55833770631}{5000000000}} - \frac{4769379582500641883561}{100000000000000000000}\right)\right)\right) \]

      10. metadata-eval 93.6%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \frac{313060547623}{100000000000}\right)\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, z\right), \frac{-3652704169880641883561}{100000000000000000000}\right)\right) \]

   5. Simplified 93.6%

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

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+42}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+31}:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y \cdot 3.13060547623\right) + \frac{y}{z} \cdot -36.52704169880642\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 83.4% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot 3.13060547623\\ \mathbf{if}\;z \leq -2.2 \cdot 10^{+42}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+31}:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* y 3.13060547623))))
   (if (<= z -2.2e+42)
     t_1
     (if (<= z 9e+31) (+ x (* y (* b 1.6453555072203998))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * 3.13060547623);
	double tmp;
	if (z <= -2.2e+42) {
		tmp = t_1;
	} else if (z <= 9e+31) {
		tmp = x + (y * (b * 1.6453555072203998));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * 3.13060547623d0)
    if (z <= (-2.2d+42)) then
        tmp = t_1
    else if (z <= 9d+31) then
        tmp = x + (y * (b * 1.6453555072203998d0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * 3.13060547623);
	double tmp;
	if (z <= -2.2e+42) {
		tmp = t_1;
	} else if (z <= 9e+31) {
		tmp = x + (y * (b * 1.6453555072203998));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y * 3.13060547623)
	tmp = 0
	if z <= -2.2e+42:
		tmp = t_1
	elif z <= 9e+31:
		tmp = x + (y * (b * 1.6453555072203998))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y * 3.13060547623))
	tmp = 0.0
	if (z <= -2.2e+42)
		tmp = t_1;
	elseif (z <= 9e+31)
		tmp = Float64(x + Float64(y * Float64(b * 1.6453555072203998)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (y * 3.13060547623);
	tmp = 0.0;
	if (z <= -2.2e+42)
		tmp = t_1;
	elseif (z <= 9e+31)
		tmp = x + (y * (b * 1.6453555072203998));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.2e+42], t$95$1, If[LessEqual[z, 9e+31], N[(x + N[(y * N[(b * 1.6453555072203998), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.2000000000000001e42 or 8.9999999999999992e31 < z

   1. Initial program 7.1%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{x + \frac{313060547623}{100000000000} \cdot y} \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{313060547623}{100000000000} \cdot y\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{313060547623}{100000000000}}\right)\right) \]

      3. *-lowering-*.f64 94.3%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\frac{313060547623}{100000000000}}\right)\right) \]

   5. Simplified 94.3%

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

   if -2.2000000000000001e42 < z < 8.9999999999999992e31

   1. Initial program 97.8%

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

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \color{blue}{\left(b + a \cdot z\right)}\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right), z\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \left(a \cdot z\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right), \color{blue}{z}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \left(z \cdot a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right), z\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      3. *-lowering-*.f64 93.8%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(b, \mathsf{*.f64}\left(z, a\right)\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right), z\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

   5. Simplified 93.8%

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

      1. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{b + z \cdot a}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}}}\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{b + z \cdot a}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}} \cdot \color{blue}{y}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{b + z \cdot a}{\left(\left(\left(z + \frac{15234687407}{1000000000}\right) \cdot z + \frac{314690115749}{10000000000}\right) \cdot z + \frac{119400905721}{10000000000}\right) \cdot z + \frac{607771387771}{1000000000000}}\right), \color{blue}{y}\right)\right) \]

   7. Applied egg-rr 94.4%

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

   8. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\color{blue}{\left(\frac{1000000000000}{607771387771} \cdot b\right)}, y\right)\right) \]
   9. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(b \cdot \frac{1000000000000}{607771387771}\right), y\right)\right) \]

      2. *-lowering-*.f64 78.6%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \frac{1000000000000}{607771387771}\right), y\right)\right) \]

   10. Simplified 78.6%

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

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+42}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+31}:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 83.4% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot 3.13060547623\\ \mathbf{if}\;z \leq -2.2 \cdot 10^{+42}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+31}:\\ \;\;\;\;x + b \cdot \left(y \cdot 1.6453555072203998\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* y 3.13060547623))))
   (if (<= z -2.2e+42)
     t_1
     (if (<= z 9e+31) (+ x (* b (* y 1.6453555072203998))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * 3.13060547623);
	double tmp;
	if (z <= -2.2e+42) {
		tmp = t_1;
	} else if (z <= 9e+31) {
		tmp = x + (b * (y * 1.6453555072203998));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * 3.13060547623d0)
    if (z <= (-2.2d+42)) then
        tmp = t_1
    else if (z <= 9d+31) then
        tmp = x + (b * (y * 1.6453555072203998d0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * 3.13060547623);
	double tmp;
	if (z <= -2.2e+42) {
		tmp = t_1;
	} else if (z <= 9e+31) {
		tmp = x + (b * (y * 1.6453555072203998));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y * 3.13060547623)
	tmp = 0
	if z <= -2.2e+42:
		tmp = t_1
	elif z <= 9e+31:
		tmp = x + (b * (y * 1.6453555072203998))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y * 3.13060547623))
	tmp = 0.0
	if (z <= -2.2e+42)
		tmp = t_1;
	elseif (z <= 9e+31)
		tmp = Float64(x + Float64(b * Float64(y * 1.6453555072203998)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (y * 3.13060547623);
	tmp = 0.0;
	if (z <= -2.2e+42)
		tmp = t_1;
	elseif (z <= 9e+31)
		tmp = x + (b * (y * 1.6453555072203998));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.2e+42], t$95$1, If[LessEqual[z, 9e+31], N[(x + N[(b * N[(y * 1.6453555072203998), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.2000000000000001e42 or 8.9999999999999992e31 < z

   1. Initial program 7.1%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{x + \frac{313060547623}{100000000000} \cdot y} \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{313060547623}{100000000000} \cdot y\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{313060547623}{100000000000}}\right)\right) \]

      3. *-lowering-*.f64 94.3%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\frac{313060547623}{100000000000}}\right)\right) \]

   5. Simplified 94.3%

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

   if -2.2000000000000001e42 < z < 8.9999999999999992e31

   1. Initial program 97.8%

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

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + \frac{1000000000000}{607771387771} \cdot \left(b \cdot y\right)} \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{1000000000000}{607771387771} \cdot \left(b \cdot y\right)\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(b \cdot y\right) \cdot \color{blue}{\frac{1000000000000}{607771387771}}\right)\right) \]

      3. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(b \cdot \color{blue}{\left(y \cdot \frac{1000000000000}{607771387771}\right)}\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \color{blue}{\left(y \cdot \frac{1000000000000}{607771387771}\right)}\right)\right) \]

      5. *-lowering-*.f64 78.6%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(y, \color{blue}{\frac{1000000000000}{607771387771}}\right)\right)\right) \]

   5. Simplified 78.6%

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

Alternative 12: 63.3% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot 3.13060547623\\ \mathbf{if}\;z \leq -4.4 \cdot 10^{-66}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-9}:\\ \;\;\;\;y \cdot \left(b \cdot 1.6453555072203998\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* y 3.13060547623))))
   (if (<= z -4.4e-66)
     t_1
     (if (<= z 9.5e-9) (* y (* b 1.6453555072203998)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * 3.13060547623);
	double tmp;
	if (z <= -4.4e-66) {
		tmp = t_1;
	} else if (z <= 9.5e-9) {
		tmp = y * (b * 1.6453555072203998);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * 3.13060547623d0)
    if (z <= (-4.4d-66)) then
        tmp = t_1
    else if (z <= 9.5d-9) then
        tmp = y * (b * 1.6453555072203998d0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * 3.13060547623);
	double tmp;
	if (z <= -4.4e-66) {
		tmp = t_1;
	} else if (z <= 9.5e-9) {
		tmp = y * (b * 1.6453555072203998);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y * 3.13060547623)
	tmp = 0
	if z <= -4.4e-66:
		tmp = t_1
	elif z <= 9.5e-9:
		tmp = y * (b * 1.6453555072203998)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y * 3.13060547623))
	tmp = 0.0
	if (z <= -4.4e-66)
		tmp = t_1;
	elseif (z <= 9.5e-9)
		tmp = Float64(y * Float64(b * 1.6453555072203998));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (y * 3.13060547623);
	tmp = 0.0;
	if (z <= -4.4e-66)
		tmp = t_1;
	elseif (z <= 9.5e-9)
		tmp = y * (b * 1.6453555072203998);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.4e-66], t$95$1, If[LessEqual[z, 9.5e-9], N[(y * N[(b * 1.6453555072203998), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.4000000000000002e-66 or 9.5000000000000007e-9 < z

   1. Initial program 28.7%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{x + \frac{313060547623}{100000000000} \cdot y} \]
   4. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{313060547623}{100000000000} \cdot y\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{313060547623}{100000000000}}\right)\right) \]

      3. *-lowering-*.f64 82.4%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\frac{313060547623}{100000000000}}\right)\right) \]

   5. Simplified 82.4%

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

   if -4.4000000000000002e-66 < z < 9.5000000000000007e-9

   1. Initial program 99.7%

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

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{\frac{b \cdot y}{\frac{607771387771}{1000000000000} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)}} \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(b \cdot y\right), \color{blue}{\left(\frac{607771387771}{1000000000000} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot b\right), \left(\color{blue}{\frac{607771387771}{1000000000000}} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), \left(\color{blue}{\frac{607771387771}{1000000000000}} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), \mathsf{+.f64}\left(\frac{607771387771}{1000000000000}, \color{blue}{\left(z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)\right)}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), \mathsf{+.f64}\left(\frac{607771387771}{1000000000000}, \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)}\right)\right)\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), \mathsf{+.f64}\left(\frac{607771387771}{1000000000000}, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{119400905721}{10000000000}, \color{blue}{\left(z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)}\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), \mathsf{+.f64}\left(\frac{607771387771}{1000000000000}, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{119400905721}{10000000000}, \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)}\right)\right)\right)\right)\right) \]

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), \mathsf{+.f64}\left(\frac{607771387771}{1000000000000}, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{119400905721}{10000000000}, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{314690115749}{10000000000}, \color{blue}{\left(z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)}\right)\right)\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), \mathsf{+.f64}\left(\frac{607771387771}{1000000000000}, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{119400905721}{10000000000}, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{314690115749}{10000000000}, \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{15234687407}{1000000000} + z\right)}\right)\right)\right)\right)\right)\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), \mathsf{+.f64}\left(\frac{607771387771}{1000000000000}, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{119400905721}{10000000000}, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{314690115749}{10000000000}, \mathsf{*.f64}\left(z, \left(z + \color{blue}{\frac{15234687407}{1000000000}}\right)\right)\right)\right)\right)\right)\right)\right) \]

      11. +-lowering-+.f64 52.5%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), \mathsf{+.f64}\left(\frac{607771387771}{1000000000000}, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{119400905721}{10000000000}, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{314690115749}{10000000000}, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(z, \color{blue}{\frac{15234687407}{1000000000}}\right)\right)\right)\right)\right)\right)\right)\right) \]

   5. Simplified 52.5%

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

   6. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\frac{1000000000000}{607771387771} \cdot \left(b \cdot y\right)} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(b \cdot y\right) \cdot \color{blue}{\frac{1000000000000}{607771387771}} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(b \cdot y\right), \color{blue}{\frac{1000000000000}{607771387771}}\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\left(y \cdot b\right), \frac{1000000000000}{607771387771}\right) \]

      4. *-lowering-*.f64 52.5%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, b\right), \frac{1000000000000}{607771387771}\right) \]

   8. Simplified 52.5%

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

      1. associate-*l* N/A

         \[\leadsto y \cdot \color{blue}{\left(b \cdot \frac{1000000000000}{607771387771}\right)} \]

      2. *-commutative N/A

         \[\leadsto \left(b \cdot \frac{1000000000000}{607771387771}\right) \cdot \color{blue}{y} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(b \cdot \frac{1000000000000}{607771387771}\right), \color{blue}{y}\right) \]

      4. *-lowering-*.f64 52.6%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \frac{1000000000000}{607771387771}\right), y\right) \]

   10. Applied egg-rr 52.6%

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

4. Final simplification 69.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{-66}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-9}:\\ \;\;\;\;y \cdot \left(b \cdot 1.6453555072203998\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 49.8% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{-134}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-5}:\\ \;\;\;\;y \cdot \left(b \cdot 1.6453555072203998\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -1.35e-134) x (if (<= x 9.5e-5) (* y (* b 1.6453555072203998)) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.35e-134) {
		tmp = x;
	} else if (x <= 9.5e-5) {
		tmp = y * (b * 1.6453555072203998);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-1.35d-134)) then
        tmp = x
    else if (x <= 9.5d-5) then
        tmp = y * (b * 1.6453555072203998d0)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.35e-134) {
		tmp = x;
	} else if (x <= 9.5e-5) {
		tmp = y * (b * 1.6453555072203998);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -1.35e-134:
		tmp = x
	elif x <= 9.5e-5:
		tmp = y * (b * 1.6453555072203998)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -1.35e-134)
		tmp = x;
	elseif (x <= 9.5e-5)
		tmp = Float64(y * Float64(b * 1.6453555072203998));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -1.35e-134)
		tmp = x;
	elseif (x <= 9.5e-5)
		tmp = y * (b * 1.6453555072203998);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -1.35e-134], x, If[LessEqual[x, 9.5e-5], N[(y * N[(b * 1.6453555072203998), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.3499999999999999e-134 or 9.5000000000000005e-5 < x

   1. Initial program 57.2%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 58.8%

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

   if -1.3499999999999999e-134 < x < 9.5000000000000005e-5

   1. Initial program 65.3%

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

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{\frac{b \cdot y}{\frac{607771387771}{1000000000000} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)}} \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(b \cdot y\right), \color{blue}{\left(\frac{607771387771}{1000000000000} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot b\right), \left(\color{blue}{\frac{607771387771}{1000000000000}} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), \left(\color{blue}{\frac{607771387771}{1000000000000}} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), \mathsf{+.f64}\left(\frac{607771387771}{1000000000000}, \color{blue}{\left(z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)\right)}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), \mathsf{+.f64}\left(\frac{607771387771}{1000000000000}, \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)}\right)\right)\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), \mathsf{+.f64}\left(\frac{607771387771}{1000000000000}, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{119400905721}{10000000000}, \color{blue}{\left(z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)}\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), \mathsf{+.f64}\left(\frac{607771387771}{1000000000000}, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{119400905721}{10000000000}, \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)}\right)\right)\right)\right)\right) \]

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), \mathsf{+.f64}\left(\frac{607771387771}{1000000000000}, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{119400905721}{10000000000}, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{314690115749}{10000000000}, \color{blue}{\left(z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)}\right)\right)\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), \mathsf{+.f64}\left(\frac{607771387771}{1000000000000}, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{119400905721}{10000000000}, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{314690115749}{10000000000}, \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{15234687407}{1000000000} + z\right)}\right)\right)\right)\right)\right)\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), \mathsf{+.f64}\left(\frac{607771387771}{1000000000000}, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{119400905721}{10000000000}, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{314690115749}{10000000000}, \mathsf{*.f64}\left(z, \left(z + \color{blue}{\frac{15234687407}{1000000000}}\right)\right)\right)\right)\right)\right)\right)\right) \]

      11. +-lowering-+.f64 42.0%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), \mathsf{+.f64}\left(\frac{607771387771}{1000000000000}, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{119400905721}{10000000000}, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{314690115749}{10000000000}, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(z, \color{blue}{\frac{15234687407}{1000000000}}\right)\right)\right)\right)\right)\right)\right)\right) \]

   5. Simplified 42.0%

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

   6. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\frac{1000000000000}{607771387771} \cdot \left(b \cdot y\right)} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(b \cdot y\right) \cdot \color{blue}{\frac{1000000000000}{607771387771}} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(b \cdot y\right), \color{blue}{\frac{1000000000000}{607771387771}}\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\left(y \cdot b\right), \frac{1000000000000}{607771387771}\right) \]

      4. *-lowering-*.f64 42.0%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, b\right), \frac{1000000000000}{607771387771}\right) \]

   8. Simplified 42.0%

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

      1. associate-*l* N/A

         \[\leadsto y \cdot \color{blue}{\left(b \cdot \frac{1000000000000}{607771387771}\right)} \]

      2. *-commutative N/A

         \[\leadsto \left(b \cdot \frac{1000000000000}{607771387771}\right) \cdot \color{blue}{y} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(b \cdot \frac{1000000000000}{607771387771}\right), \color{blue}{y}\right) \]

      4. *-lowering-*.f64 42.1%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, \frac{1000000000000}{607771387771}\right), y\right) \]

   10. Applied egg-rr 42.1%

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

4. Final simplification 51.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{-134}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-5}:\\ \;\;\;\;y \cdot \left(b \cdot 1.6453555072203998\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 49.7% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{-135}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 0.0105:\\ \;\;\;\;b \cdot \left(y \cdot 1.6453555072203998\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -3.4e-135) x (if (<= x 0.0105) (* b (* y 1.6453555072203998)) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -3.4e-135) {
		tmp = x;
	} else if (x <= 0.0105) {
		tmp = b * (y * 1.6453555072203998);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-3.4d-135)) then
        tmp = x
    else if (x <= 0.0105d0) then
        tmp = b * (y * 1.6453555072203998d0)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -3.4e-135) {
		tmp = x;
	} else if (x <= 0.0105) {
		tmp = b * (y * 1.6453555072203998);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -3.4e-135:
		tmp = x
	elif x <= 0.0105:
		tmp = b * (y * 1.6453555072203998)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -3.4e-135)
		tmp = x;
	elseif (x <= 0.0105)
		tmp = Float64(b * Float64(y * 1.6453555072203998));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -3.4e-135)
		tmp = x;
	elseif (x <= 0.0105)
		tmp = b * (y * 1.6453555072203998);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -3.4e-135], x, If[LessEqual[x, 0.0105], N[(b * N[(y * 1.6453555072203998), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -3.39999999999999989e-135 or 0.0105000000000000007 < x

   1. Initial program 57.2%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 58.8%

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

   if -3.39999999999999989e-135 < x < 0.0105000000000000007

   1. Initial program 65.3%

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

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{\frac{b \cdot y}{\frac{607771387771}{1000000000000} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)}} \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(b \cdot y\right), \color{blue}{\left(\frac{607771387771}{1000000000000} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot b\right), \left(\color{blue}{\frac{607771387771}{1000000000000}} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), \left(\color{blue}{\frac{607771387771}{1000000000000}} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), \mathsf{+.f64}\left(\frac{607771387771}{1000000000000}, \color{blue}{\left(z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)\right)}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), \mathsf{+.f64}\left(\frac{607771387771}{1000000000000}, \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)}\right)\right)\right) \]

      6. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), \mathsf{+.f64}\left(\frac{607771387771}{1000000000000}, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{119400905721}{10000000000}, \color{blue}{\left(z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)}\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), \mathsf{+.f64}\left(\frac{607771387771}{1000000000000}, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{119400905721}{10000000000}, \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)}\right)\right)\right)\right)\right) \]

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), \mathsf{+.f64}\left(\frac{607771387771}{1000000000000}, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{119400905721}{10000000000}, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{314690115749}{10000000000}, \color{blue}{\left(z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)}\right)\right)\right)\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), \mathsf{+.f64}\left(\frac{607771387771}{1000000000000}, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{119400905721}{10000000000}, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{314690115749}{10000000000}, \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{15234687407}{1000000000} + z\right)}\right)\right)\right)\right)\right)\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), \mathsf{+.f64}\left(\frac{607771387771}{1000000000000}, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{119400905721}{10000000000}, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{314690115749}{10000000000}, \mathsf{*.f64}\left(z, \left(z + \color{blue}{\frac{15234687407}{1000000000}}\right)\right)\right)\right)\right)\right)\right)\right) \]

      11. +-lowering-+.f64 42.0%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), \mathsf{+.f64}\left(\frac{607771387771}{1000000000000}, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{119400905721}{10000000000}, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\frac{314690115749}{10000000000}, \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(z, \color{blue}{\frac{15234687407}{1000000000}}\right)\right)\right)\right)\right)\right)\right)\right) \]

   5. Simplified 42.0%

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

   6. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\frac{1000000000000}{607771387771} \cdot \left(b \cdot y\right)} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(b \cdot y\right) \cdot \color{blue}{\frac{1000000000000}{607771387771}} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(b \cdot y\right), \color{blue}{\frac{1000000000000}{607771387771}}\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\left(y \cdot b\right), \frac{1000000000000}{607771387771}\right) \]

      4. *-lowering-*.f64 42.0%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, b\right), \frac{1000000000000}{607771387771}\right) \]

   8. Simplified 42.0%

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

      1. *-commutative N/A

         \[\leadsto \frac{1000000000000}{607771387771} \cdot \color{blue}{\left(y \cdot b\right)} \]

      2. associate-*r* N/A

         \[\leadsto \left(\frac{1000000000000}{607771387771} \cdot y\right) \cdot \color{blue}{b} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{1000000000000}{607771387771} \cdot y\right), \color{blue}{b}\right) \]

      4. *-lowering-*.f64 42.1%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1000000000000}{607771387771}, y\right), b\right) \]

   10. Applied egg-rr 42.1%

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

4. Final simplification 51.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{-135}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 0.0105:\\ \;\;\;\;b \cdot \left(y \cdot 1.6453555072203998\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 45.0% accurate, 37.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

function code(x, y, z, t, a, b)
	return x
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := x

Derivation

1. Initial program 60.6%

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

3. Taylor expanded in x around inf

   \[\leadsto \color{blue}{x} \]
4. Step-by-step derivation

5. Simplified 40.5%

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

Developer Target 1: 98.5% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024158 
(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))))