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

Percentage Accurate: 58.9% → 97.7%

Time: 17.7s

Alternatives: 16

Speedup: 2.2×

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: 97.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771\\ t_2 := b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right)\right)\right)\\ \mathbf{if}\;\frac{y \cdot t\_2}{t\_1} \leq \infty:\\ \;\;\;\;y \cdot \frac{t\_2}{t\_1} + x\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x + y \cdot 3.13060547623\right) + \left(\left(\frac{y \cdot 11.1667541262}{z} + y \cdot \frac{t}{z \cdot z}\right) - \frac{y \cdot -556.47806218377}{z \cdot z}\right)\right) - \left(\frac{y \cdot 47.69379582500642}{z} + \frac{y \cdot 98.5170599679272}{z \cdot z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+
          (*
           z
           (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721))
          0.607771387771))
        (t_2
         (+
          b
          (*
           z
           (+ a (* z (+ t (* z (+ (* z 3.13060547623) 11.1667541262)))))))))
   (if (<= (/ (* y t_2) t_1) INFINITY)
     (+ (* y (/ t_2 t_1)) x)
     (-
      (+
       (+ x (* y 3.13060547623))
       (-
        (+ (/ (* y 11.1667541262) z) (* y (/ t (* z z))))
        (/ (* y -556.47806218377) (* z z))))
      (+ (/ (* y 47.69379582500642) z) (/ (* y 98.5170599679272) (* z z)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771;
	double t_2 = b + (z * (a + (z * (t + (z * ((z * 3.13060547623) + 11.1667541262))))));
	double tmp;
	if (((y * t_2) / t_1) <= ((double) INFINITY)) {
		tmp = (y * (t_2 / t_1)) + x;
	} else {
		tmp = ((x + (y * 3.13060547623)) + ((((y * 11.1667541262) / z) + (y * (t / (z * z)))) - ((y * -556.47806218377) / (z * z)))) - (((y * 47.69379582500642) / z) + ((y * 98.5170599679272) / (z * z)));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771;
	double t_2 = b + (z * (a + (z * (t + (z * ((z * 3.13060547623) + 11.1667541262))))));
	double tmp;
	if (((y * t_2) / t_1) <= Double.POSITIVE_INFINITY) {
		tmp = (y * (t_2 / t_1)) + x;
	} else {
		tmp = ((x + (y * 3.13060547623)) + ((((y * 11.1667541262) / z) + (y * (t / (z * z)))) - ((y * -556.47806218377) / (z * z)))) - (((y * 47.69379582500642) / z) + ((y * 98.5170599679272) / (z * z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771
	t_2 = b + (z * (a + (z * (t + (z * ((z * 3.13060547623) + 11.1667541262))))))
	tmp = 0
	if ((y * t_2) / t_1) <= math.inf:
		tmp = (y * (t_2 / t_1)) + x
	else:
		tmp = ((x + (y * 3.13060547623)) + ((((y * 11.1667541262) / z) + (y * (t / (z * z)))) - ((y * -556.47806218377) / (z * z)))) - (((y * 47.69379582500642) / z) + ((y * 98.5170599679272) / (z * z)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)
	t_2 = Float64(b + Float64(z * Float64(a + Float64(z * Float64(t + Float64(z * Float64(Float64(z * 3.13060547623) + 11.1667541262)))))))
	tmp = 0.0
	if (Float64(Float64(y * t_2) / t_1) <= Inf)
		tmp = Float64(Float64(y * Float64(t_2 / t_1)) + x);
	else
		tmp = Float64(Float64(Float64(x + Float64(y * 3.13060547623)) + Float64(Float64(Float64(Float64(y * 11.1667541262) / z) + Float64(y * Float64(t / Float64(z * z)))) - Float64(Float64(y * -556.47806218377) / Float64(z * z)))) - Float64(Float64(Float64(y * 47.69379582500642) / z) + Float64(Float64(y * 98.5170599679272) / Float64(z * z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771;
	t_2 = b + (z * (a + (z * (t + (z * ((z * 3.13060547623) + 11.1667541262))))));
	tmp = 0.0;
	if (((y * t_2) / t_1) <= Inf)
		tmp = (y * (t_2 / t_1)) + x;
	else
		tmp = ((x + (y * 3.13060547623)) + ((((y * 11.1667541262) / z) + (y * (t / (z * z)))) - ((y * -556.47806218377) / (z * z)))) - (((y * 47.69379582500642) / z) + ((y * 98.5170599679272) / (z * z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z * N[(N[(z * N[(N[(z * N[(z + 15.234687407), $MachinePrecision]), $MachinePrecision] + 31.4690115749), $MachinePrecision]), $MachinePrecision] + 11.9400905721), $MachinePrecision]), $MachinePrecision] + 0.607771387771), $MachinePrecision]}, Block[{t$95$2 = N[(b + N[(z * N[(a + N[(z * N[(t + N[(z * N[(N[(z * 3.13060547623), $MachinePrecision] + 11.1667541262), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(y * t$95$2), $MachinePrecision] / t$95$1), $MachinePrecision], Infinity], N[(N[(y * N[(t$95$2 / t$95$1), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(N[(N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(N[(y * 11.1667541262), $MachinePrecision] / z), $MachinePrecision] + N[(y * N[(t / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y * -556.47806218377), $MachinePrecision] / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(y * 47.69379582500642), $MachinePrecision] / z), $MachinePrecision] + N[(N[(y * 98.5170599679272), $MachinePrecision] / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 93.2%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   2. Add Preprocessing
   3. 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 97.3%

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

   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

      \[\leadsto \color{blue}{\left(x + \left(\frac{313060547623}{100000000000} \cdot y + \left(\frac{55833770631}{5000000000} \cdot \frac{y}{z} + \frac{t \cdot y}{{z}^{2}}\right)\right)\right) - \left(\frac{15234687407}{1000000000} \cdot \frac{\frac{55833770631}{5000000000} \cdot y - \frac{4769379582500641883561}{100000000000000000000} \cdot y}{{z}^{2}} + \left(\frac{4769379582500641883561}{100000000000000000000} \cdot \frac{y}{z} + \frac{98517059967927196814627}{1000000000000000000000} \cdot \frac{y}{{z}^{2}}\right)\right)} \]

   5. Simplified 98.9%

      \[\leadsto \color{blue}{\left(\left(x + y \cdot 3.13060547623\right) + \left(\left(\frac{y \cdot 11.1667541262}{z} + y \cdot \frac{t}{z \cdot z}\right) - \frac{y \cdot -556.47806218377}{z \cdot z}\right)\right) - \left(\frac{y \cdot 47.69379582500642}{z} + \frac{y \cdot 98.5170599679272}{z \cdot z}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 97.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right)\right)\right)\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771} \leq \infty:\\ \;\;\;\;y \cdot \frac{b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right)\right)\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771} + x\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x + y \cdot 3.13060547623\right) + \left(\left(\frac{y \cdot 11.1667541262}{z} + y \cdot \frac{t}{z \cdot z}\right) - \frac{y \cdot -556.47806218377}{z \cdot z}\right)\right) - \left(\frac{y \cdot 47.69379582500642}{z} + \frac{y \cdot 98.5170599679272}{z \cdot z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 97.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771\\ t_2 := b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right)\right)\right)\\ \mathbf{if}\;\frac{y \cdot t\_2}{t\_1} \leq \infty:\\ \;\;\;\;y \cdot \frac{t\_2}{t\_1} + x\\ \mathbf{else}:\\ \;\;\;\;\left(x + y \cdot 3.13060547623\right) + \frac{y}{z} \cdot -36.52704169880642\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+
          (*
           z
           (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721))
          0.607771387771))
        (t_2
         (+
          b
          (*
           z
           (+ a (* z (+ t (* z (+ (* z 3.13060547623) 11.1667541262)))))))))
   (if (<= (/ (* y t_2) t_1) INFINITY)
     (+ (* y (/ t_2 t_1)) x)
     (+ (+ x (* y 3.13060547623)) (* (/ y z) -36.52704169880642)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771;
	double t_2 = b + (z * (a + (z * (t + (z * ((z * 3.13060547623) + 11.1667541262))))));
	double tmp;
	if (((y * t_2) / t_1) <= ((double) INFINITY)) {
		tmp = (y * (t_2 / t_1)) + x;
	} else {
		tmp = (x + (y * 3.13060547623)) + ((y / z) * -36.52704169880642);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771;
	double t_2 = b + (z * (a + (z * (t + (z * ((z * 3.13060547623) + 11.1667541262))))));
	double tmp;
	if (((y * t_2) / t_1) <= Double.POSITIVE_INFINITY) {
		tmp = (y * (t_2 / t_1)) + x;
	} else {
		tmp = (x + (y * 3.13060547623)) + ((y / z) * -36.52704169880642);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771
	t_2 = b + (z * (a + (z * (t + (z * ((z * 3.13060547623) + 11.1667541262))))))
	tmp = 0
	if ((y * t_2) / t_1) <= math.inf:
		tmp = (y * (t_2 / t_1)) + x
	else:
		tmp = (x + (y * 3.13060547623)) + ((y / z) * -36.52704169880642)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)
	t_2 = Float64(b + Float64(z * Float64(a + Float64(z * Float64(t + Float64(z * Float64(Float64(z * 3.13060547623) + 11.1667541262)))))))
	tmp = 0.0
	if (Float64(Float64(y * t_2) / t_1) <= Inf)
		tmp = Float64(Float64(y * Float64(t_2 / t_1)) + x);
	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)
	t_1 = (z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771;
	t_2 = b + (z * (a + (z * (t + (z * ((z * 3.13060547623) + 11.1667541262))))));
	tmp = 0.0;
	if (((y * t_2) / t_1) <= Inf)
		tmp = (y * (t_2 / t_1)) + x;
	else
		tmp = (x + (y * 3.13060547623)) + ((y / z) * -36.52704169880642);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z * N[(N[(z * N[(N[(z * N[(z + 15.234687407), $MachinePrecision]), $MachinePrecision] + 31.4690115749), $MachinePrecision]), $MachinePrecision] + 11.9400905721), $MachinePrecision]), $MachinePrecision] + 0.607771387771), $MachinePrecision]}, Block[{t$95$2 = N[(b + N[(z * N[(a + N[(z * N[(t + N[(z * N[(N[(z * 3.13060547623), $MachinePrecision] + 11.1667541262), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(y * t$95$2), $MachinePrecision] / t$95$1), $MachinePrecision], Infinity], N[(N[(y * N[(t$95$2 / t$95$1), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision] + N[(N[(y / z), $MachinePrecision] * -36.52704169880642), $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 93.2%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   2. Add Preprocessing
   3. 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 97.3%

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

   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

      \[\leadsto \color{blue}{\left(x + \left(\frac{313060547623}{100000000000} \cdot y + \frac{55833770631}{5000000000} \cdot \frac{y}{z}\right)\right) - \frac{4769379582500641883561}{100000000000000000000} \cdot \frac{y}{z}} \]
   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 97.8%

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

   5. Simplified 97.8%

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

4. Final simplification 97.5%

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

Alternative 3: 94.8% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y * Float64(b + Float64(z * Float64(a + Float64(z * Float64(t + Float64(z * Float64(Float64(z * 3.13060547623) + 11.1667541262)))))))) / Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = Float64(t_1 + x);
	else
		tmp = Float64(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)
	t_1 = (y * (b + (z * (a + (z * (t + (z * ((z * 3.13060547623) + 11.1667541262)))))))) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771);
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1 + x;
	else
		tmp = (x + (y * 3.13060547623)) + ((y / z) * -36.52704169880642);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y * N[(b + N[(z * N[(a + N[(z * N[(t + N[(z * N[(N[(z * 3.13060547623), $MachinePrecision] + 11.1667541262), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(z * N[(N[(z * N[(N[(z * N[(z + 15.234687407), $MachinePrecision]), $MachinePrecision] + 31.4690115749), $MachinePrecision]), $MachinePrecision] + 11.9400905721), $MachinePrecision]), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], N[(t$95$1 + x), $MachinePrecision], N[(N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision] + N[(N[(y / z), $MachinePrecision] * -36.52704169880642), $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 93.2%

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

   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

      \[\leadsto \color{blue}{\left(x + \left(\frac{313060547623}{100000000000} \cdot y + \frac{55833770631}{5000000000} \cdot \frac{y}{z}\right)\right) - \frac{4769379582500641883561}{100000000000000000000} \cdot \frac{y}{z}} \]
   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 97.8%

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

   5. Simplified 97.8%

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

4. Final simplification 94.9%

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

Alternative 4: 93.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot 3.13060547623\\ \mathbf{if}\;z \leq -3.3 \cdot 10^{+58}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2:\\ \;\;\;\;x + \frac{y \cdot b + z \cdot \left(y \cdot a + y \cdot \left(z \cdot t\right)\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+60}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right)\right)\right)\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{else}:\\ \;\;\;\;t\_1 + \frac{y}{z} \cdot -36.52704169880642\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* y 3.13060547623))))
   (if (<= z -3.3e+58)
     t_1
     (if (<= z -2.0)
       (+
        x
        (/
         (+ (* y b) (* z (+ (* y a) (* y (* z t)))))
         (+
          (*
           z
           (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721))
          0.607771387771)))
       (if (<= z 1.1e+60)
         (+
          x
          (/
           (*
            y
            (+
             b
             (*
              z
              (+ a (* z (+ t (* z (+ (* z 3.13060547623) 11.1667541262))))))))
           (+ 0.607771387771 (* z 11.9400905721))))
         (+ 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 <= -3.3e+58) {
		tmp = t_1;
	} else if (z <= -2.0) {
		tmp = x + (((y * b) + (z * ((y * a) + (y * (z * t))))) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771));
	} else if (z <= 1.1e+60) {
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * ((z * 3.13060547623) + 11.1667541262)))))))) / (0.607771387771 + (z * 11.9400905721)));
	} 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 <= (-3.3d+58)) then
        tmp = t_1
    else if (z <= (-2.0d0)) then
        tmp = x + (((y * b) + (z * ((y * a) + (y * (z * t))))) / ((z * ((z * ((z * (z + 15.234687407d0)) + 31.4690115749d0)) + 11.9400905721d0)) + 0.607771387771d0))
    else if (z <= 1.1d+60) then
        tmp = x + ((y * (b + (z * (a + (z * (t + (z * ((z * 3.13060547623d0) + 11.1667541262d0)))))))) / (0.607771387771d0 + (z * 11.9400905721d0)))
    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 <= -3.3e+58) {
		tmp = t_1;
	} else if (z <= -2.0) {
		tmp = x + (((y * b) + (z * ((y * a) + (y * (z * t))))) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771));
	} else if (z <= 1.1e+60) {
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * ((z * 3.13060547623) + 11.1667541262)))))))) / (0.607771387771 + (z * 11.9400905721)));
	} 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 <= -3.3e+58:
		tmp = t_1
	elif z <= -2.0:
		tmp = x + (((y * b) + (z * ((y * a) + (y * (z * t))))) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771))
	elif z <= 1.1e+60:
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * ((z * 3.13060547623) + 11.1667541262)))))))) / (0.607771387771 + (z * 11.9400905721)))
	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 <= -3.3e+58)
		tmp = t_1;
	elseif (z <= -2.0)
		tmp = Float64(x + Float64(Float64(Float64(y * b) + Float64(z * Float64(Float64(y * a) + Float64(y * Float64(z * t))))) / Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)));
	elseif (z <= 1.1e+60)
		tmp = Float64(x + Float64(Float64(y * Float64(b + Float64(z * Float64(a + Float64(z * Float64(t + Float64(z * Float64(Float64(z * 3.13060547623) + 11.1667541262)))))))) / Float64(0.607771387771 + Float64(z * 11.9400905721))));
	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 <= -3.3e+58)
		tmp = t_1;
	elseif (z <= -2.0)
		tmp = x + (((y * b) + (z * ((y * a) + (y * (z * t))))) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771));
	elseif (z <= 1.1e+60)
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * ((z * 3.13060547623) + 11.1667541262)))))))) / (0.607771387771 + (z * 11.9400905721)));
	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, -3.3e+58], t$95$1, If[LessEqual[z, -2.0], N[(x + N[(N[(N[(y * b), $MachinePrecision] + N[(z * N[(N[(y * a), $MachinePrecision] + N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(z * N[(N[(z * N[(N[(z * N[(z + 15.234687407), $MachinePrecision]), $MachinePrecision] + 31.4690115749), $MachinePrecision]), $MachinePrecision] + 11.9400905721), $MachinePrecision]), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.1e+60], N[(x + N[(N[(y * N[(b + N[(z * N[(a + N[(z * N[(t + N[(z * N[(N[(z * 3.13060547623), $MachinePrecision] + 11.1667541262), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(0.607771387771 + N[(z * 11.9400905721), $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 < -3.29999999999999983e58

   1. Initial program 0.1%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   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 97.9%

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

   5. Simplified 97.9%

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

   if -3.29999999999999983e58 < z < -2

   1. Initial program 52.4%

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

   3. Taylor expanded in z around 0

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

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

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

      2. *-commutative N/A

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

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

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

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

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

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

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

      6. *-commutative N/A

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

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

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

      8. associate-*r* N/A

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

      9. *-commutative N/A

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

      10. associate-*l* N/A

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

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

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

      12. *-commutative N/A

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

      13. *-lowering-*.f64 70.9%

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

   5. Simplified 70.9%

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

   if -2 < z < 1.09999999999999998e60

   1. Initial program 99.0%

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

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{313060547623}{100000000000}\right), \frac{55833770631}{5000000000}\right), z\right), t\right), z\right), a\right), z\right), b\right)\right), \mathsf{+.f64}\left(\color{blue}{\left(\frac{119400905721}{10000000000} \cdot z\right)}, \frac{607771387771}{1000000000000}\right)\right)\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

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

      2. *-lowering-*.f64 96.5%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{313060547623}{100000000000}\right), \frac{55833770631}{5000000000}\right), z\right), t\right), z\right), a\right), z\right), b\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{119400905721}{10000000000}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

   5. Simplified 96.5%

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

   if 1.09999999999999998e60 < z

   1. Initial program 2.2%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\left(x + \left(\frac{313060547623}{100000000000} \cdot y + \frac{55833770631}{5000000000} \cdot \frac{y}{z}\right)\right) - \frac{4769379582500641883561}{100000000000000000000} \cdot \frac{y}{z}} \]
   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 95.7%

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

   5. Simplified 95.7%

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

4. Final simplification 95.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+58}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{elif}\;z \leq -2:\\ \;\;\;\;x + \frac{y \cdot b + z \cdot \left(y \cdot a + y \cdot \left(z \cdot t\right)\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+60}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right)\right)\right)\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y \cdot 3.13060547623\right) + \frac{y}{z} \cdot -36.52704169880642\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 92.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot 3.13060547623\\ \mathbf{if}\;z \leq -12.5:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+58}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right)\right)\right)\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{else}:\\ \;\;\;\;t\_1 + \frac{y}{z} \cdot -36.52704169880642\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* y 3.13060547623))))
   (if (<= z -12.5)
     t_1
     (if (<= z 4.8e+58)
       (+
        x
        (/
         (*
          y
          (+
           b
           (*
            z
            (+ a (* z (+ t (* z (+ (* z 3.13060547623) 11.1667541262))))))))
         (+ 0.607771387771 (* z 11.9400905721))))
       (+ 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 <= -12.5) {
		tmp = t_1;
	} else if (z <= 4.8e+58) {
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * ((z * 3.13060547623) + 11.1667541262)))))))) / (0.607771387771 + (z * 11.9400905721)));
	} 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 <= (-12.5d0)) then
        tmp = t_1
    else if (z <= 4.8d+58) then
        tmp = x + ((y * (b + (z * (a + (z * (t + (z * ((z * 3.13060547623d0) + 11.1667541262d0)))))))) / (0.607771387771d0 + (z * 11.9400905721d0)))
    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 <= -12.5) {
		tmp = t_1;
	} else if (z <= 4.8e+58) {
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * ((z * 3.13060547623) + 11.1667541262)))))))) / (0.607771387771 + (z * 11.9400905721)));
	} 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 <= -12.5:
		tmp = t_1
	elif z <= 4.8e+58:
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * ((z * 3.13060547623) + 11.1667541262)))))))) / (0.607771387771 + (z * 11.9400905721)))
	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 <= -12.5)
		tmp = t_1;
	elseif (z <= 4.8e+58)
		tmp = Float64(x + Float64(Float64(y * Float64(b + Float64(z * Float64(a + Float64(z * Float64(t + Float64(z * Float64(Float64(z * 3.13060547623) + 11.1667541262)))))))) / Float64(0.607771387771 + Float64(z * 11.9400905721))));
	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 <= -12.5)
		tmp = t_1;
	elseif (z <= 4.8e+58)
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * ((z * 3.13060547623) + 11.1667541262)))))))) / (0.607771387771 + (z * 11.9400905721)));
	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, -12.5], t$95$1, If[LessEqual[z, 4.8e+58], N[(x + N[(N[(y * N[(b + N[(z * N[(a + N[(z * N[(t + N[(z * N[(N[(z * 3.13060547623), $MachinePrecision] + 11.1667541262), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(0.607771387771 + N[(z * 11.9400905721), $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 < -12.5

   1. Initial program 9.0%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   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 85.3%

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

   5. Simplified 85.3%

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

   if -12.5 < z < 4.8e58

   1. Initial program 99.0%

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

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{313060547623}{100000000000}\right), \frac{55833770631}{5000000000}\right), z\right), t\right), z\right), a\right), z\right), b\right)\right), \mathsf{+.f64}\left(\color{blue}{\left(\frac{119400905721}{10000000000} \cdot z\right)}, \frac{607771387771}{1000000000000}\right)\right)\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

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

      2. *-lowering-*.f64 96.5%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{313060547623}{100000000000}\right), \frac{55833770631}{5000000000}\right), z\right), t\right), z\right), a\right), z\right), b\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{119400905721}{10000000000}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

   5. Simplified 96.5%

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

   if 4.8e58 < z

   1. Initial program 2.2%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\left(x + \left(\frac{313060547623}{100000000000} \cdot y + \frac{55833770631}{5000000000} \cdot \frac{y}{z}\right)\right) - \frac{4769379582500641883561}{100000000000000000000} \cdot \frac{y}{z}} \]
   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 95.7%

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

   5. Simplified 95.7%

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

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -12.5:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+58}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right)\right)\right)\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y \cdot 3.13060547623\right) + \frac{y}{z} \cdot -36.52704169880642\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 92.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot 3.13060547623\\ \mathbf{if}\;z \leq -12.5:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+58}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot 11.1667541262\right)\right)\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{else}:\\ \;\;\;\;t\_1 + \frac{y}{z} \cdot -36.52704169880642\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* y 3.13060547623))))
   (if (<= z -12.5)
     t_1
     (if (<= z 4.8e+58)
       (+
        x
        (/
         (* y (+ b (* z (+ a (* z (+ t (* z 11.1667541262)))))))
         (+ 0.607771387771 (* z 11.9400905721))))
       (+ 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 <= -12.5) {
		tmp = t_1;
	} else if (z <= 4.8e+58) {
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))) / (0.607771387771 + (z * 11.9400905721)));
	} 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 <= (-12.5d0)) then
        tmp = t_1
    else if (z <= 4.8d+58) then
        tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262d0))))))) / (0.607771387771d0 + (z * 11.9400905721d0)))
    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 <= -12.5) {
		tmp = t_1;
	} else if (z <= 4.8e+58) {
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))) / (0.607771387771 + (z * 11.9400905721)));
	} 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 <= -12.5:
		tmp = t_1
	elif z <= 4.8e+58:
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))) / (0.607771387771 + (z * 11.9400905721)))
	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 <= -12.5)
		tmp = t_1;
	elseif (z <= 4.8e+58)
		tmp = Float64(x + Float64(Float64(y * Float64(b + Float64(z * Float64(a + Float64(z * Float64(t + Float64(z * 11.1667541262))))))) / Float64(0.607771387771 + Float64(z * 11.9400905721))));
	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 <= -12.5)
		tmp = t_1;
	elseif (z <= 4.8e+58)
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))) / (0.607771387771 + (z * 11.9400905721)));
	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, -12.5], t$95$1, If[LessEqual[z, 4.8e+58], N[(x + N[(N[(y * N[(b + N[(z * N[(a + N[(z * N[(t + N[(z * 11.1667541262), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(0.607771387771 + N[(z * 11.9400905721), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(N[(y / z), $MachinePrecision] * -36.52704169880642), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -12.5

   1. Initial program 9.0%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   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 85.3%

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

   5. Simplified 85.3%

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

   if -12.5 < z < 4.8e58

   1. Initial program 99.0%

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

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{313060547623}{100000000000}\right), \frac{55833770631}{5000000000}\right), z\right), t\right), z\right), a\right), z\right), b\right)\right), \mathsf{+.f64}\left(\color{blue}{\left(\frac{119400905721}{10000000000} \cdot z\right)}, \frac{607771387771}{1000000000000}\right)\right)\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

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

      2. *-lowering-*.f64 96.5%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{313060547623}{100000000000}\right), \frac{55833770631}{5000000000}\right), z\right), t\right), z\right), a\right), z\right), b\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{119400905721}{10000000000}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

   5. Simplified 96.5%

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

   6. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(\frac{55833770631}{5000000000} \cdot z\right)}, t\right), z\right), a\right), z\right), b\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{119400905721}{10000000000}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\left(z \cdot \frac{55833770631}{5000000000}\right), t\right), z\right), a\right), z\right), b\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{119400905721}{10000000000}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

      2. *-lowering-*.f64 96.5%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{55833770631}{5000000000}\right), t\right), z\right), a\right), z\right), b\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{119400905721}{10000000000}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

   8. Simplified 96.5%

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

   if 4.8e58 < z

   1. Initial program 2.2%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\left(x + \left(\frac{313060547623}{100000000000} \cdot y + \frac{55833770631}{5000000000} \cdot \frac{y}{z}\right)\right) - \frac{4769379582500641883561}{100000000000000000000} \cdot \frac{y}{z}} \]
   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 95.7%

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

   5. Simplified 95.7%

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

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -12.5:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+58}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot 11.1667541262\right)\right)\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y \cdot 3.13060547623\right) + \frac{y}{z} \cdot -36.52704169880642\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 92.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot 3.13060547623\\ \mathbf{if}\;z \leq -12.5:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+58}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot t\right)\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{else}:\\ \;\;\;\;t\_1 + \frac{y}{z} \cdot -36.52704169880642\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* y 3.13060547623))))
   (if (<= z -12.5)
     t_1
     (if (<= z 4.8e+58)
       (+
        x
        (/
         (* y (+ b (* z (+ a (* z t)))))
         (+ 0.607771387771 (* z 11.9400905721))))
       (+ 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 <= -12.5) {
		tmp = t_1;
	} else if (z <= 4.8e+58) {
		tmp = x + ((y * (b + (z * (a + (z * t))))) / (0.607771387771 + (z * 11.9400905721)));
	} 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 <= (-12.5d0)) then
        tmp = t_1
    else if (z <= 4.8d+58) then
        tmp = x + ((y * (b + (z * (a + (z * t))))) / (0.607771387771d0 + (z * 11.9400905721d0)))
    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 <= -12.5) {
		tmp = t_1;
	} else if (z <= 4.8e+58) {
		tmp = x + ((y * (b + (z * (a + (z * t))))) / (0.607771387771 + (z * 11.9400905721)));
	} 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 <= -12.5:
		tmp = t_1
	elif z <= 4.8e+58:
		tmp = x + ((y * (b + (z * (a + (z * t))))) / (0.607771387771 + (z * 11.9400905721)))
	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 <= -12.5)
		tmp = t_1;
	elseif (z <= 4.8e+58)
		tmp = Float64(x + Float64(Float64(y * Float64(b + Float64(z * Float64(a + Float64(z * t))))) / Float64(0.607771387771 + Float64(z * 11.9400905721))));
	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 <= -12.5)
		tmp = t_1;
	elseif (z <= 4.8e+58)
		tmp = x + ((y * (b + (z * (a + (z * t))))) / (0.607771387771 + (z * 11.9400905721)));
	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, -12.5], t$95$1, If[LessEqual[z, 4.8e+58], N[(x + N[(N[(y * N[(b + N[(z * N[(a + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(0.607771387771 + N[(z * 11.9400905721), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(N[(y / z), $MachinePrecision] * -36.52704169880642), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -12.5

   1. Initial program 9.0%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   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 85.3%

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

   5. Simplified 85.3%

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

   if -12.5 < z < 4.8e58

   1. Initial program 99.0%

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

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{313060547623}{100000000000}\right), \frac{55833770631}{5000000000}\right), z\right), t\right), z\right), a\right), z\right), b\right)\right), \mathsf{+.f64}\left(\color{blue}{\left(\frac{119400905721}{10000000000} \cdot z\right)}, \frac{607771387771}{1000000000000}\right)\right)\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

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

      2. *-lowering-*.f64 96.5%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{313060547623}{100000000000}\right), \frac{55833770631}{5000000000}\right), z\right), t\right), z\right), a\right), z\right), b\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(z, \frac{119400905721}{10000000000}\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]

   5. Simplified 96.5%

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

   6. Taylor expanded in z around 0

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

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

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

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

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

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

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

      4. *-commutative N/A

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

      5. *-lowering-*.f64 95.8%

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

   8. Simplified 95.8%

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

   if 4.8e58 < z

   1. Initial program 2.2%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\left(x + \left(\frac{313060547623}{100000000000} \cdot y + \frac{55833770631}{5000000000} \cdot \frac{y}{z}\right)\right) - \frac{4769379582500641883561}{100000000000000000000} \cdot \frac{y}{z}} \]
   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 95.7%

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

   5. Simplified 95.7%

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

4. Final simplification 93.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -12.5:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+58}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot t\right)\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y \cdot 3.13060547623\right) + \frac{y}{z} \cdot -36.52704169880642\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 62.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot 3.13060547623\\ \mathbf{if}\;z \leq -2.8 \cdot 10^{-72}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-266}:\\ \;\;\;\;\left(y \cdot b\right) \cdot 1.6453555072203998\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-75}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+32}:\\ \;\;\;\;y \cdot \left(b \cdot 1.6453555072203998\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* y 3.13060547623))))
   (if (<= z -2.8e-72)
     t_1
     (if (<= z -6e-266)
       (* (* y b) 1.6453555072203998)
       (if (<= z 2.1e-75)
         x
         (if (<= z 1.75e+32) (* 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 <= -2.8e-72) {
		tmp = t_1;
	} else if (z <= -6e-266) {
		tmp = (y * b) * 1.6453555072203998;
	} else if (z <= 2.1e-75) {
		tmp = x;
	} else if (z <= 1.75e+32) {
		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 <= (-2.8d-72)) then
        tmp = t_1
    else if (z <= (-6d-266)) then
        tmp = (y * b) * 1.6453555072203998d0
    else if (z <= 2.1d-75) then
        tmp = x
    else if (z <= 1.75d+32) 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 <= -2.8e-72) {
		tmp = t_1;
	} else if (z <= -6e-266) {
		tmp = (y * b) * 1.6453555072203998;
	} else if (z <= 2.1e-75) {
		tmp = x;
	} else if (z <= 1.75e+32) {
		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 <= -2.8e-72:
		tmp = t_1
	elif z <= -6e-266:
		tmp = (y * b) * 1.6453555072203998
	elif z <= 2.1e-75:
		tmp = x
	elif z <= 1.75e+32:
		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 <= -2.8e-72)
		tmp = t_1;
	elseif (z <= -6e-266)
		tmp = Float64(Float64(y * b) * 1.6453555072203998);
	elseif (z <= 2.1e-75)
		tmp = x;
	elseif (z <= 1.75e+32)
		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 <= -2.8e-72)
		tmp = t_1;
	elseif (z <= -6e-266)
		tmp = (y * b) * 1.6453555072203998;
	elseif (z <= 2.1e-75)
		tmp = x;
	elseif (z <= 1.75e+32)
		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, -2.8e-72], t$95$1, If[LessEqual[z, -6e-266], N[(N[(y * b), $MachinePrecision] * 1.6453555072203998), $MachinePrecision], If[LessEqual[z, 2.1e-75], x, If[LessEqual[z, 1.75e+32], N[(y * N[(b * 1.6453555072203998), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.7999999999999998e-72 or 1.75e32 < z

   1. Initial program 16.3%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{x + \frac{313060547623}{100000000000} \cdot y} \]
   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 84.4%

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

   5. Simplified 84.4%

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

   if -2.7999999999999998e-72 < z < -5.9999999999999999e-266

   1. Initial program 99.5%

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

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \color{blue}{\left(b + a \cdot z\right)}\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right), z\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]
   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. Taylor expanded in z around 0

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

   8. Simplified 95.4%

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

   9. Taylor expanded in b around inf

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

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

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

       2. *-commutative N/A

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

       3. *-lowering-*.f64 52.8%

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

   11. Simplified 52.8%

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

   if -5.9999999999999999e-266 < z < 2.1000000000000001e-75

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 57.7%

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

   if 2.1000000000000001e-75 < z < 1.75e32

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \color{blue}{\left(b + a \cdot z\right)}\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right), z\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]
   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 78.8%

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

   5. Simplified 78.8%

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

   6. Taylor expanded in z around 0

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

   8. Simplified 75.2%

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

   9. Taylor expanded in y around inf

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

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

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

       2. +-commutative N/A

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

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

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

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

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

       5. *-commutative N/A

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

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

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

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

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

       8. *-lowering-*.f64 67.1%

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

   11. Simplified 67.1%

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

   12. Taylor expanded in b around inf

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

       1. *-commutative N/A

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

       2. *-lowering-*.f64 41.3%

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

   14. Simplified 41.3%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{-72}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-266}:\\ \;\;\;\;\left(y \cdot b\right) \cdot 1.6453555072203998\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-75}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+32}:\\ \;\;\;\;y \cdot \left(b \cdot 1.6453555072203998\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 89.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot 3.13060547623\\ \mathbf{if}\;z \leq -6.1 \cdot 10^{+26}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+58}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot a\right)}{0.607771387771}\\ \mathbf{else}:\\ \;\;\;\;t\_1 + \frac{y}{z} \cdot -36.52704169880642\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* y 3.13060547623))))
   (if (<= z -6.1e+26)
     t_1
     (if (<= z 4.8e+58)
       (+ x (/ (* y (+ b (* z a))) 0.607771387771))
       (+ 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 <= -6.1e+26) {
		tmp = t_1;
	} else if (z <= 4.8e+58) {
		tmp = x + ((y * (b + (z * a))) / 0.607771387771);
	} 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 <= (-6.1d+26)) then
        tmp = t_1
    else if (z <= 4.8d+58) then
        tmp = x + ((y * (b + (z * a))) / 0.607771387771d0)
    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 <= -6.1e+26) {
		tmp = t_1;
	} else if (z <= 4.8e+58) {
		tmp = x + ((y * (b + (z * a))) / 0.607771387771);
	} 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 <= -6.1e+26:
		tmp = t_1
	elif z <= 4.8e+58:
		tmp = x + ((y * (b + (z * a))) / 0.607771387771)
	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 <= -6.1e+26)
		tmp = t_1;
	elseif (z <= 4.8e+58)
		tmp = Float64(x + Float64(Float64(y * Float64(b + Float64(z * a))) / 0.607771387771));
	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 <= -6.1e+26)
		tmp = t_1;
	elseif (z <= 4.8e+58)
		tmp = x + ((y * (b + (z * a))) / 0.607771387771);
	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, -6.1e+26], t$95$1, If[LessEqual[z, 4.8e+58], N[(x + N[(N[(y * N[(b + N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / 0.607771387771), $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 < -6.1000000000000003e26

   1. Initial program 7.4%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{x + \frac{313060547623}{100000000000} \cdot y} \]
   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 88.2%

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

   5. Simplified 88.2%

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

   if -6.1000000000000003e26 < z < 4.8e58

   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 93.2%

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

   5. Simplified 93.2%

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

   6. Taylor expanded in z around 0

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

   8. Simplified 91.4%

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

   if 4.8e58 < z

   1. Initial program 2.2%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\left(x + \left(\frac{313060547623}{100000000000} \cdot y + \frac{55833770631}{5000000000} \cdot \frac{y}{z}\right)\right) - \frac{4769379582500641883561}{100000000000000000000} \cdot \frac{y}{z}} \]
   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 95.7%

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

   5. Simplified 95.7%

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

Alternative 10: 89.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot 3.13060547623\\ \mathbf{if}\;z \leq -6.8 \cdot 10^{+26}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+58}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot a\right)}{0.607771387771}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* y 3.13060547623))))
   (if (<= z -6.8e+26)
     t_1
     (if (<= z 4.8e+58) (+ x (/ (* y (+ b (* z a))) 0.607771387771)) 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 <= -6.8e+26) {
		tmp = t_1;
	} else if (z <= 4.8e+58) {
		tmp = x + ((y * (b + (z * a))) / 0.607771387771);
	} 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 <= (-6.8d+26)) then
        tmp = t_1
    else if (z <= 4.8d+58) then
        tmp = x + ((y * (b + (z * a))) / 0.607771387771d0)
    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 <= -6.8e+26) {
		tmp = t_1;
	} else if (z <= 4.8e+58) {
		tmp = x + ((y * (b + (z * a))) / 0.607771387771);
	} 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 <= -6.8e+26:
		tmp = t_1
	elif z <= 4.8e+58:
		tmp = x + ((y * (b + (z * a))) / 0.607771387771)
	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 <= -6.8e+26)
		tmp = t_1;
	elseif (z <= 4.8e+58)
		tmp = Float64(x + Float64(Float64(y * Float64(b + Float64(z * a))) / 0.607771387771));
	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 <= -6.8e+26)
		tmp = t_1;
	elseif (z <= 4.8e+58)
		tmp = x + ((y * (b + (z * a))) / 0.607771387771);
	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, -6.8e+26], t$95$1, If[LessEqual[z, 4.8e+58], N[(x + N[(N[(y * N[(b + N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / 0.607771387771), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -6.8000000000000005e26 or 4.8e58 < z

   1. Initial program 5.0%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   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 91.7%

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

   5. Simplified 91.7%

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

   if -6.8000000000000005e26 < z < 4.8e58

   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 93.2%

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

   5. Simplified 93.2%

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

   6. Taylor expanded in z around 0

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

   8. Simplified 91.4%

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

Alternative 11: 89.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot 3.13060547623\\ \mathbf{if}\;z \leq -7.5 \cdot 10^{+26}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+58}:\\ \;\;\;\;x + y \cdot \frac{b + z \cdot a}{0.607771387771}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* y 3.13060547623))))
   (if (<= z -7.5e+26)
     t_1
     (if (<= z 4.8e+58) (+ x (* y (/ (+ b (* z a)) 0.607771387771))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * 3.13060547623);
	double tmp;
	if (z <= -7.5e+26) {
		tmp = t_1;
	} else if (z <= 4.8e+58) {
		tmp = x + (y * ((b + (z * a)) / 0.607771387771));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * 3.13060547623d0)
    if (z <= (-7.5d+26)) then
        tmp = t_1
    else if (z <= 4.8d+58) then
        tmp = x + (y * ((b + (z * a)) / 0.607771387771d0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * 3.13060547623);
	double tmp;
	if (z <= -7.5e+26) {
		tmp = t_1;
	} else if (z <= 4.8e+58) {
		tmp = x + (y * ((b + (z * a)) / 0.607771387771));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y * 3.13060547623)
	tmp = 0
	if z <= -7.5e+26:
		tmp = t_1
	elif z <= 4.8e+58:
		tmp = x + (y * ((b + (z * a)) / 0.607771387771))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y * 3.13060547623))
	tmp = 0.0
	if (z <= -7.5e+26)
		tmp = t_1;
	elseif (z <= 4.8e+58)
		tmp = Float64(x + Float64(y * Float64(Float64(b + Float64(z * a)) / 0.607771387771)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (y * 3.13060547623);
	tmp = 0.0;
	if (z <= -7.5e+26)
		tmp = t_1;
	elseif (z <= 4.8e+58)
		tmp = x + (y * ((b + (z * a)) / 0.607771387771));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.5e+26], t$95$1, If[LessEqual[z, 4.8e+58], N[(x + N[(y * N[(N[(b + N[(z * a), $MachinePrecision]), $MachinePrecision] / 0.607771387771), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -7.49999999999999941e26 or 4.8e58 < z

   1. Initial program 5.0%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   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 91.7%

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

   5. Simplified 91.7%

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

   if -7.49999999999999941e26 < z < 4.8e58

   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 93.2%

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

   5. Simplified 93.2%

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

   6. Taylor expanded in z around 0

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

   8. Simplified 91.4%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

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

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

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

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

      6. *-lowering-*.f64 91.3%

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

   10. Applied egg-rr 91.3%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+26}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+58}:\\ \;\;\;\;x + y \cdot \frac{b + z \cdot a}{0.607771387771}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 82.3% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot 3.13060547623\\ \mathbf{if}\;z \leq -6.1 \cdot 10^{+26}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+58}:\\ \;\;\;\;x + \left(y \cdot b\right) \cdot 1.6453555072203998\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* y 3.13060547623))))
   (if (<= z -6.1e+26)
     t_1
     (if (<= z 4.8e+58) (+ 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 <= -6.1e+26) {
		tmp = t_1;
	} else if (z <= 4.8e+58) {
		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 <= (-6.1d+26)) then
        tmp = t_1
    else if (z <= 4.8d+58) 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 <= -6.1e+26) {
		tmp = t_1;
	} else if (z <= 4.8e+58) {
		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 <= -6.1e+26:
		tmp = t_1
	elif z <= 4.8e+58:
		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 <= -6.1e+26)
		tmp = t_1;
	elseif (z <= 4.8e+58)
		tmp = Float64(x + Float64(Float64(y * 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 <= -6.1e+26)
		tmp = t_1;
	elseif (z <= 4.8e+58)
		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, -6.1e+26], t$95$1, If[LessEqual[z, 4.8e+58], N[(x + N[(N[(y * b), $MachinePrecision] * 1.6453555072203998), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -6.1000000000000003e26 or 4.8e58 < z

   1. Initial program 5.0%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   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 91.7%

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

   5. Simplified 91.7%

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

   if -6.1000000000000003e26 < z < 4.8e58

   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 93.2%

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

   5. Simplified 93.2%

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

   6. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + \frac{1000000000000}{607771387771} \cdot \left(b \cdot y\right)} \]
   7. 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. *-lowering-*.f64 N/A

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

      4. *-commutative N/A

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

      5. *-lowering-*.f64 78.3%

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

   8. Simplified 78.3%

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

Alternative 13: 82.3% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot 3.13060547623\\ \mathbf{if}\;z \leq -5.9 \cdot 10^{+26}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+58}:\\ \;\;\;\;x + b \cdot \left(y \cdot 1.6453555072203998\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* y 3.13060547623))))
   (if (<= z -5.9e+26)
     t_1
     (if (<= z 4.8e+58) (+ 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 <= -5.9e+26) {
		tmp = t_1;
	} else if (z <= 4.8e+58) {
		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 <= (-5.9d+26)) then
        tmp = t_1
    else if (z <= 4.8d+58) 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 <= -5.9e+26) {
		tmp = t_1;
	} else if (z <= 4.8e+58) {
		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 <= -5.9e+26:
		tmp = t_1
	elif z <= 4.8e+58:
		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 <= -5.9e+26)
		tmp = t_1;
	elseif (z <= 4.8e+58)
		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 <= -5.9e+26)
		tmp = t_1;
	elseif (z <= 4.8e+58)
		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, -5.9e+26], t$95$1, If[LessEqual[z, 4.8e+58], N[(x + N[(b * N[(y * 1.6453555072203998), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.9000000000000003e26 or 4.8e58 < z

   1. Initial program 5.0%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   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 91.7%

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

   5. Simplified 91.7%

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

   if -5.9000000000000003e26 < z < 4.8e58

   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

      \[\leadsto \color{blue}{x + \frac{1000000000000}{607771387771} \cdot \left(b \cdot y\right)} \]
   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 78.3%

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

   5. Simplified 78.3%

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

Alternative 14: 51.0% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+128}:\\ \;\;\;\;y \cdot 3.13060547623\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+108}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot b\right) \cdot 1.6453555072203998\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.8e+128)
   (* y 3.13060547623)
   (if (<= y 2.4e+108) x (* (* y b) 1.6453555072203998))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.8e+128) {
		tmp = y * 3.13060547623;
	} else if (y <= 2.4e+108) {
		tmp = x;
	} else {
		tmp = (y * b) * 1.6453555072203998;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-1.8d+128)) then
        tmp = y * 3.13060547623d0
    else if (y <= 2.4d+108) then
        tmp = x
    else
        tmp = (y * b) * 1.6453555072203998d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.8e+128) {
		tmp = y * 3.13060547623;
	} else if (y <= 2.4e+108) {
		tmp = x;
	} else {
		tmp = (y * b) * 1.6453555072203998;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.8e+128:
		tmp = y * 3.13060547623
	elif y <= 2.4e+108:
		tmp = x
	else:
		tmp = (y * b) * 1.6453555072203998
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.8e+128)
		tmp = Float64(y * 3.13060547623);
	elseif (y <= 2.4e+108)
		tmp = x;
	else
		tmp = Float64(Float64(y * b) * 1.6453555072203998);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.8e+128)
		tmp = y * 3.13060547623;
	elseif (y <= 2.4e+108)
		tmp = x;
	else
		tmp = (y * b) * 1.6453555072203998;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.8e+128], N[(y * 3.13060547623), $MachinePrecision], If[LessEqual[y, 2.4e+108], x, N[(N[(y * b), $MachinePrecision] * 1.6453555072203998), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.80000000000000014e128

   1. Initial program 51.1%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   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 52.7%

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

   5. Simplified 52.7%

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

   6. Taylor expanded in x around 0

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

      1. *-commutative N/A

         \[\leadsto y \cdot \color{blue}{\frac{313060547623}{100000000000}} \]

      2. *-lowering-*.f64 39.7%

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

   8. Simplified 39.7%

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

   if -1.80000000000000014e128 < y < 2.40000000000000019e108

   1. Initial program 61.3%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 58.3%

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

   if 2.40000000000000019e108 < y

   1. Initial program 58.6%

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

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \color{blue}{\left(b + a \cdot z\right)}\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{+.f64}\left(z, \frac{15234687407}{1000000000}\right), z\right), \frac{314690115749}{10000000000}\right), z\right), \frac{119400905721}{10000000000}\right), z\right), \frac{607771387771}{1000000000000}\right)\right)\right) \]
   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 58.9%

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

   5. Simplified 58.9%

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

   6. Taylor expanded in z around 0

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

   8. Simplified 59.9%

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

   9. Taylor expanded in b around inf

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

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

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

       2. *-commutative N/A

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

       3. *-lowering-*.f64 39.1%

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

   11. Simplified 39.1%

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

4. Final simplification 51.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+128}:\\ \;\;\;\;y \cdot 3.13060547623\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+108}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot b\right) \cdot 1.6453555072203998\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 48.6% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.3 \cdot 10^{+55}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{-41}:\\ \;\;\;\;y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -3.3e+55) x (if (<= x 1.45e-41) (* y 3.13060547623) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -3.3e+55) {
		tmp = x;
	} else if (x <= 1.45e-41) {
		tmp = y * 3.13060547623;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-3.3d+55)) then
        tmp = x
    else if (x <= 1.45d-41) then
        tmp = y * 3.13060547623d0
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -3.3e+55) {
		tmp = x;
	} else if (x <= 1.45e-41) {
		tmp = y * 3.13060547623;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -3.3e+55:
		tmp = x
	elif x <= 1.45e-41:
		tmp = y * 3.13060547623
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -3.3e+55)
		tmp = x;
	elseif (x <= 1.45e-41)
		tmp = Float64(y * 3.13060547623);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -3.3e+55)
		tmp = x;
	elseif (x <= 1.45e-41)
		tmp = y * 3.13060547623;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -3.3e+55], x, If[LessEqual[x, 1.45e-41], N[(y * 3.13060547623), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -3.3e55 or 1.44999999999999989e-41 < x

   1. Initial program 60.8%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 67.4%

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

   if -3.3e55 < x < 1.44999999999999989e-41

   1. Initial program 57.3%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{x + \frac{313060547623}{100000000000} \cdot y} \]
   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 47.8%

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

   5. Simplified 47.8%

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

   6. Taylor expanded in x around 0

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

      1. *-commutative N/A

         \[\leadsto y \cdot \color{blue}{\frac{313060547623}{100000000000}} \]

      2. *-lowering-*.f64 36.7%

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

   8. Simplified 36.7%

      \[\leadsto \color{blue}{y \cdot 3.13060547623} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 16: 44.8% accurate, 37.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 59.0%

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

3. Taylor expanded in x around inf

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

5. Simplified 41.9%

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

Developer Target 1: 98.4% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024152 
(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))))