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

Percentage Accurate: 58.7% → 98.1%

Time: 20.7s

Alternatives: 22

Speedup: 7.4×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 58.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.1% accurate, 0.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(N[(y * N[(N[(z * N[(a + N[(z * N[(t + N[(z * N[(11.1667541262 + N[(z * 3.13060547623), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(N[(z * N[(N[(z * N[(N[(z * N[(z + 15.234687407), $MachinePrecision]), $MachinePrecision] + 31.4690115749), $MachinePrecision]), $MachinePrecision] + 11.9400905721), $MachinePrecision]), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(N[(z * N[(z * N[(z * N[(z * 3.13060547623 + 11.1667541262), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision] + b), $MachinePrecision] / N[(z * N[(z * N[(z * N[(z + 15.234687407), $MachinePrecision] + 31.4690115749), $MachinePrecision] + 11.9400905721), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision], N[(x + N[(N[(-36.52704169880642 * N[(y / z), $MachinePrecision]), $MachinePrecision] + N[(N[(y * 3.13060547623), $MachinePrecision] + N[(y / N[(N[Power[z, 2.0], $MachinePrecision] / N[(t + 457.9610022158428), $MachinePrecision]), $MachinePrecision]), $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 313060547623/100000000000) 55833770631/5000000000) z) t) z) a) z) b)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z 15234687407/1000000000) z) 314690115749/10000000000) z) 119400905721/10000000000) z) 607771387771/1000000000000)) < +inf.0

   1. Initial program 92.6%

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

   3. Simplified 97.5%

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

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

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   4. Taylor expanded in z around inf 85.9%

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

      1. *-un-lft-identity 85.9%

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

      2. associate-/l* 99.9%

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

      3. +-commutative 99.9%

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

   6. Applied egg-rr 99.9%

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

4. Final simplification 98.3%

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

Alternative 2: 98.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771\\ t_2 := z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\right)\right)\\ \mathbf{if}\;\frac{y \cdot \left(t_2 + b\right)}{t_1} \leq \infty:\\ \;\;\;\;x + y \cdot \left(\frac{b}{t_1} + \frac{t_2}{t_1}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(-36.52704169880642 \cdot \frac{y}{z} + \left(y \cdot 3.13060547623 + \frac{y}{\frac{{z}^{2}}{t + 457.9610022158428}}\right)\right)\\ \end{array} \end{array} \]

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
         (* z (+ a (* z (+ t (* z (+ 11.1667541262 (* z 3.13060547623)))))))))
   (if (<= (/ (* y (+ t_2 b)) t_1) INFINITY)
     (+ x (* y (+ (/ b t_1) (/ t_2 t_1))))
     (+
      x
      (+
       (* -36.52704169880642 (/ y z))
       (+
        (* y 3.13060547623)
        (/ y (/ (pow z 2.0) (+ t 457.9610022158428)))))))))

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 = z * (a + (z * (t + (z * (11.1667541262 + (z * 3.13060547623))))));
	double tmp;
	if (((y * (t_2 + b)) / t_1) <= ((double) INFINITY)) {
		tmp = x + (y * ((b / t_1) + (t_2 / t_1)));
	} else {
		tmp = x + ((-36.52704169880642 * (y / z)) + ((y * 3.13060547623) + (y / (pow(z, 2.0) / (t + 457.9610022158428)))));
	}
	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 = z * (a + (z * (t + (z * (11.1667541262 + (z * 3.13060547623))))));
	double tmp;
	if (((y * (t_2 + b)) / t_1) <= Double.POSITIVE_INFINITY) {
		tmp = x + (y * ((b / t_1) + (t_2 / t_1)));
	} else {
		tmp = x + ((-36.52704169880642 * (y / z)) + ((y * 3.13060547623) + (y / (Math.pow(z, 2.0) / (t + 457.9610022158428)))));
	}
	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 = z * (a + (z * (t + (z * (11.1667541262 + (z * 3.13060547623))))))
	tmp = 0
	if ((y * (t_2 + b)) / t_1) <= math.inf:
		tmp = x + (y * ((b / t_1) + (t_2 / t_1)))
	else:
		tmp = x + ((-36.52704169880642 * (y / z)) + ((y * 3.13060547623) + (y / (math.pow(z, 2.0) / (t + 457.9610022158428)))))
	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(z * Float64(a + Float64(z * Float64(t + Float64(z * Float64(11.1667541262 + Float64(z * 3.13060547623)))))))
	tmp = 0.0
	if (Float64(Float64(y * Float64(t_2 + b)) / t_1) <= Inf)
		tmp = Float64(x + Float64(y * Float64(Float64(b / t_1) + Float64(t_2 / t_1))));
	else
		tmp = Float64(x + Float64(Float64(-36.52704169880642 * Float64(y / z)) + Float64(Float64(y * 3.13060547623) + Float64(y / Float64((z ^ 2.0) / Float64(t + 457.9610022158428))))));
	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 = z * (a + (z * (t + (z * (11.1667541262 + (z * 3.13060547623))))));
	tmp = 0.0;
	if (((y * (t_2 + b)) / t_1) <= Inf)
		tmp = x + (y * ((b / t_1) + (t_2 / t_1)));
	else
		tmp = x + ((-36.52704169880642 * (y / z)) + ((y * 3.13060547623) + (y / ((z ^ 2.0) / (t + 457.9610022158428)))));
	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[(z * N[(a + N[(z * N[(t + N[(z * N[(11.1667541262 + N[(z * 3.13060547623), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(y * N[(t$95$2 + b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], Infinity], N[(x + N[(y * N[(N[(b / t$95$1), $MachinePrecision] + N[(t$95$2 / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(-36.52704169880642 * N[(y / z), $MachinePrecision]), $MachinePrecision] + N[(N[(y * 3.13060547623), $MachinePrecision] + N[(y / N[(N[Power[z, 2.0], $MachinePrecision] / N[(t + 457.9610022158428), $MachinePrecision]), $MachinePrecision]), $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 313060547623/100000000000) 55833770631/5000000000) z) t) z) a) z) b)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z 15234687407/1000000000) z) 314690115749/10000000000) z) 119400905721/10000000000) z) 607771387771/1000000000000)) < +inf.0

   1. Initial program 92.6%

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

   3. Simplified 97.5%

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

   4. Taylor expanded in y around 0 97.5%

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

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

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   4. Taylor expanded in z around inf 85.9%

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

      1. *-un-lft-identity 85.9%

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

      2. associate-/l* 99.9%

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

      3. +-commutative 99.9%

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

   6. Applied egg-rr 99.9%

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

4. Final simplification 98.3%

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

Alternative 3: 98.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771\\ t_2 := z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\right)\right)\\ \mathbf{if}\;\frac{y \cdot \left(t_2 + b\right)}{t_1} \leq \infty:\\ \;\;\;\;x + y \cdot \left(\frac{b}{t_1} + \frac{t_2}{t_1}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(\frac{t}{{z}^{2}} - -3.13060547623\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+
          (*
           z
           (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721))
          0.607771387771))
        (t_2
         (* z (+ a (* z (+ t (* z (+ 11.1667541262 (* z 3.13060547623)))))))))
   (if (<= (/ (* y (+ t_2 b)) t_1) INFINITY)
     (+ x (* y (+ (/ b t_1) (/ t_2 t_1))))
     (+ x (* y (- (/ t (pow z 2.0)) -3.13060547623))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771;
	double t_2 = z * (a + (z * (t + (z * (11.1667541262 + (z * 3.13060547623))))));
	double tmp;
	if (((y * (t_2 + b)) / t_1) <= ((double) INFINITY)) {
		tmp = x + (y * ((b / t_1) + (t_2 / t_1)));
	} else {
		tmp = x + (y * ((t / pow(z, 2.0)) - -3.13060547623));
	}
	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 = z * (a + (z * (t + (z * (11.1667541262 + (z * 3.13060547623))))));
	double tmp;
	if (((y * (t_2 + b)) / t_1) <= Double.POSITIVE_INFINITY) {
		tmp = x + (y * ((b / t_1) + (t_2 / t_1)));
	} else {
		tmp = x + (y * ((t / Math.pow(z, 2.0)) - -3.13060547623));
	}
	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 = z * (a + (z * (t + (z * (11.1667541262 + (z * 3.13060547623))))))
	tmp = 0
	if ((y * (t_2 + b)) / t_1) <= math.inf:
		tmp = x + (y * ((b / t_1) + (t_2 / t_1)))
	else:
		tmp = x + (y * ((t / math.pow(z, 2.0)) - -3.13060547623))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)
	t_2 = Float64(z * Float64(a + Float64(z * Float64(t + Float64(z * Float64(11.1667541262 + Float64(z * 3.13060547623)))))))
	tmp = 0.0
	if (Float64(Float64(y * Float64(t_2 + b)) / t_1) <= Inf)
		tmp = Float64(x + Float64(y * Float64(Float64(b / t_1) + Float64(t_2 / t_1))));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(t / (z ^ 2.0)) - -3.13060547623)));
	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 = z * (a + (z * (t + (z * (11.1667541262 + (z * 3.13060547623))))));
	tmp = 0.0;
	if (((y * (t_2 + b)) / t_1) <= Inf)
		tmp = x + (y * ((b / t_1) + (t_2 / t_1)));
	else
		tmp = x + (y * ((t / (z ^ 2.0)) - -3.13060547623));
	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[(z * N[(a + N[(z * N[(t + N[(z * N[(11.1667541262 + N[(z * 3.13060547623), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(y * N[(t$95$2 + b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], Infinity], N[(x + N[(y * N[(N[(b / t$95$1), $MachinePrecision] + N[(t$95$2 / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(t / N[Power[z, 2.0], $MachinePrecision]), $MachinePrecision] - -3.13060547623), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 92.6%

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

   3. Simplified 97.5%

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

   4. Taylor expanded in y around 0 97.5%

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

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

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   4. Taylor expanded in z around inf 85.9%

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

   5. Taylor expanded in y around -inf 99.9%

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

      1. mul-1-neg 99.9%

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

      2. *-commutative 99.9%

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

      3. distribute-rgt-neg-in 99.9%

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

      4. sub-neg 99.9%

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

      5. +-commutative 99.9%

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

      6. mul-1-neg 99.9%

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

      7. unsub-neg 99.9%

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

      8. associate-*r/ 99.9%

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

      9. metadata-eval 99.9%

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

      10. +-commutative 99.9%

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

      11. metadata-eval 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in t around inf 99.9%

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

      1. associate-*r/ 99.9%

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

      2. mul-1-neg 99.9%

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

   10. Simplified 99.9%

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

4. Final simplification 98.3%

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

Alternative 4: 97.1% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 92.6%

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

   3. Simplified 97.5%

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

   4. Taylor expanded in y around 0 97.5%

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

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

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   4. Taylor expanded in z around inf 94.3%

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

4. Final simplification 96.5%

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

Alternative 5: 94.9% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 92.6%

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

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

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   4. Taylor expanded in z around inf 94.3%

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

4. Final simplification 93.1%

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

Alternative 6: 94.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3200000000:\\ \;\;\;\;x - y \cdot \left(-3.13060547623 + \frac{36.52704169880642}{z}\right)\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+27}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot 11.1667541262\right)\right)\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -3200000000.0)
   (- x (* y (+ -3.13060547623 (/ 36.52704169880642 z))))
   (if (<= z 7.8e+27)
     (+
      x
      (/
       (* y (+ b (* z (+ a (* z (+ t (* z 11.1667541262)))))))
       (+
        (*
         z
         (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721))
        0.607771387771)))
     (+ x (* y 3.13060547623)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -3200000000.0) {
		tmp = x - (y * (-3.13060547623 + (36.52704169880642 / z)));
	} else if (z <= 7.8e+27) {
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771));
	} else {
		tmp = x + (y * 3.13060547623);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-3200000000.0d0)) then
        tmp = x - (y * ((-3.13060547623d0) + (36.52704169880642d0 / z)))
    else if (z <= 7.8d+27) then
        tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262d0))))))) / ((z * ((z * ((z * (z + 15.234687407d0)) + 31.4690115749d0)) + 11.9400905721d0)) + 0.607771387771d0))
    else
        tmp = x + (y * 3.13060547623d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -3200000000.0) {
		tmp = x - (y * (-3.13060547623 + (36.52704169880642 / z)));
	} else if (z <= 7.8e+27) {
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771));
	} else {
		tmp = x + (y * 3.13060547623);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -3200000000.0:
		tmp = x - (y * (-3.13060547623 + (36.52704169880642 / z)))
	elif z <= 7.8e+27:
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771))
	else:
		tmp = x + (y * 3.13060547623)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -3200000000.0)
		tmp = Float64(x - Float64(y * Float64(-3.13060547623 + Float64(36.52704169880642 / z))));
	elseif (z <= 7.8e+27)
		tmp = Float64(x + Float64(Float64(y * Float64(b + Float64(z * Float64(a + Float64(z * Float64(t + Float64(z * 11.1667541262))))))) / Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)));
	else
		tmp = Float64(x + Float64(y * 3.13060547623));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -3200000000.0)
		tmp = x - (y * (-3.13060547623 + (36.52704169880642 / z)));
	elseif (z <= 7.8e+27)
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771));
	else
		tmp = x + (y * 3.13060547623);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -3200000000.0], N[(x - N[(y * N[(-3.13060547623 + N[(36.52704169880642 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.8e+27], N[(x + N[(N[(y * N[(b + N[(z * N[(a + N[(z * N[(t + N[(z * 11.1667541262), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(z * N[(N[(z * N[(N[(z * N[(z + 15.234687407), $MachinePrecision]), $MachinePrecision] + 31.4690115749), $MachinePrecision]), $MachinePrecision] + 11.9400905721), $MachinePrecision]), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.2e9

   1. Initial program 14.1%

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

   3. Simplified 26.6%

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

   4. Taylor expanded in z around inf 81.0%

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

   5. Taylor expanded in y around -inf 90.5%

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

      1. mul-1-neg 90.5%

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

      2. *-commutative 90.5%

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

      3. distribute-rgt-neg-in 90.5%

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

      4. sub-neg 90.5%

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

      5. +-commutative 90.5%

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

      6. mul-1-neg 90.5%

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

      7. unsub-neg 90.5%

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

      8. associate-*r/ 90.5%

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

      9. metadata-eval 90.5%

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

      10. +-commutative 90.5%

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

      11. metadata-eval 90.5%

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

   7. Simplified 90.5%

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

   8. Taylor expanded in z around inf 85.8%

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

   if -3.2e9 < z < 7.7999999999999997e27

   1. Initial program 99.1%

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

   2. Taylor expanded in z around 0 99.1%

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

      1. *-commutative 94.4%

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

   4. Simplified 99.1%

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

   if 7.7999999999999997e27 < z

   1. Initial program 6.7%

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

   3. Simplified 8.8%

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

   4. Taylor expanded in z around inf 91.5%

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

4. Final simplification 94.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3200000000:\\ \;\;\;\;x - y \cdot \left(-3.13060547623 + \frac{36.52704169880642}{z}\right)\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+27}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot 11.1667541262\right)\right)\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \]

Alternative 7: 92.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3200000000:\\ \;\;\;\;x - y \cdot \left(-3.13060547623 + \frac{36.52704169880642}{z}\right)\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-37}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot 11.1667541262\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot 31.4690115749\right)}\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{+33}:\\ \;\;\;\;x + \frac{a \cdot \left(y \cdot z\right) + y \cdot b}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -3200000000.0)
   (- x (* y (+ -3.13060547623 (/ 36.52704169880642 z))))
   (if (<= z 6e-37)
     (+
      x
      (/
       (* y (+ b (* z (+ a (* z (+ t (* z 11.1667541262)))))))
       (+ 0.607771387771 (* z (+ 11.9400905721 (* z 31.4690115749))))))
     (if (<= z 8.6e+33)
       (+
        x
        (/
         (+ (* a (* y z)) (* y b))
         (+
          (*
           z
           (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721))
          0.607771387771)))
       (+ x (* y 3.13060547623))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -3200000000.0) {
		tmp = x - (y * (-3.13060547623 + (36.52704169880642 / z)));
	} else if (z <= 6e-37) {
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))) / (0.607771387771 + (z * (11.9400905721 + (z * 31.4690115749)))));
	} else if (z <= 8.6e+33) {
		tmp = x + (((a * (y * z)) + (y * b)) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771));
	} else {
		tmp = x + (y * 3.13060547623);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-3200000000.0d0)) then
        tmp = x - (y * ((-3.13060547623d0) + (36.52704169880642d0 / z)))
    else if (z <= 6d-37) then
        tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262d0))))))) / (0.607771387771d0 + (z * (11.9400905721d0 + (z * 31.4690115749d0)))))
    else if (z <= 8.6d+33) then
        tmp = x + (((a * (y * z)) + (y * b)) / ((z * ((z * ((z * (z + 15.234687407d0)) + 31.4690115749d0)) + 11.9400905721d0)) + 0.607771387771d0))
    else
        tmp = x + (y * 3.13060547623d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -3200000000.0) {
		tmp = x - (y * (-3.13060547623 + (36.52704169880642 / z)));
	} else if (z <= 6e-37) {
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))) / (0.607771387771 + (z * (11.9400905721 + (z * 31.4690115749)))));
	} else if (z <= 8.6e+33) {
		tmp = x + (((a * (y * z)) + (y * b)) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771));
	} else {
		tmp = x + (y * 3.13060547623);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -3200000000.0:
		tmp = x - (y * (-3.13060547623 + (36.52704169880642 / z)))
	elif z <= 6e-37:
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))) / (0.607771387771 + (z * (11.9400905721 + (z * 31.4690115749)))))
	elif z <= 8.6e+33:
		tmp = x + (((a * (y * z)) + (y * b)) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771))
	else:
		tmp = x + (y * 3.13060547623)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -3200000000.0)
		tmp = Float64(x - Float64(y * Float64(-3.13060547623 + Float64(36.52704169880642 / z))));
	elseif (z <= 6e-37)
		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 * Float64(11.9400905721 + Float64(z * 31.4690115749))))));
	elseif (z <= 8.6e+33)
		tmp = Float64(x + Float64(Float64(Float64(a * Float64(y * z)) + Float64(y * b)) / Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)));
	else
		tmp = Float64(x + Float64(y * 3.13060547623));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -3200000000.0)
		tmp = x - (y * (-3.13060547623 + (36.52704169880642 / z)));
	elseif (z <= 6e-37)
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))) / (0.607771387771 + (z * (11.9400905721 + (z * 31.4690115749)))));
	elseif (z <= 8.6e+33)
		tmp = x + (((a * (y * z)) + (y * b)) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771));
	else
		tmp = x + (y * 3.13060547623);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -3200000000.0], N[(x - N[(y * N[(-3.13060547623 + N[(36.52704169880642 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6e-37], 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 * N[(11.9400905721 + N[(z * 31.4690115749), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.6e+33], N[(x + N[(N[(N[(a * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(N[(z * N[(N[(z * N[(N[(z * N[(z + 15.234687407), $MachinePrecision]), $MachinePrecision] + 31.4690115749), $MachinePrecision]), $MachinePrecision] + 11.9400905721), $MachinePrecision]), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.2e9

   1. Initial program 14.1%

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

   3. Simplified 26.6%

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

   4. Taylor expanded in z around inf 81.0%

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

   5. Taylor expanded in y around -inf 90.5%

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

      1. mul-1-neg 90.5%

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

      2. *-commutative 90.5%

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

      3. distribute-rgt-neg-in 90.5%

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

      4. sub-neg 90.5%

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

      5. +-commutative 90.5%

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

      6. mul-1-neg 90.5%

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

      7. unsub-neg 90.5%

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

      8. associate-*r/ 90.5%

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

      9. metadata-eval 90.5%

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

      10. +-commutative 90.5%

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

      11. metadata-eval 90.5%

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

   7. Simplified 90.5%

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

   8. Taylor expanded in z around inf 85.8%

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

   if -3.2e9 < z < 6e-37

   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. Taylor expanded in z around 0 98.1%

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

      1. *-commutative 94.0%

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

   4. Simplified 98.1%

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

   5. Taylor expanded in z around 0 98.1%

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

      1. *-commutative 98.1%

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

   7. Simplified 98.1%

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

   if 6e-37 < z < 8.60000000000000057e33

   1. Initial program 94.1%

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

   2. Taylor expanded in z around 0 99.8%

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

   if 8.60000000000000057e33 < z

   1. Initial program 6.7%

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

   3. Simplified 8.8%

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

   4. Taylor expanded in z around inf 91.5%

      \[\leadsto \color{blue}{x + 3.13060547623 \cdot y} \]
3. Recombined 4 regimes into one program.

4. Final simplification 94.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3200000000:\\ \;\;\;\;x - y \cdot \left(-3.13060547623 + \frac{36.52704169880642}{z}\right)\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-37}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot 11.1667541262\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot 31.4690115749\right)}\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{+33}:\\ \;\;\;\;x + \frac{a \cdot \left(y \cdot z\right) + y \cdot b}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \]

Alternative 8: 92.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1300:\\ \;\;\;\;x - y \cdot \left(-3.13060547623 + \frac{36.52704169880642}{z}\right)\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-37}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot 11.1667541262\right)\right)\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+32}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot a\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1300.0)
   (- x (* y (+ -3.13060547623 (/ 36.52704169880642 z))))
   (if (<= z 6e-37)
     (+
      x
      (/
       (* y (+ b (* z (+ a (* z (+ t (* z 11.1667541262)))))))
       (+ 0.607771387771 (* z 11.9400905721))))
     (if (<= z 7e+32)
       (+
        x
        (/
         (* y (+ b (* z a)))
         (+
          (*
           z
           (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721))
          0.607771387771)))
       (+ x (* y 3.13060547623))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1300.0) {
		tmp = x - (y * (-3.13060547623 + (36.52704169880642 / z)));
	} else if (z <= 6e-37) {
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))) / (0.607771387771 + (z * 11.9400905721)));
	} else if (z <= 7e+32) {
		tmp = x + ((y * (b + (z * a))) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771));
	} else {
		tmp = x + (y * 3.13060547623);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-1300.0d0)) then
        tmp = x - (y * ((-3.13060547623d0) + (36.52704169880642d0 / z)))
    else if (z <= 6d-37) then
        tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262d0))))))) / (0.607771387771d0 + (z * 11.9400905721d0)))
    else if (z <= 7d+32) then
        tmp = x + ((y * (b + (z * a))) / ((z * ((z * ((z * (z + 15.234687407d0)) + 31.4690115749d0)) + 11.9400905721d0)) + 0.607771387771d0))
    else
        tmp = x + (y * 3.13060547623d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1300.0) {
		tmp = x - (y * (-3.13060547623 + (36.52704169880642 / z)));
	} else if (z <= 6e-37) {
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))) / (0.607771387771 + (z * 11.9400905721)));
	} else if (z <= 7e+32) {
		tmp = x + ((y * (b + (z * a))) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771));
	} else {
		tmp = x + (y * 3.13060547623);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1300.0:
		tmp = x - (y * (-3.13060547623 + (36.52704169880642 / z)))
	elif z <= 6e-37:
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))) / (0.607771387771 + (z * 11.9400905721)))
	elif z <= 7e+32:
		tmp = x + ((y * (b + (z * a))) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771))
	else:
		tmp = x + (y * 3.13060547623)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1300.0)
		tmp = Float64(x - Float64(y * Float64(-3.13060547623 + Float64(36.52704169880642 / z))));
	elseif (z <= 6e-37)
		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))));
	elseif (z <= 7e+32)
		tmp = Float64(x + Float64(Float64(y * Float64(b + Float64(z * a))) / Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)));
	else
		tmp = Float64(x + Float64(y * 3.13060547623));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1300.0)
		tmp = x - (y * (-3.13060547623 + (36.52704169880642 / z)));
	elseif (z <= 6e-37)
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))) / (0.607771387771 + (z * 11.9400905721)));
	elseif (z <= 7e+32)
		tmp = x + ((y * (b + (z * a))) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771));
	else
		tmp = x + (y * 3.13060547623);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1300.0], N[(x - N[(y * N[(-3.13060547623 + N[(36.52704169880642 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6e-37], 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], If[LessEqual[z, 7e+32], N[(x + N[(N[(y * N[(b + N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(z * N[(N[(z * N[(N[(z * N[(z + 15.234687407), $MachinePrecision]), $MachinePrecision] + 31.4690115749), $MachinePrecision]), $MachinePrecision] + 11.9400905721), $MachinePrecision]), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1300

   1. Initial program 16.9%

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

   3. Simplified 28.9%

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

   4. Taylor expanded in z around inf 80.5%

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

   5. Taylor expanded in y around -inf 89.7%

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

      1. mul-1-neg 89.7%

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

      2. *-commutative 89.7%

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

      3. distribute-rgt-neg-in 89.7%

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

      4. sub-neg 89.7%

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

      5. +-commutative 89.7%

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

      6. mul-1-neg 89.7%

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

      7. unsub-neg 89.7%

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

      8. associate-*r/ 89.7%

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

      9. metadata-eval 89.7%

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

      10. +-commutative 89.7%

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

      11. metadata-eval 89.7%

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

   7. Simplified 89.7%

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

   8. Taylor expanded in z around inf 84.7%

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

   if -1300 < z < 6e-37

   1. Initial program 99.6%

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

   2. Taylor expanded in z around 0 98.7%

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

      1. *-commutative 94.6%

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

   4. Simplified 98.7%

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

   5. Taylor expanded in z around 0 98.7%

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

      1. *-commutative 98.7%

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

   7. Simplified 98.7%

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

   8. Taylor expanded in z around 0 98.6%

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

      1. *-commutative 98.6%

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

   10. Simplified 98.6%

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

   if 6e-37 < z < 7.0000000000000002e32

   1. Initial program 94.1%

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

   2. Taylor expanded in z around 0 99.8%

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

   3. Taylor expanded in y around 0 99.6%

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

      1. *-commutative 99.6%

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

   5. Simplified 99.6%

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

   if 7.0000000000000002e32 < z

   1. Initial program 6.7%

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

   3. Simplified 8.8%

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

   4. Taylor expanded in z around inf 91.5%

      \[\leadsto \color{blue}{x + 3.13060547623 \cdot y} \]
3. Recombined 4 regimes into one program.

4. Final simplification 94.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1300:\\ \;\;\;\;x - y \cdot \left(-3.13060547623 + \frac{36.52704169880642}{z}\right)\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-37}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot 11.1667541262\right)\right)\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+32}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot a\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \]

Alternative 9: 92.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1060000000:\\ \;\;\;\;x - y \cdot \left(-3.13060547623 + \frac{36.52704169880642}{z}\right)\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-37}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot 11.1667541262\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot 31.4690115749\right)}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+32}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot a\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1060000000.0)
   (- x (* y (+ -3.13060547623 (/ 36.52704169880642 z))))
   (if (<= z 6e-37)
     (+
      x
      (/
       (* y (+ b (* z (+ a (* z (+ t (* z 11.1667541262)))))))
       (+ 0.607771387771 (* z (+ 11.9400905721 (* z 31.4690115749))))))
     (if (<= z 5.5e+32)
       (+
        x
        (/
         (* y (+ b (* z a)))
         (+
          (*
           z
           (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721))
          0.607771387771)))
       (+ x (* y 3.13060547623))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1060000000.0) {
		tmp = x - (y * (-3.13060547623 + (36.52704169880642 / z)));
	} else if (z <= 6e-37) {
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))) / (0.607771387771 + (z * (11.9400905721 + (z * 31.4690115749)))));
	} else if (z <= 5.5e+32) {
		tmp = x + ((y * (b + (z * a))) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771));
	} else {
		tmp = x + (y * 3.13060547623);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-1060000000.0d0)) then
        tmp = x - (y * ((-3.13060547623d0) + (36.52704169880642d0 / z)))
    else if (z <= 6d-37) then
        tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262d0))))))) / (0.607771387771d0 + (z * (11.9400905721d0 + (z * 31.4690115749d0)))))
    else if (z <= 5.5d+32) then
        tmp = x + ((y * (b + (z * a))) / ((z * ((z * ((z * (z + 15.234687407d0)) + 31.4690115749d0)) + 11.9400905721d0)) + 0.607771387771d0))
    else
        tmp = x + (y * 3.13060547623d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1060000000.0) {
		tmp = x - (y * (-3.13060547623 + (36.52704169880642 / z)));
	} else if (z <= 6e-37) {
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))) / (0.607771387771 + (z * (11.9400905721 + (z * 31.4690115749)))));
	} else if (z <= 5.5e+32) {
		tmp = x + ((y * (b + (z * a))) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771));
	} else {
		tmp = x + (y * 3.13060547623);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1060000000.0:
		tmp = x - (y * (-3.13060547623 + (36.52704169880642 / z)))
	elif z <= 6e-37:
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))) / (0.607771387771 + (z * (11.9400905721 + (z * 31.4690115749)))))
	elif z <= 5.5e+32:
		tmp = x + ((y * (b + (z * a))) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771))
	else:
		tmp = x + (y * 3.13060547623)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1060000000.0)
		tmp = Float64(x - Float64(y * Float64(-3.13060547623 + Float64(36.52704169880642 / z))));
	elseif (z <= 6e-37)
		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 * Float64(11.9400905721 + Float64(z * 31.4690115749))))));
	elseif (z <= 5.5e+32)
		tmp = Float64(x + Float64(Float64(y * Float64(b + Float64(z * a))) / Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)));
	else
		tmp = Float64(x + Float64(y * 3.13060547623));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1060000000.0)
		tmp = x - (y * (-3.13060547623 + (36.52704169880642 / z)));
	elseif (z <= 6e-37)
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))) / (0.607771387771 + (z * (11.9400905721 + (z * 31.4690115749)))));
	elseif (z <= 5.5e+32)
		tmp = x + ((y * (b + (z * a))) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771));
	else
		tmp = x + (y * 3.13060547623);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1060000000.0], N[(x - N[(y * N[(-3.13060547623 + N[(36.52704169880642 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6e-37], 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 * N[(11.9400905721 + N[(z * 31.4690115749), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.5e+32], N[(x + N[(N[(y * N[(b + N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(z * N[(N[(z * N[(N[(z * N[(z + 15.234687407), $MachinePrecision]), $MachinePrecision] + 31.4690115749), $MachinePrecision]), $MachinePrecision] + 11.9400905721), $MachinePrecision]), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.06e9

   1. Initial program 14.1%

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

   3. Simplified 26.6%

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

   4. Taylor expanded in z around inf 81.0%

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

   5. Taylor expanded in y around -inf 90.5%

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

      1. mul-1-neg 90.5%

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

      2. *-commutative 90.5%

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

      3. distribute-rgt-neg-in 90.5%

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

      4. sub-neg 90.5%

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

      5. +-commutative 90.5%

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

      6. mul-1-neg 90.5%

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

      7. unsub-neg 90.5%

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

      8. associate-*r/ 90.5%

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

      9. metadata-eval 90.5%

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

      10. +-commutative 90.5%

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

      11. metadata-eval 90.5%

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

   7. Simplified 90.5%

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

   8. Taylor expanded in z around inf 85.8%

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

   if -1.06e9 < z < 6e-37

   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. Taylor expanded in z around 0 98.1%

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

      1. *-commutative 94.0%

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

   4. Simplified 98.1%

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

   5. Taylor expanded in z around 0 98.1%

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

      1. *-commutative 98.1%

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

   7. Simplified 98.1%

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

   if 6e-37 < z < 5.49999999999999984e32

   1. Initial program 94.1%

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

   2. Taylor expanded in z around 0 99.8%

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

   3. Taylor expanded in y around 0 99.6%

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

      1. *-commutative 99.6%

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

   5. Simplified 99.6%

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

   if 5.49999999999999984e32 < z

   1. Initial program 6.7%

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

   3. Simplified 8.8%

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

   4. Taylor expanded in z around inf 91.5%

      \[\leadsto \color{blue}{x + 3.13060547623 \cdot y} \]
3. Recombined 4 regimes into one program.

4. Final simplification 94.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1060000000:\\ \;\;\;\;x - y \cdot \left(-3.13060547623 + \frac{36.52704169880642}{z}\right)\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-37}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot 11.1667541262\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot 31.4690115749\right)}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+32}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot a\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \]

Alternative 10: 89.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9:\\ \;\;\;\;x - y \cdot \left(-3.13060547623 + \frac{36.52704169880642}{z}\right)\\ \mathbf{elif}\;z \leq 0.34:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot a\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot 31.4690115749\right)}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+56}:\\ \;\;\;\;x + \frac{a \cdot \left(y \cdot z\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\\ \mathbf{elif}\;z \leq 3.45 \cdot 10^{+83}:\\ \;\;\;\;x + y \cdot \left(z \cdot 0.35484921728862673\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.9)
   (- x (* y (+ -3.13060547623 (/ 36.52704169880642 z))))
   (if (<= z 0.34)
     (+
      x
      (/
       (* y (+ b (* z a)))
       (+ 0.607771387771 (* z (+ 11.9400905721 (* z 31.4690115749))))))
     (if (<= z 7.5e+56)
       (+
        x
        (/
         (* a (* y z))
         (+
          (*
           z
           (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721))
          0.607771387771)))
       (if (<= z 3.45e+83)
         (+ x (* y (* z 0.35484921728862673)))
         (+ x (* y 3.13060547623)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.9) {
		tmp = x - (y * (-3.13060547623 + (36.52704169880642 / z)));
	} else if (z <= 0.34) {
		tmp = x + ((y * (b + (z * a))) / (0.607771387771 + (z * (11.9400905721 + (z * 31.4690115749)))));
	} else if (z <= 7.5e+56) {
		tmp = x + ((a * (y * z)) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771));
	} else if (z <= 3.45e+83) {
		tmp = x + (y * (z * 0.35484921728862673));
	} else {
		tmp = x + (y * 3.13060547623);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-1.9d0)) then
        tmp = x - (y * ((-3.13060547623d0) + (36.52704169880642d0 / z)))
    else if (z <= 0.34d0) then
        tmp = x + ((y * (b + (z * a))) / (0.607771387771d0 + (z * (11.9400905721d0 + (z * 31.4690115749d0)))))
    else if (z <= 7.5d+56) then
        tmp = x + ((a * (y * z)) / ((z * ((z * ((z * (z + 15.234687407d0)) + 31.4690115749d0)) + 11.9400905721d0)) + 0.607771387771d0))
    else if (z <= 3.45d+83) then
        tmp = x + (y * (z * 0.35484921728862673d0))
    else
        tmp = x + (y * 3.13060547623d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.9) {
		tmp = x - (y * (-3.13060547623 + (36.52704169880642 / z)));
	} else if (z <= 0.34) {
		tmp = x + ((y * (b + (z * a))) / (0.607771387771 + (z * (11.9400905721 + (z * 31.4690115749)))));
	} else if (z <= 7.5e+56) {
		tmp = x + ((a * (y * z)) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771));
	} else if (z <= 3.45e+83) {
		tmp = x + (y * (z * 0.35484921728862673));
	} else {
		tmp = x + (y * 3.13060547623);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.9:
		tmp = x - (y * (-3.13060547623 + (36.52704169880642 / z)))
	elif z <= 0.34:
		tmp = x + ((y * (b + (z * a))) / (0.607771387771 + (z * (11.9400905721 + (z * 31.4690115749)))))
	elif z <= 7.5e+56:
		tmp = x + ((a * (y * z)) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771))
	elif z <= 3.45e+83:
		tmp = x + (y * (z * 0.35484921728862673))
	else:
		tmp = x + (y * 3.13060547623)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.9)
		tmp = Float64(x - Float64(y * Float64(-3.13060547623 + Float64(36.52704169880642 / z))));
	elseif (z <= 0.34)
		tmp = Float64(x + Float64(Float64(y * Float64(b + Float64(z * a))) / Float64(0.607771387771 + Float64(z * Float64(11.9400905721 + Float64(z * 31.4690115749))))));
	elseif (z <= 7.5e+56)
		tmp = Float64(x + Float64(Float64(a * Float64(y * z)) / Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)));
	elseif (z <= 3.45e+83)
		tmp = Float64(x + Float64(y * Float64(z * 0.35484921728862673)));
	else
		tmp = Float64(x + Float64(y * 3.13060547623));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1.9)
		tmp = x - (y * (-3.13060547623 + (36.52704169880642 / z)));
	elseif (z <= 0.34)
		tmp = x + ((y * (b + (z * a))) / (0.607771387771 + (z * (11.9400905721 + (z * 31.4690115749)))));
	elseif (z <= 7.5e+56)
		tmp = x + ((a * (y * z)) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771));
	elseif (z <= 3.45e+83)
		tmp = x + (y * (z * 0.35484921728862673));
	else
		tmp = x + (y * 3.13060547623);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.9], N[(x - N[(y * N[(-3.13060547623 + N[(36.52704169880642 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.34], N[(x + N[(N[(y * N[(b + N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(0.607771387771 + N[(z * N[(11.9400905721 + N[(z * 31.4690115749), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.5e+56], N[(x + N[(N[(a * N[(y * z), $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, 3.45e+83], N[(x + N[(y * N[(z * 0.35484921728862673), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.8999999999999999

   1. Initial program 19.5%

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

   3. Simplified 31.2%

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

   4. Taylor expanded in z around inf 79.5%

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

   5. Taylor expanded in y around -inf 88.5%

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

      1. mul-1-neg 88.5%

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

      2. *-commutative 88.5%

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

      3. distribute-rgt-neg-in 88.5%

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

      4. sub-neg 88.5%

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

      5. +-commutative 88.5%

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

      6. mul-1-neg 88.5%

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

      7. unsub-neg 88.5%

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

      8. associate-*r/ 88.5%

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

      9. metadata-eval 88.5%

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

      10. +-commutative 88.5%

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

      11. metadata-eval 88.5%

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

   7. Simplified 88.5%

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

   8. Taylor expanded in z around inf 83.6%

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

   if -1.8999999999999999 < z < 0.340000000000000024

   1. Initial program 99.6%

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

   2. Taylor expanded in z around 0 93.4%

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

   3. Taylor expanded in y around 0 95.5%

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

      1. *-commutative 95.5%

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

   5. Simplified 95.5%

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

   6. Taylor expanded in z around 0 95.1%

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

      1. *-commutative 95.1%

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

   8. Simplified 95.1%

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

   if 0.340000000000000024 < z < 7.4999999999999999e56

   1. Initial program 85.7%

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

   2. Taylor expanded in a around inf 88.8%

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

      1. *-commutative 88.8%

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

   4. Simplified 88.8%

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

   if 7.4999999999999999e56 < z < 3.4500000000000001e83

   1. Initial program 17.6%

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

   2. Taylor expanded in z around 0 19.7%

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

      1. *-commutative 65.7%

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

   4. Simplified 19.7%

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

   5. Taylor expanded in z around 0 48.9%

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

      1. *-commutative 48.9%

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

   7. Simplified 48.9%

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

   8. Taylor expanded in z around inf 69.3%

      \[\leadsto x + \color{blue}{0.35484921728862673 \cdot \left(y \cdot z\right)} \]
   9. Step-by-step derivation

      1. *-commutative 69.3%

         \[\leadsto x + \color{blue}{\left(y \cdot z\right) \cdot 0.35484921728862673} \]

      2. associate-*l* 69.3%

         \[\leadsto x + \color{blue}{y \cdot \left(z \cdot 0.35484921728862673\right)} \]

   10. Simplified 69.3%

       \[\leadsto x + \color{blue}{y \cdot \left(z \cdot 0.35484921728862673\right)} \]

   if 3.4500000000000001e83 < z

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   4. Taylor expanded in z around inf 97.2%

      \[\leadsto \color{blue}{x + 3.13060547623 \cdot y} \]
3. Recombined 5 regimes into one program.

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9:\\ \;\;\;\;x - y \cdot \left(-3.13060547623 + \frac{36.52704169880642}{z}\right)\\ \mathbf{elif}\;z \leq 0.34:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot a\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot 31.4690115749\right)}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+56}:\\ \;\;\;\;x + \frac{a \cdot \left(y \cdot z\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\\ \mathbf{elif}\;z \leq 3.45 \cdot 10^{+83}:\\ \;\;\;\;x + y \cdot \left(z \cdot 0.35484921728862673\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \]

Alternative 11: 92.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1300:\\ \;\;\;\;x - y \cdot \left(-3.13060547623 + \frac{36.52704169880642}{z}\right)\\ \mathbf{elif}\;z \leq 0.37:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot 11.1667541262\right)\right)\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+31}:\\ \;\;\;\;x + \frac{a \cdot \left(y \cdot z\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1300.0)
   (- x (* y (+ -3.13060547623 (/ 36.52704169880642 z))))
   (if (<= z 0.37)
     (+
      x
      (/
       (* y (+ b (* z (+ a (* z (+ t (* z 11.1667541262)))))))
       (+ 0.607771387771 (* z 11.9400905721))))
     (if (<= z 8e+31)
       (+
        x
        (/
         (* a (* y z))
         (+
          (*
           z
           (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721))
          0.607771387771)))
       (+ x (* y 3.13060547623))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1300.0) {
		tmp = x - (y * (-3.13060547623 + (36.52704169880642 / z)));
	} else if (z <= 0.37) {
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))) / (0.607771387771 + (z * 11.9400905721)));
	} else if (z <= 8e+31) {
		tmp = x + ((a * (y * z)) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771));
	} else {
		tmp = x + (y * 3.13060547623);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-1300.0d0)) then
        tmp = x - (y * ((-3.13060547623d0) + (36.52704169880642d0 / z)))
    else if (z <= 0.37d0) then
        tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262d0))))))) / (0.607771387771d0 + (z * 11.9400905721d0)))
    else if (z <= 8d+31) then
        tmp = x + ((a * (y * z)) / ((z * ((z * ((z * (z + 15.234687407d0)) + 31.4690115749d0)) + 11.9400905721d0)) + 0.607771387771d0))
    else
        tmp = x + (y * 3.13060547623d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1300.0) {
		tmp = x - (y * (-3.13060547623 + (36.52704169880642 / z)));
	} else if (z <= 0.37) {
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))) / (0.607771387771 + (z * 11.9400905721)));
	} else if (z <= 8e+31) {
		tmp = x + ((a * (y * z)) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771));
	} else {
		tmp = x + (y * 3.13060547623);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1300.0:
		tmp = x - (y * (-3.13060547623 + (36.52704169880642 / z)))
	elif z <= 0.37:
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))) / (0.607771387771 + (z * 11.9400905721)))
	elif z <= 8e+31:
		tmp = x + ((a * (y * z)) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771))
	else:
		tmp = x + (y * 3.13060547623)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1300.0)
		tmp = Float64(x - Float64(y * Float64(-3.13060547623 + Float64(36.52704169880642 / z))));
	elseif (z <= 0.37)
		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))));
	elseif (z <= 8e+31)
		tmp = Float64(x + Float64(Float64(a * Float64(y * z)) / Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)));
	else
		tmp = Float64(x + Float64(y * 3.13060547623));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1300.0)
		tmp = x - (y * (-3.13060547623 + (36.52704169880642 / z)));
	elseif (z <= 0.37)
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))) / (0.607771387771 + (z * 11.9400905721)));
	elseif (z <= 8e+31)
		tmp = x + ((a * (y * z)) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771));
	else
		tmp = x + (y * 3.13060547623);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1300.0], N[(x - N[(y * N[(-3.13060547623 + N[(36.52704169880642 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.37], 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], If[LessEqual[z, 8e+31], N[(x + N[(N[(a * N[(y * z), $MachinePrecision]), $MachinePrecision] / N[(N[(z * N[(N[(z * N[(N[(z * N[(z + 15.234687407), $MachinePrecision]), $MachinePrecision] + 31.4690115749), $MachinePrecision]), $MachinePrecision] + 11.9400905721), $MachinePrecision]), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1300

   1. Initial program 16.9%

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

   3. Simplified 28.9%

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

   4. Taylor expanded in z around inf 80.5%

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

   5. Taylor expanded in y around -inf 89.7%

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

      1. mul-1-neg 89.7%

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

      2. *-commutative 89.7%

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

      3. distribute-rgt-neg-in 89.7%

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

      4. sub-neg 89.7%

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

      5. +-commutative 89.7%

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

      6. mul-1-neg 89.7%

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

      7. unsub-neg 89.7%

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

      8. associate-*r/ 89.7%

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

      9. metadata-eval 89.7%

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

      10. +-commutative 89.7%

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

      11. metadata-eval 89.7%

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

   7. Simplified 89.7%

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

   8. Taylor expanded in z around inf 84.7%

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

   if -1300 < z < 0.37

   1. Initial program 99.6%

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

   2. Taylor expanded in z around 0 98.4%

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

      1. *-commutative 94.5%

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

   4. Simplified 98.4%

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

   5. Taylor expanded in z around 0 98.4%

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

      1. *-commutative 98.4%

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

   7. Simplified 98.4%

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

   8. Taylor expanded in z around 0 98.1%

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

      1. *-commutative 98.1%

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

   10. Simplified 98.1%

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

   if 0.37 < z < 7.9999999999999997e31

   1. Initial program 91.1%

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

   2. Taylor expanded in a around inf 95.4%

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

      1. *-commutative 95.4%

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

   4. Simplified 95.4%

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

   if 7.9999999999999997e31 < z

   1. Initial program 6.7%

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

   3. Simplified 8.8%

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

   4. Taylor expanded in z around inf 91.5%

      \[\leadsto \color{blue}{x + 3.13060547623 \cdot y} \]
3. Recombined 4 regimes into one program.

4. Final simplification 93.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1300:\\ \;\;\;\;x - y \cdot \left(-3.13060547623 + \frac{36.52704169880642}{z}\right)\\ \mathbf{elif}\;z \leq 0.37:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot 11.1667541262\right)\right)\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+31}:\\ \;\;\;\;x + \frac{a \cdot \left(y \cdot z\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \]

Alternative 12: 89.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3:\\ \;\;\;\;x - y \cdot \left(-3.13060547623 + \frac{36.52704169880642}{z}\right)\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+31}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot a\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot 31.4690115749\right)}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -2.3)
   (- x (* y (+ -3.13060547623 (/ 36.52704169880642 z))))
   (if (<= z 2.05e+31)
     (+
      x
      (/
       (* y (+ b (* z a)))
       (+ 0.607771387771 (* z (+ 11.9400905721 (* z 31.4690115749))))))
     (+ x (* y 3.13060547623)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.3) {
		tmp = x - (y * (-3.13060547623 + (36.52704169880642 / z)));
	} else if (z <= 2.05e+31) {
		tmp = x + ((y * (b + (z * a))) / (0.607771387771 + (z * (11.9400905721 + (z * 31.4690115749)))));
	} else {
		tmp = x + (y * 3.13060547623);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-2.3d0)) then
        tmp = x - (y * ((-3.13060547623d0) + (36.52704169880642d0 / z)))
    else if (z <= 2.05d+31) then
        tmp = x + ((y * (b + (z * a))) / (0.607771387771d0 + (z * (11.9400905721d0 + (z * 31.4690115749d0)))))
    else
        tmp = x + (y * 3.13060547623d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.3) {
		tmp = x - (y * (-3.13060547623 + (36.52704169880642 / z)));
	} else if (z <= 2.05e+31) {
		tmp = x + ((y * (b + (z * a))) / (0.607771387771 + (z * (11.9400905721 + (z * 31.4690115749)))));
	} else {
		tmp = x + (y * 3.13060547623);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -2.3:
		tmp = x - (y * (-3.13060547623 + (36.52704169880642 / z)))
	elif z <= 2.05e+31:
		tmp = x + ((y * (b + (z * a))) / (0.607771387771 + (z * (11.9400905721 + (z * 31.4690115749)))))
	else:
		tmp = x + (y * 3.13060547623)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -2.3)
		tmp = Float64(x - Float64(y * Float64(-3.13060547623 + Float64(36.52704169880642 / z))));
	elseif (z <= 2.05e+31)
		tmp = Float64(x + Float64(Float64(y * Float64(b + Float64(z * a))) / Float64(0.607771387771 + Float64(z * Float64(11.9400905721 + Float64(z * 31.4690115749))))));
	else
		tmp = Float64(x + Float64(y * 3.13060547623));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -2.3)
		tmp = x - (y * (-3.13060547623 + (36.52704169880642 / z)));
	elseif (z <= 2.05e+31)
		tmp = x + ((y * (b + (z * a))) / (0.607771387771 + (z * (11.9400905721 + (z * 31.4690115749)))));
	else
		tmp = x + (y * 3.13060547623);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -2.3], N[(x - N[(y * N[(-3.13060547623 + N[(36.52704169880642 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.05e+31], N[(x + N[(N[(y * N[(b + N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(0.607771387771 + N[(z * N[(11.9400905721 + N[(z * 31.4690115749), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.2999999999999998

   1. Initial program 19.5%

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

   3. Simplified 31.2%

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

   4. Taylor expanded in z around inf 79.5%

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

   5. Taylor expanded in y around -inf 88.5%

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

      1. mul-1-neg 88.5%

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

      2. *-commutative 88.5%

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

      3. distribute-rgt-neg-in 88.5%

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

      4. sub-neg 88.5%

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

      5. +-commutative 88.5%

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

      6. mul-1-neg 88.5%

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

      7. unsub-neg 88.5%

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

      8. associate-*r/ 88.5%

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

      9. metadata-eval 88.5%

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

      10. +-commutative 88.5%

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

      11. metadata-eval 88.5%

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

   7. Simplified 88.5%

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

   8. Taylor expanded in z around inf 83.6%

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

   if -2.2999999999999998 < z < 2.0500000000000001e31

   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. Taylor expanded in z around 0 93.8%

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

   3. Taylor expanded in y around 0 95.8%

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

      1. *-commutative 95.8%

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

   5. Simplified 95.8%

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

   6. Taylor expanded in z around 0 92.5%

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

      1. *-commutative 92.5%

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

   8. Simplified 92.5%

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

   if 2.0500000000000001e31 < z

   1. Initial program 6.7%

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

   3. Simplified 8.8%

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

   4. Taylor expanded in z around inf 91.5%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3:\\ \;\;\;\;x - y \cdot \left(-3.13060547623 + \frac{36.52704169880642}{z}\right)\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+31}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot a\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot 31.4690115749\right)}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \]

Alternative 13: 83.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot \left(-3.13060547623 + \frac{36.52704169880642}{z}\right)\\ \mathbf{if}\;z \leq -1.9:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-111}:\\ \;\;\;\;x - y \cdot \left(z \cdot \left(b \cdot 32.324150453290734 - a \cdot 1.6453555072203998\right)\right)\\ \mathbf{elif}\;z \leq 0.236:\\ \;\;\;\;x + b \cdot \left(\left(y \cdot z\right) \cdot -32.324150453290734 + y \cdot 1.6453555072203998\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- x (* y (+ -3.13060547623 (/ 36.52704169880642 z))))))
   (if (<= z -1.9)
     t_1
     (if (<= z -3.6e-111)
       (- x (* y (* z (- (* b 32.324150453290734) (* a 1.6453555072203998)))))
       (if (<= z 0.236)
         (+
          x
          (* b (+ (* (* y z) -32.324150453290734) (* 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 + (36.52704169880642 / z)));
	double tmp;
	if (z <= -1.9) {
		tmp = t_1;
	} else if (z <= -3.6e-111) {
		tmp = x - (y * (z * ((b * 32.324150453290734) - (a * 1.6453555072203998))));
	} else if (z <= 0.236) {
		tmp = x + (b * (((y * z) * -32.324150453290734) + (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) + (36.52704169880642d0 / z)))
    if (z <= (-1.9d0)) then
        tmp = t_1
    else if (z <= (-3.6d-111)) then
        tmp = x - (y * (z * ((b * 32.324150453290734d0) - (a * 1.6453555072203998d0))))
    else if (z <= 0.236d0) then
        tmp = x + (b * (((y * z) * (-32.324150453290734d0)) + (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 + (36.52704169880642 / z)));
	double tmp;
	if (z <= -1.9) {
		tmp = t_1;
	} else if (z <= -3.6e-111) {
		tmp = x - (y * (z * ((b * 32.324150453290734) - (a * 1.6453555072203998))));
	} else if (z <= 0.236) {
		tmp = x + (b * (((y * z) * -32.324150453290734) + (y * 1.6453555072203998)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x - (y * (-3.13060547623 + (36.52704169880642 / z)))
	tmp = 0
	if z <= -1.9:
		tmp = t_1
	elif z <= -3.6e-111:
		tmp = x - (y * (z * ((b * 32.324150453290734) - (a * 1.6453555072203998))))
	elif z <= 0.236:
		tmp = x + (b * (((y * z) * -32.324150453290734) + (y * 1.6453555072203998)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x - Float64(y * Float64(-3.13060547623 + Float64(36.52704169880642 / z))))
	tmp = 0.0
	if (z <= -1.9)
		tmp = t_1;
	elseif (z <= -3.6e-111)
		tmp = Float64(x - Float64(y * Float64(z * Float64(Float64(b * 32.324150453290734) - Float64(a * 1.6453555072203998)))));
	elseif (z <= 0.236)
		tmp = Float64(x + Float64(b * Float64(Float64(Float64(y * z) * -32.324150453290734) + 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 + (36.52704169880642 / z)));
	tmp = 0.0;
	if (z <= -1.9)
		tmp = t_1;
	elseif (z <= -3.6e-111)
		tmp = x - (y * (z * ((b * 32.324150453290734) - (a * 1.6453555072203998))));
	elseif (z <= 0.236)
		tmp = x + (b * (((y * z) * -32.324150453290734) + (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 * N[(-3.13060547623 + N[(36.52704169880642 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.9], t$95$1, If[LessEqual[z, -3.6e-111], N[(x - N[(y * N[(z * N[(N[(b * 32.324150453290734), $MachinePrecision] - N[(a * 1.6453555072203998), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.236], N[(x + N[(b * N[(N[(N[(y * z), $MachinePrecision] * -32.324150453290734), $MachinePrecision] + N[(y * 1.6453555072203998), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.8999999999999999 or 0.23599999999999999 < z

   1. Initial program 20.6%

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

   3. Simplified 27.6%

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

   4. Taylor expanded in z around inf 79.2%

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

   5. Taylor expanded in y around -inf 88.9%

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

      1. mul-1-neg 88.9%

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

      2. *-commutative 88.9%

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

      3. distribute-rgt-neg-in 88.9%

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

      4. sub-neg 88.9%

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

      5. +-commutative 88.9%

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

      6. mul-1-neg 88.9%

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

      7. unsub-neg 88.9%

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

      8. associate-*r/ 88.9%

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

      9. metadata-eval 88.9%

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

      10. +-commutative 88.9%

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

      11. metadata-eval 88.9%

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

   7. Simplified 88.9%

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

   8. Taylor expanded in z around inf 83.2%

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

   if -1.8999999999999999 < z < -3.6000000000000001e-111

   1. Initial program 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around 0 80.8%

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

   5. Taylor expanded in z around inf 79.8%

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

   if -3.6000000000000001e-111 < z < 0.23599999999999999

   1. Initial program 99.6%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in z around 0 92.4%

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

   5. Taylor expanded in b around inf 83.9%

      \[\leadsto x + \color{blue}{b \cdot \left(-32.324150453290734 \cdot \left(y \cdot z\right) + 1.6453555072203998 \cdot y\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9:\\ \;\;\;\;x - y \cdot \left(-3.13060547623 + \frac{36.52704169880642}{z}\right)\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-111}:\\ \;\;\;\;x - y \cdot \left(z \cdot \left(b \cdot 32.324150453290734 - a \cdot 1.6453555072203998\right)\right)\\ \mathbf{elif}\;z \leq 0.236:\\ \;\;\;\;x + b \cdot \left(\left(y \cdot z\right) \cdot -32.324150453290734 + y \cdot 1.6453555072203998\right)\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \left(-3.13060547623 + \frac{36.52704169880642}{z}\right)\\ \end{array} \]

Alternative 14: 89.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1300:\\ \;\;\;\;x - y \cdot \left(-3.13060547623 + \frac{36.52704169880642}{z}\right)\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+28}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot a\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1300.0)
   (- x (* y (+ -3.13060547623 (/ 36.52704169880642 z))))
   (if (<= z 2e+28)
     (+ x (/ (* y (+ b (* z a))) (+ 0.607771387771 (* z 11.9400905721))))
     (+ x (* y 3.13060547623)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1300.0) {
		tmp = x - (y * (-3.13060547623 + (36.52704169880642 / z)));
	} else if (z <= 2e+28) {
		tmp = x + ((y * (b + (z * a))) / (0.607771387771 + (z * 11.9400905721)));
	} else {
		tmp = x + (y * 3.13060547623);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-1300.0d0)) then
        tmp = x - (y * ((-3.13060547623d0) + (36.52704169880642d0 / z)))
    else if (z <= 2d+28) then
        tmp = x + ((y * (b + (z * a))) / (0.607771387771d0 + (z * 11.9400905721d0)))
    else
        tmp = x + (y * 3.13060547623d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1300.0) {
		tmp = x - (y * (-3.13060547623 + (36.52704169880642 / z)));
	} else if (z <= 2e+28) {
		tmp = x + ((y * (b + (z * a))) / (0.607771387771 + (z * 11.9400905721)));
	} else {
		tmp = x + (y * 3.13060547623);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1300.0:
		tmp = x - (y * (-3.13060547623 + (36.52704169880642 / z)))
	elif z <= 2e+28:
		tmp = x + ((y * (b + (z * a))) / (0.607771387771 + (z * 11.9400905721)))
	else:
		tmp = x + (y * 3.13060547623)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1300.0)
		tmp = Float64(x - Float64(y * Float64(-3.13060547623 + Float64(36.52704169880642 / z))));
	elseif (z <= 2e+28)
		tmp = Float64(x + Float64(Float64(y * Float64(b + Float64(z * a))) / Float64(0.607771387771 + Float64(z * 11.9400905721))));
	else
		tmp = Float64(x + Float64(y * 3.13060547623));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1300.0)
		tmp = x - (y * (-3.13060547623 + (36.52704169880642 / z)));
	elseif (z <= 2e+28)
		tmp = x + ((y * (b + (z * a))) / (0.607771387771 + (z * 11.9400905721)));
	else
		tmp = x + (y * 3.13060547623);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1300.0], N[(x - N[(y * N[(-3.13060547623 + N[(36.52704169880642 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2e+28], N[(x + N[(N[(y * N[(b + N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(0.607771387771 + N[(z * 11.9400905721), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1300

   1. Initial program 16.9%

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

   3. Simplified 28.9%

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

   4. Taylor expanded in z around inf 80.5%

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

   5. Taylor expanded in y around -inf 89.7%

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

      1. mul-1-neg 89.7%

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

      2. *-commutative 89.7%

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

      3. distribute-rgt-neg-in 89.7%

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

      4. sub-neg 89.7%

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

      5. +-commutative 89.7%

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

      6. mul-1-neg 89.7%

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

      7. unsub-neg 89.7%

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

      8. associate-*r/ 89.7%

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

      9. metadata-eval 89.7%

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

      10. +-commutative 89.7%

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

      11. metadata-eval 89.7%

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

   7. Simplified 89.7%

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

   8. Taylor expanded in z around inf 84.7%

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

   if -1300 < z < 1.99999999999999992e28

   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. Taylor expanded in z around 0 93.9%

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

   3. Taylor expanded in y around 0 95.9%

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

      1. *-commutative 95.9%

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

   5. Simplified 95.9%

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

   6. Taylor expanded in z around 0 91.6%

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

      1. *-commutative 76.4%

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

   8. Simplified 91.6%

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

   if 1.99999999999999992e28 < z

   1. Initial program 6.7%

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

   3. Simplified 8.8%

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

   4. Taylor expanded in z around inf 91.5%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1300:\\ \;\;\;\;x - y \cdot \left(-3.13060547623 + \frac{36.52704169880642}{z}\right)\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+28}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot a\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \]

Alternative 15: 89.6% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9:\\ \;\;\;\;x - y \cdot \left(-3.13060547623 + \frac{36.52704169880642}{z}\right)\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+27}:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998 + \left(z \cdot a\right) \cdot 1.6453555072203998\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.9)
   (- x (* y (+ -3.13060547623 (/ 36.52704169880642 z))))
   (if (<= z 3.2e+27)
     (+ x (* y (+ (* b 1.6453555072203998) (* (* z a) 1.6453555072203998))))
     (+ x (* y 3.13060547623)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.9) {
		tmp = x - (y * (-3.13060547623 + (36.52704169880642 / z)));
	} else if (z <= 3.2e+27) {
		tmp = x + (y * ((b * 1.6453555072203998) + ((z * a) * 1.6453555072203998)));
	} else {
		tmp = x + (y * 3.13060547623);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-1.9d0)) then
        tmp = x - (y * ((-3.13060547623d0) + (36.52704169880642d0 / z)))
    else if (z <= 3.2d+27) then
        tmp = x + (y * ((b * 1.6453555072203998d0) + ((z * a) * 1.6453555072203998d0)))
    else
        tmp = x + (y * 3.13060547623d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.9) {
		tmp = x - (y * (-3.13060547623 + (36.52704169880642 / z)));
	} else if (z <= 3.2e+27) {
		tmp = x + (y * ((b * 1.6453555072203998) + ((z * a) * 1.6453555072203998)));
	} else {
		tmp = x + (y * 3.13060547623);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.9:
		tmp = x - (y * (-3.13060547623 + (36.52704169880642 / z)))
	elif z <= 3.2e+27:
		tmp = x + (y * ((b * 1.6453555072203998) + ((z * a) * 1.6453555072203998)))
	else:
		tmp = x + (y * 3.13060547623)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.9)
		tmp = Float64(x - Float64(y * Float64(-3.13060547623 + Float64(36.52704169880642 / z))));
	elseif (z <= 3.2e+27)
		tmp = Float64(x + Float64(y * Float64(Float64(b * 1.6453555072203998) + Float64(Float64(z * a) * 1.6453555072203998))));
	else
		tmp = Float64(x + Float64(y * 3.13060547623));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1.9)
		tmp = x - (y * (-3.13060547623 + (36.52704169880642 / z)));
	elseif (z <= 3.2e+27)
		tmp = x + (y * ((b * 1.6453555072203998) + ((z * a) * 1.6453555072203998)));
	else
		tmp = x + (y * 3.13060547623);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.9], N[(x - N[(y * N[(-3.13060547623 + N[(36.52704169880642 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.2e+27], N[(x + N[(y * N[(N[(b * 1.6453555072203998), $MachinePrecision] + N[(N[(z * a), $MachinePrecision] * 1.6453555072203998), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.8999999999999999

   1. Initial program 19.5%

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

   3. Simplified 31.2%

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

   4. Taylor expanded in z around inf 79.5%

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

   5. Taylor expanded in y around -inf 88.5%

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

      1. mul-1-neg 88.5%

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

      2. *-commutative 88.5%

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

      3. distribute-rgt-neg-in 88.5%

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

      4. sub-neg 88.5%

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

      5. +-commutative 88.5%

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

      6. mul-1-neg 88.5%

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

      7. unsub-neg 88.5%

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

      8. associate-*r/ 88.5%

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

      9. metadata-eval 88.5%

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

      10. +-commutative 88.5%

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

      11. metadata-eval 88.5%

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

   7. Simplified 88.5%

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

   8. Taylor expanded in z around inf 83.6%

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

   if -1.8999999999999999 < z < 3.20000000000000015e27

   1. Initial program 99.0%

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

   3. Simplified 99.1%

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

   4. Taylor expanded in z around 0 87.8%

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

   5. Taylor expanded in a around inf 89.8%

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

      1. *-commutative 89.8%

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

      2. associate-*l* 89.8%

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

   7. Simplified 89.8%

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

   8. Taylor expanded in y around 0 91.8%

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

   if 3.20000000000000015e27 < z

   1. Initial program 6.7%

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

   3. Simplified 8.8%

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

   4. Taylor expanded in z around inf 91.5%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9:\\ \;\;\;\;x - y \cdot \left(-3.13060547623 + \frac{36.52704169880642}{z}\right)\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+27}:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998 + \left(z \cdot a\right) \cdot 1.6453555072203998\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \]

Alternative 16: 83.2% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1700 \lor \neg \left(z \leq 0.37\right):\\ \;\;\;\;x - y \cdot \left(-3.13060547623 + \frac{36.52704169880642}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot b}{0.607771387771 + z \cdot 11.9400905721}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1700.0) (not (<= z 0.37)))
   (- x (* y (+ -3.13060547623 (/ 36.52704169880642 z))))
   (+ x (/ (* y b) (+ 0.607771387771 (* z 11.9400905721))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1700.0) || !(z <= 0.37)) {
		tmp = x - (y * (-3.13060547623 + (36.52704169880642 / z)));
	} else {
		tmp = x + ((y * b) / (0.607771387771 + (z * 11.9400905721)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-1700.0d0)) .or. (.not. (z <= 0.37d0))) then
        tmp = x - (y * ((-3.13060547623d0) + (36.52704169880642d0 / z)))
    else
        tmp = x + ((y * b) / (0.607771387771d0 + (z * 11.9400905721d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1700.0) || !(z <= 0.37)) {
		tmp = x - (y * (-3.13060547623 + (36.52704169880642 / z)));
	} else {
		tmp = x + ((y * b) / (0.607771387771 + (z * 11.9400905721)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1700.0) or not (z <= 0.37):
		tmp = x - (y * (-3.13060547623 + (36.52704169880642 / z)))
	else:
		tmp = x + ((y * b) / (0.607771387771 + (z * 11.9400905721)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1700.0) || !(z <= 0.37))
		tmp = Float64(x - Float64(y * Float64(-3.13060547623 + Float64(36.52704169880642 / z))));
	else
		tmp = Float64(x + Float64(Float64(y * b) / Float64(0.607771387771 + Float64(z * 11.9400905721))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1700.0) || ~((z <= 0.37)))
		tmp = x - (y * (-3.13060547623 + (36.52704169880642 / z)));
	else
		tmp = x + ((y * b) / (0.607771387771 + (z * 11.9400905721)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1700.0], N[Not[LessEqual[z, 0.37]], $MachinePrecision]], N[(x - N[(y * N[(-3.13060547623 + N[(36.52704169880642 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * b), $MachinePrecision] / N[(0.607771387771 + N[(z * 11.9400905721), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1700 or 0.37 < z

   1. Initial program 19.2%

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

   3. Simplified 26.4%

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

   4. Taylor expanded in z around inf 79.7%

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

   5. Taylor expanded in y around -inf 89.6%

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

      1. mul-1-neg 89.6%

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

      2. *-commutative 89.6%

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

      3. distribute-rgt-neg-in 89.6%

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

      4. sub-neg 89.6%

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

      5. +-commutative 89.6%

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

      6. mul-1-neg 89.6%

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

      7. unsub-neg 89.6%

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

      8. associate-*r/ 89.6%

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

      9. metadata-eval 89.6%

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

      10. +-commutative 89.6%

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

      11. metadata-eval 89.6%

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

   7. Simplified 89.6%

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

   8. Taylor expanded in z around inf 83.8%

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

   if -1700 < z < 0.37

   1. Initial program 99.6%

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

   2. Taylor expanded in z around 0 79.5%

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

   3. Taylor expanded in z around 0 78.9%

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

      1. *-commutative 78.9%

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

   5. Simplified 78.9%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1700 \lor \neg \left(z \leq 0.37\right):\\ \;\;\;\;x - y \cdot \left(-3.13060547623 + \frac{36.52704169880642}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot b}{0.607771387771 + z \cdot 11.9400905721}\\ \end{array} \]

Alternative 17: 83.1% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \lor \neg \left(z \leq 0.37\right):\\ \;\;\;\;x - y \cdot \left(-3.13060547623 + \frac{36.52704169880642}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2.4) (not (<= z 0.37)))
   (- x (* y (+ -3.13060547623 (/ 36.52704169880642 z))))
   (+ x (* y (* b 1.6453555072203998)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.4) || !(z <= 0.37)) {
		tmp = x - (y * (-3.13060547623 + (36.52704169880642 / z)));
	} else {
		tmp = x + (y * (b * 1.6453555072203998));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-2.4d0)) .or. (.not. (z <= 0.37d0))) then
        tmp = x - (y * ((-3.13060547623d0) + (36.52704169880642d0 / z)))
    else
        tmp = x + (y * (b * 1.6453555072203998d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.4) || !(z <= 0.37)) {
		tmp = x - (y * (-3.13060547623 + (36.52704169880642 / z)));
	} else {
		tmp = x + (y * (b * 1.6453555072203998));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -2.4) or not (z <= 0.37):
		tmp = x - (y * (-3.13060547623 + (36.52704169880642 / z)))
	else:
		tmp = x + (y * (b * 1.6453555072203998))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2.4) || !(z <= 0.37))
		tmp = Float64(x - Float64(y * Float64(-3.13060547623 + Float64(36.52704169880642 / z))));
	else
		tmp = Float64(x + Float64(y * Float64(b * 1.6453555072203998)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -2.4) || ~((z <= 0.37)))
		tmp = x - (y * (-3.13060547623 + (36.52704169880642 / z)));
	else
		tmp = x + (y * (b * 1.6453555072203998));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2.4], N[Not[LessEqual[z, 0.37]], $MachinePrecision]], N[(x - N[(y * N[(-3.13060547623 + N[(36.52704169880642 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(b * 1.6453555072203998), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.39999999999999991 or 0.37 < z

   1. Initial program 20.6%

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

   3. Simplified 27.6%

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

   4. Taylor expanded in z around inf 79.2%

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

   5. Taylor expanded in y around -inf 88.9%

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

      1. mul-1-neg 88.9%

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

      2. *-commutative 88.9%

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

      3. distribute-rgt-neg-in 88.9%

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

      4. sub-neg 88.9%

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

      5. +-commutative 88.9%

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

      6. mul-1-neg 88.9%

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

      7. unsub-neg 88.9%

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

      8. associate-*r/ 88.9%

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

      9. metadata-eval 88.9%

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

      10. +-commutative 88.9%

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

      11. metadata-eval 88.9%

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

   7. Simplified 88.9%

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

   8. Taylor expanded in z around inf 83.2%

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

   if -2.39999999999999991 < z < 0.37

   1. Initial program 99.6%

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

   2. Taylor expanded in z around 0 93.4%

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

   3. Taylor expanded in z around 0 78.5%

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

      1. *-commutative 78.5%

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

      2. *-commutative 78.5%

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

      3. associate-*l* 78.5%

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

   5. Simplified 78.5%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \lor \neg \left(z \leq 0.37\right):\\ \;\;\;\;x - y \cdot \left(-3.13060547623 + \frac{36.52704169880642}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998\right)\\ \end{array} \]

Alternative 18: 83.1% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.95 \lor \neg \left(z \leq 140\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot b\right) \cdot 1.6453555072203998\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.95) (not (<= z 140.0)))
   (+ x (* y 3.13060547623))
   (+ x (* (* y b) 1.6453555072203998))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.95) || !(z <= 140.0)) {
		tmp = x + (y * 3.13060547623);
	} else {
		tmp = x + ((y * b) * 1.6453555072203998);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-1.95d0)) .or. (.not. (z <= 140.0d0))) then
        tmp = x + (y * 3.13060547623d0)
    else
        tmp = x + ((y * b) * 1.6453555072203998d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.95) || !(z <= 140.0)) {
		tmp = x + (y * 3.13060547623);
	} else {
		tmp = x + ((y * b) * 1.6453555072203998);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.95) or not (z <= 140.0):
		tmp = x + (y * 3.13060547623)
	else:
		tmp = x + ((y * b) * 1.6453555072203998)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.95) || !(z <= 140.0))
		tmp = Float64(x + Float64(y * 3.13060547623));
	else
		tmp = Float64(x + 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 ((z <= -1.95) || ~((z <= 140.0)))
		tmp = x + (y * 3.13060547623);
	else
		tmp = x + ((y * b) * 1.6453555072203998);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.95], N[Not[LessEqual[z, 140.0]], $MachinePrecision]], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * b), $MachinePrecision] * 1.6453555072203998), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.94999999999999996 or 140 < z

   1. Initial program 18.5%

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

   3. Simplified 25.7%

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

   4. Taylor expanded in z around inf 84.1%

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

   if -1.94999999999999996 < z < 140

   1. Initial program 99.6%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in z around 0 77.6%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \lor \neg \left(z \leq 140\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot b\right) \cdot 1.6453555072203998\\ \end{array} \]

Alternative 19: 83.1% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.95 \lor \neg \left(z \leq 140\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.95) (not (<= z 140.0)))
   (+ x (* y 3.13060547623))
   (+ x (* y (* b 1.6453555072203998)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.95) || !(z <= 140.0)) {
		tmp = x + (y * 3.13060547623);
	} else {
		tmp = x + (y * (b * 1.6453555072203998));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-1.95d0)) .or. (.not. (z <= 140.0d0))) then
        tmp = x + (y * 3.13060547623d0)
    else
        tmp = x + (y * (b * 1.6453555072203998d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.95) || !(z <= 140.0)) {
		tmp = x + (y * 3.13060547623);
	} else {
		tmp = x + (y * (b * 1.6453555072203998));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.95) or not (z <= 140.0):
		tmp = x + (y * 3.13060547623)
	else:
		tmp = x + (y * (b * 1.6453555072203998))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.95) || !(z <= 140.0))
		tmp = Float64(x + Float64(y * 3.13060547623));
	else
		tmp = Float64(x + Float64(y * Float64(b * 1.6453555072203998)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.95) || ~((z <= 140.0)))
		tmp = x + (y * 3.13060547623);
	else
		tmp = x + (y * (b * 1.6453555072203998));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.95], N[Not[LessEqual[z, 140.0]], $MachinePrecision]], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(b * 1.6453555072203998), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.94999999999999996 or 140 < z

   1. Initial program 18.5%

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

   3. Simplified 25.7%

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

   4. Taylor expanded in z around inf 84.1%

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

   if -1.94999999999999996 < z < 140

   1. Initial program 99.6%

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

   2. Taylor expanded in z around 0 93.5%

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

   3. Taylor expanded in z around 0 77.6%

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

      1. *-commutative 77.6%

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

      2. *-commutative 77.6%

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

      3. associate-*l* 77.6%

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

   5. Simplified 77.6%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \lor \neg \left(z \leq 140\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998\right)\\ \end{array} \]

Alternative 20: 48.8% accurate, 5.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.00052 \lor \neg \left(y \leq 2.4 \cdot 10^{-31}\right):\\ \;\;\;\;y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -0.00052) (not (<= y 2.4e-31))) (* y 3.13060547623) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -0.00052) || !(y <= 2.4e-31)) {
		tmp = y * 3.13060547623;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-0.00052d0)) .or. (.not. (y <= 2.4d-31))) then
        tmp = y * 3.13060547623d0
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -0.00052) || !(y <= 2.4e-31)) {
		tmp = y * 3.13060547623;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -0.00052) or not (y <= 2.4e-31):
		tmp = y * 3.13060547623
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -0.00052) || !(y <= 2.4e-31))
		tmp = Float64(y * 3.13060547623);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -0.00052) || ~((y <= 2.4e-31)))
		tmp = y * 3.13060547623;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -0.00052], N[Not[LessEqual[y, 2.4e-31]], $MachinePrecision]], N[(y * 3.13060547623), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -5.19999999999999954e-4 or 2.4e-31 < y

   1. Initial program 64.9%

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

   3. Simplified 70.7%

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

   4. Taylor expanded in z around inf 37.2%

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

   5. Taylor expanded in x around 0 29.3%

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

      1. *-commutative 29.3%

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

   7. Simplified 29.3%

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

   if -5.19999999999999954e-4 < y < 2.4e-31

   1. Initial program 59.5%

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

   3. Simplified 59.6%

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

   4. Taylor expanded in y around 0 76.5%

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

4. Final simplification 49.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.00052 \lor \neg \left(y \leq 2.4 \cdot 10^{-31}\right):\\ \;\;\;\;y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 21: 61.6% accurate, 7.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 62.6%

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

3. Simplified 65.9%

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

4. Taylor expanded in z around inf 55.4%

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

5. Final simplification 55.4%

   \[\leadsto x + y \cdot 3.13060547623 \]

Alternative 22: 44.3% accurate, 37.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 62.6%

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

3. Simplified 65.9%

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

4. Taylor expanded in y around 0 40.6%

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

5. Final simplification 40.6%

   \[\leadsto x \]

Developer target: 98.3% accurate, 0.9× 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 2023334 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, D"
  :precision binary64

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

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