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

Percentage Accurate: 58.2% → 97.8%

Time: 14.5s

Alternatives: 18

Speedup: 11.3×

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: 58.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\mathsf{fma}\left(15.234687407 + z, z, 31.4690115749\right), z, 11.9400905721\right) \cdot z\\ \mathbf{if}\;z \leq -4.5 \cdot 10^{+30} \lor \neg \left(z \leq 3.7 \cdot 10^{+37}\right):\\ \;\;\;\;x + \left(\mathsf{fma}\left(3.13060547623, y, \mathsf{fma}\left(\frac{t}{z}, \frac{y}{z}, \frac{y}{z} \cdot 11.1667541262\right)\right) - \mathsf{fma}\left(\frac{y \cdot -36.52704169880642}{z}, \frac{15.234687407}{z}, \mathsf{fma}\left(\frac{y}{z \cdot z}, 98.5170599679272, 47.69379582500642 \cdot \frac{y}{z}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(3.13060547623, z, 11.1667541262\right), z, t\right), z, a\right), z, b\right) \cdot y}{{t\_1}^{2} - 0.36938605979308725}, t\_1 - 0.607771387771, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (* (fma (fma (+ 15.234687407 z) z 31.4690115749) z 11.9400905721) z)))
   (if (or (<= z -4.5e+30) (not (<= z 3.7e+37)))
     (+
      x
      (-
       (fma 3.13060547623 y (fma (/ t z) (/ y z) (* (/ y z) 11.1667541262)))
       (fma
        (/ (* y -36.52704169880642) z)
        (/ 15.234687407 z)
        (fma (/ y (* z z)) 98.5170599679272 (* 47.69379582500642 (/ y z))))))
     (fma
      (/
       (* (fma (fma (fma (fma 3.13060547623 z 11.1667541262) z t) z a) z b) y)
       (- (pow t_1 2.0) 0.36938605979308725))
      (- t_1 0.607771387771)
      x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(fma((15.234687407 + z), z, 31.4690115749), z, 11.9400905721) * z;
	double tmp;
	if ((z <= -4.5e+30) || !(z <= 3.7e+37)) {
		tmp = x + (fma(3.13060547623, y, fma((t / z), (y / z), ((y / z) * 11.1667541262))) - fma(((y * -36.52704169880642) / z), (15.234687407 / z), fma((y / (z * z)), 98.5170599679272, (47.69379582500642 * (y / z)))));
	} else {
		tmp = fma(((fma(fma(fma(fma(3.13060547623, z, 11.1667541262), z, t), z, a), z, b) * y) / (pow(t_1, 2.0) - 0.36938605979308725)), (t_1 - 0.607771387771), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(fma(fma(Float64(15.234687407 + z), z, 31.4690115749), z, 11.9400905721) * z)
	tmp = 0.0
	if ((z <= -4.5e+30) || !(z <= 3.7e+37))
		tmp = Float64(x + Float64(fma(3.13060547623, y, fma(Float64(t / z), Float64(y / z), Float64(Float64(y / z) * 11.1667541262))) - fma(Float64(Float64(y * -36.52704169880642) / z), Float64(15.234687407 / z), fma(Float64(y / Float64(z * z)), 98.5170599679272, Float64(47.69379582500642 * Float64(y / z))))));
	else
		tmp = fma(Float64(Float64(fma(fma(fma(fma(3.13060547623, z, 11.1667541262), z, t), z, a), z, b) * y) / Float64((t_1 ^ 2.0) - 0.36938605979308725)), Float64(t_1 - 0.607771387771), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(15.234687407 + z), $MachinePrecision] * z + 31.4690115749), $MachinePrecision] * z + 11.9400905721), $MachinePrecision] * z), $MachinePrecision]}, If[Or[LessEqual[z, -4.5e+30], N[Not[LessEqual[z, 3.7e+37]], $MachinePrecision]], N[(x + N[(N[(3.13060547623 * y + N[(N[(t / z), $MachinePrecision] * N[(y / z), $MachinePrecision] + N[(N[(y / z), $MachinePrecision] * 11.1667541262), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(y * -36.52704169880642), $MachinePrecision] / z), $MachinePrecision] * N[(15.234687407 / z), $MachinePrecision] + N[(N[(y / N[(z * z), $MachinePrecision]), $MachinePrecision] * 98.5170599679272 + N[(47.69379582500642 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(N[(N[(3.13060547623 * z + 11.1667541262), $MachinePrecision] * z + t), $MachinePrecision] * z + a), $MachinePrecision] * z + b), $MachinePrecision] * y), $MachinePrecision] / N[(N[Power[t$95$1, 2.0], $MachinePrecision] - 0.36938605979308725), $MachinePrecision]), $MachinePrecision] * N[(t$95$1 - 0.607771387771), $MachinePrecision] + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.49999999999999995e30 or 3.6999999999999999e37 < z

   1. Initial program 9.0%

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

   3. Taylor expanded in a around -inf

      \[\leadsto x + \color{blue}{-1 \cdot \left(a \cdot \left(-1 \cdot \frac{y \cdot z}{\frac{607771387771}{1000000000000} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)} + -1 \cdot \frac{y \cdot \left(b + {z}^{2} \cdot \left(t + z \cdot \left(\frac{55833770631}{5000000000} + \frac{313060547623}{100000000000} \cdot z\right)\right)\right)}{a \cdot \left(\frac{607771387771}{1000000000000} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)\right)}\right)\right)} \]

   5. Applied rewrites 5.6%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 96.7%

      \[\leadsto x + \left(\mathsf{fma}\left(3.13060547623, y, \mathsf{fma}\left(\frac{t}{z}, \frac{y}{z}, \frac{y}{z} \cdot 11.1667541262\right)\right) - \color{blue}{\mathsf{fma}\left(\frac{y \cdot -36.52704169880642}{z}, \frac{15.234687407}{z}, \mathsf{fma}\left(\frac{y}{z \cdot z}, 98.5170599679272, 47.69379582500642 \cdot \frac{y}{z}\right)\right)}\right) \]

   if -4.49999999999999995e30 < z < 3.6999999999999999e37

   1. Initial program 98.5%

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

   4. Applied rewrites 98.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(3.13060547623, z, 11.1667541262\right), z, t\right), z, a\right), z, b\right) \cdot y}{{\left(\mathsf{fma}\left(\mathsf{fma}\left(15.234687407 + z, z, 31.4690115749\right), z, 11.9400905721\right) \cdot z\right)}^{2} - 0.36938605979308725}, \mathsf{fma}\left(\mathsf{fma}\left(15.234687407 + z, z, 31.4690115749\right), z, 11.9400905721\right) \cdot z - 0.607771387771, x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 97.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+30} \lor \neg \left(z \leq 3.7 \cdot 10^{+37}\right):\\ \;\;\;\;x + \left(\mathsf{fma}\left(3.13060547623, y, \mathsf{fma}\left(\frac{t}{z}, \frac{y}{z}, \frac{y}{z} \cdot 11.1667541262\right)\right) - \mathsf{fma}\left(\frac{y \cdot -36.52704169880642}{z}, \frac{15.234687407}{z}, \mathsf{fma}\left(\frac{y}{z \cdot z}, 98.5170599679272, 47.69379582500642 \cdot \frac{y}{z}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(3.13060547623, z, 11.1667541262\right), z, t\right), z, a\right), z, b\right) \cdot y}{{\left(\mathsf{fma}\left(\mathsf{fma}\left(15.234687407 + z, z, 31.4690115749\right), z, 11.9400905721\right) \cdot z\right)}^{2} - 0.36938605979308725}, \mathsf{fma}\left(\mathsf{fma}\left(15.234687407 + z, z, 31.4690115749\right), z, 11.9400905721\right) \cdot z - 0.607771387771, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 71.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-7} \lor \neg \left(t\_1 \leq 2 \cdot 10^{+102} \lor \neg \left(t\_1 \leq \infty\right)\right):\\ \;\;\;\;\left(b \cdot y\right) \cdot 1.6453555072203998\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (/
          (*
           y
           (+
            (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z)
            b))
          (+
           (*
            (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721)
            z)
           0.607771387771))))
   (if (or (<= t_1 -5e-7) (not (or (<= t_1 2e+102) (not (<= t_1 INFINITY)))))
     (* (* b y) 1.6453555072203998)
     (fma 3.13060547623 y x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * ((((((((z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b)) / (((((((z + 15.234687407) * z) + 31.4690115749) * z) + 11.9400905721) * z) + 0.607771387771);
	double tmp;
	if ((t_1 <= -5e-7) || !((t_1 <= 2e+102) || !(t_1 <= ((double) INFINITY)))) {
		tmp = (b * y) * 1.6453555072203998;
	} else {
		tmp = fma(3.13060547623, y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = 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))
	tmp = 0.0
	if ((t_1 <= -5e-7) || !((t_1 <= 2e+102) || !(t_1 <= Inf)))
		tmp = Float64(Float64(b * y) * 1.6453555072203998);
	else
		tmp = fma(3.13060547623, y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = 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]}, If[Or[LessEqual[t$95$1, -5e-7], N[Not[Or[LessEqual[t$95$1, 2e+102], N[Not[LessEqual[t$95$1, Infinity]], $MachinePrecision]]], $MachinePrecision]], N[(N[(b * y), $MachinePrecision] * 1.6453555072203998), $MachinePrecision], N[(3.13060547623 * y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z #s(literal 313060547623/100000000000 binary64)) #s(literal 55833770631/5000000000 binary64)) z) t) z) a) z) b)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z #s(literal 15234687407/1000000000 binary64)) z) #s(literal 314690115749/10000000000 binary64)) z) #s(literal 119400905721/10000000000 binary64)) z) #s(literal 607771387771/1000000000000 binary64))) < -4.99999999999999977e-7 or 1.99999999999999995e102 < (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z #s(literal 313060547623/100000000000 binary64)) #s(literal 55833770631/5000000000 binary64)) z) t) z) a) z) b)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z #s(literal 15234687407/1000000000 binary64)) z) #s(literal 314690115749/10000000000 binary64)) z) #s(literal 119400905721/10000000000 binary64)) z) #s(literal 607771387771/1000000000000 binary64))) < +inf.0

   1. Initial program 85.6%

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

   3. Taylor expanded in z around 0

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

      1. lower-*.f64 67.2

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

   5. Applied rewrites 67.2%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 67.2

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

   7. Applied rewrites 67.2%

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

   8. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-*.f64 63.0

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

   10. Applied rewrites 63.0%

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

   11. Taylor expanded in x around 0

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

   13. Applied rewrites 48.7%

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

   if -4.99999999999999977e-7 < (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z #s(literal 313060547623/100000000000 binary64)) #s(literal 55833770631/5000000000 binary64)) z) t) z) a) z) b)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z #s(literal 15234687407/1000000000 binary64)) z) #s(literal 314690115749/10000000000 binary64)) z) #s(literal 119400905721/10000000000 binary64)) z) #s(literal 607771387771/1000000000000 binary64))) < 1.99999999999999995e102 or +inf.0 < (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z #s(literal 313060547623/100000000000 binary64)) #s(literal 55833770631/5000000000 binary64)) z) t) z) a) z) b)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z #s(literal 15234687407/1000000000 binary64)) z) #s(literal 314690115749/10000000000 binary64)) z) #s(literal 119400905721/10000000000 binary64)) z) #s(literal 607771387771/1000000000000 binary64)))

   1. Initial program 46.2%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-fma.f64 84.2

         \[\leadsto \color{blue}{\mathsf{fma}\left(3.13060547623, y, x\right)} \]

   5. Applied rewrites 84.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(3.13060547623, y, x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \leq -5 \cdot 10^{-7} \lor \neg \left(\frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \leq 2 \cdot 10^{+102} \lor \neg \left(\frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \leq \infty\right)\right):\\ \;\;\;\;\left(b \cdot y\right) \cdot 1.6453555072203998\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 95.0% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Julia

function code(x, y, z, t, a, b)
	t_1 = 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)))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = fma(3.13060547623, y, x);
	end
	return tmp
end

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 92.7%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-fma.f64 94.8

         \[\leadsto \color{blue}{\mathsf{fma}\left(3.13060547623, y, x\right)} \]

   5. Applied rewrites 94.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(3.13060547623, y, x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 93.5%

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

Alternative 4: 93.2% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 92.7%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(1 + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(\frac{55833770631}{5000000000} + \frac{313060547623}{100000000000} \cdot z\right)\right)\right)\right)}{x \cdot \left(\frac{607771387771}{1000000000000} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)\right)}\right)} \]

   5. Applied rewrites 91.6%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-fma.f64 94.8

         \[\leadsto \color{blue}{\mathsf{fma}\left(3.13060547623, y, x\right)} \]

   5. Applied rewrites 94.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(3.13060547623, y, x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 92.8%

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

Alternative 5: 97.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+30} \lor \neg \left(z \leq 1.35 \cdot 10^{+39}\right):\\ \;\;\;\;x + \left(\mathsf{fma}\left(3.13060547623, y, \mathsf{fma}\left(\frac{t}{z}, \frac{y}{z}, \frac{y}{z} \cdot 11.1667541262\right)\right) - \mathsf{fma}\left(\frac{y \cdot -36.52704169880642}{z}, \frac{15.234687407}{z}, \mathsf{fma}\left(\frac{y}{z \cdot z}, 98.5170599679272, 47.69379582500642 \cdot \frac{y}{z}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -4.5e+30) (not (<= z 1.35e+39)))
   (+
    x
    (-
     (fma 3.13060547623 y (fma (/ t z) (/ y z) (* (/ y z) 11.1667541262)))
     (fma
      (/ (* y -36.52704169880642) z)
      (/ 15.234687407 z)
      (fma (/ y (* z z)) 98.5170599679272 (* 47.69379582500642 (/ y z))))))
   (+
    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) {
	double tmp;
	if ((z <= -4.5e+30) || !(z <= 1.35e+39)) {
		tmp = x + (fma(3.13060547623, y, fma((t / z), (y / z), ((y / z) * 11.1667541262))) - fma(((y * -36.52704169880642) / z), (15.234687407 / z), fma((y / (z * z)), 98.5170599679272, (47.69379582500642 * (y / z)))));
	} else {
		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));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -4.5e+30) || !(z <= 1.35e+39))
		tmp = Float64(x + Float64(fma(3.13060547623, y, fma(Float64(t / z), Float64(y / z), Float64(Float64(y / z) * 11.1667541262))) - fma(Float64(Float64(y * -36.52704169880642) / z), Float64(15.234687407 / z), fma(Float64(y / Float64(z * z)), 98.5170599679272, Float64(47.69379582500642 * Float64(y / z))))));
	else
		tmp = 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
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -4.5e+30], N[Not[LessEqual[z, 1.35e+39]], $MachinePrecision]], N[(x + N[(N[(3.13060547623 * y + N[(N[(t / z), $MachinePrecision] * N[(y / z), $MachinePrecision] + N[(N[(y / z), $MachinePrecision] * 11.1667541262), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(y * -36.52704169880642), $MachinePrecision] / z), $MachinePrecision] * N[(15.234687407 / z), $MachinePrecision] + N[(N[(y / N[(z * z), $MachinePrecision]), $MachinePrecision] * 98.5170599679272 + N[(47.69379582500642 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 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]]

Derivation

1. Split input into 2 regimes

2. if z < -4.49999999999999995e30 or 1.35000000000000002e39 < z

   1. Initial program 9.0%

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

   3. Taylor expanded in a around -inf

      \[\leadsto x + \color{blue}{-1 \cdot \left(a \cdot \left(-1 \cdot \frac{y \cdot z}{\frac{607771387771}{1000000000000} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)} + -1 \cdot \frac{y \cdot \left(b + {z}^{2} \cdot \left(t + z \cdot \left(\frac{55833770631}{5000000000} + \frac{313060547623}{100000000000} \cdot z\right)\right)\right)}{a \cdot \left(\frac{607771387771}{1000000000000} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)\right)}\right)\right)} \]

   5. Applied rewrites 5.6%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 96.7%

      \[\leadsto x + \left(\mathsf{fma}\left(3.13060547623, y, \mathsf{fma}\left(\frac{t}{z}, \frac{y}{z}, \frac{y}{z} \cdot 11.1667541262\right)\right) - \color{blue}{\mathsf{fma}\left(\frac{y \cdot -36.52704169880642}{z}, \frac{15.234687407}{z}, \mathsf{fma}\left(\frac{y}{z \cdot z}, 98.5170599679272, 47.69379582500642 \cdot \frac{y}{z}\right)\right)}\right) \]

   if -4.49999999999999995e30 < z < 1.35000000000000002e39

   1. Initial program 98.5%

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

4. Final simplification 97.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+30} \lor \neg \left(z \leq 1.35 \cdot 10^{+39}\right):\\ \;\;\;\;x + \left(\mathsf{fma}\left(3.13060547623, y, \mathsf{fma}\left(\frac{t}{z}, \frac{y}{z}, \frac{y}{z} \cdot 11.1667541262\right)\right) - \mathsf{fma}\left(\frac{y \cdot -36.52704169880642}{z}, \frac{15.234687407}{z}, \mathsf{fma}\left(\frac{y}{z \cdot z}, 98.5170599679272, 47.69379582500642 \cdot \frac{y}{z}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 96.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+30} \lor \neg \left(z \leq 1.35 \cdot 10^{+39}\right):\\ \;\;\;\;x + \left(\mathsf{fma}\left(3.13060547623, y, \frac{\mathsf{fma}\left(\frac{y}{z}, t, 11.1667541262 \cdot y\right)}{z}\right) - \mathsf{fma}\left(47.69379582500642, \frac{y}{z}, \frac{\frac{\mathsf{fma}\left(98.5170599679272, y, y \cdot -556.47806218377\right)}{z}}{z}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -4.5e+30) (not (<= z 1.35e+39)))
   (+
    x
    (-
     (fma 3.13060547623 y (/ (fma (/ y z) t (* 11.1667541262 y)) z))
     (fma
      47.69379582500642
      (/ y z)
      (/ (/ (fma 98.5170599679272 y (* y -556.47806218377)) z) z))))
   (+
    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) {
	double tmp;
	if ((z <= -4.5e+30) || !(z <= 1.35e+39)) {
		tmp = x + (fma(3.13060547623, y, (fma((y / z), t, (11.1667541262 * y)) / z)) - fma(47.69379582500642, (y / z), ((fma(98.5170599679272, y, (y * -556.47806218377)) / z) / z)));
	} else {
		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));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -4.5e+30) || !(z <= 1.35e+39))
		tmp = Float64(x + Float64(fma(3.13060547623, y, Float64(fma(Float64(y / z), t, Float64(11.1667541262 * y)) / z)) - fma(47.69379582500642, Float64(y / z), Float64(Float64(fma(98.5170599679272, y, Float64(y * -556.47806218377)) / z) / z))));
	else
		tmp = 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
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -4.5e+30], N[Not[LessEqual[z, 1.35e+39]], $MachinePrecision]], N[(x + N[(N[(3.13060547623 * y + N[(N[(N[(y / z), $MachinePrecision] * t + N[(11.1667541262 * y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] - N[(47.69379582500642 * N[(y / z), $MachinePrecision] + N[(N[(N[(98.5170599679272 * y + N[(y * -556.47806218377), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 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]]

Derivation

1. Split input into 2 regimes

2. if z < -4.49999999999999995e30 or 1.35000000000000002e39 < z

   1. Initial program 9.0%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 90.8%

      \[\leadsto x + \color{blue}{\left(\mathsf{fma}\left(3.13060547623, y, \frac{\mathsf{fma}\left(\frac{y}{z}, t, 11.1667541262 \cdot y\right)}{z}\right) - \mathsf{fma}\left(47.69379582500642, \frac{y}{z}, \frac{\frac{\mathsf{fma}\left(98.5170599679272, y, y \cdot -556.47806218377\right)}{z}}{z}\right)\right)} \]

   if -4.49999999999999995e30 < z < 1.35000000000000002e39

   1. Initial program 98.5%

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

4. Final simplification 95.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+30} \lor \neg \left(z \leq 1.35 \cdot 10^{+39}\right):\\ \;\;\;\;x + \left(\mathsf{fma}\left(3.13060547623, y, \frac{\mathsf{fma}\left(\frac{y}{z}, t, 11.1667541262 \cdot y\right)}{z}\right) - \mathsf{fma}\left(47.69379582500642, \frac{y}{z}, \frac{\frac{\mathsf{fma}\left(98.5170599679272, y, y \cdot -556.47806218377\right)}{z}}{z}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 93.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(15.234687407 + z, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)\\ \mathbf{if}\;z \leq -1.22 \cdot 10^{+45}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-24}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(3.13060547623, z, 11.1667541262\right), z, t\right), z, a\right) \cdot z}{t\_1}, x\right)\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+65}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z \cdot z, \mathsf{fma}\left(3.13060547623, z, 11.1667541262\right), a\right), z, b\right), \frac{y}{t\_1}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (fma
          (fma (fma (+ 15.234687407 z) z 31.4690115749) z 11.9400905721)
          z
          0.607771387771)))
   (if (<= z -1.22e+45)
     (fma 3.13060547623 y x)
     (if (<= z -2.1e-24)
       (fma
        y
        (/ (* (fma (fma (fma 3.13060547623 z 11.1667541262) z t) z a) z) t_1)
        x)
       (if (<= z 1.9e+65)
         (fma
          (fma (fma (* z z) (fma 3.13060547623 z 11.1667541262) a) z b)
          (/ y t_1)
          x)
         (fma 3.13060547623 y x))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(fma(fma((15.234687407 + z), z, 31.4690115749), z, 11.9400905721), z, 0.607771387771);
	double tmp;
	if (z <= -1.22e+45) {
		tmp = fma(3.13060547623, y, x);
	} else if (z <= -2.1e-24) {
		tmp = fma(y, ((fma(fma(fma(3.13060547623, z, 11.1667541262), z, t), z, a) * z) / t_1), x);
	} else if (z <= 1.9e+65) {
		tmp = fma(fma(fma((z * z), fma(3.13060547623, z, 11.1667541262), a), z, b), (y / t_1), x);
	} else {
		tmp = fma(3.13060547623, y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = fma(fma(fma(Float64(15.234687407 + z), z, 31.4690115749), z, 11.9400905721), z, 0.607771387771)
	tmp = 0.0
	if (z <= -1.22e+45)
		tmp = fma(3.13060547623, y, x);
	elseif (z <= -2.1e-24)
		tmp = fma(y, Float64(Float64(fma(fma(fma(3.13060547623, z, 11.1667541262), z, t), z, a) * z) / t_1), x);
	elseif (z <= 1.9e+65)
		tmp = fma(fma(fma(Float64(z * z), fma(3.13060547623, z, 11.1667541262), a), z, b), Float64(y / t_1), x);
	else
		tmp = fma(3.13060547623, y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(15.234687407 + z), $MachinePrecision] * z + 31.4690115749), $MachinePrecision] * z + 11.9400905721), $MachinePrecision] * z + 0.607771387771), $MachinePrecision]}, If[LessEqual[z, -1.22e+45], N[(3.13060547623 * y + x), $MachinePrecision], If[LessEqual[z, -2.1e-24], N[(y * N[(N[(N[(N[(N[(3.13060547623 * z + 11.1667541262), $MachinePrecision] * z + t), $MachinePrecision] * z + a), $MachinePrecision] * z), $MachinePrecision] / t$95$1), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[z, 1.9e+65], N[(N[(N[(N[(z * z), $MachinePrecision] * N[(3.13060547623 * z + 11.1667541262), $MachinePrecision] + a), $MachinePrecision] * z + b), $MachinePrecision] * N[(y / t$95$1), $MachinePrecision] + x), $MachinePrecision], N[(3.13060547623 * y + x), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.21999999999999997e45 or 1.90000000000000006e65 < z

   1. Initial program 7.5%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-fma.f64 92.7

         \[\leadsto \color{blue}{\mathsf{fma}\left(3.13060547623, y, x\right)} \]

   5. Applied rewrites 92.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(3.13060547623, y, x\right)} \]

   if -1.21999999999999997e45 < z < -2.0999999999999999e-24

   1. Initial program 85.8%

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

   3. Taylor expanded in z around 0

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

      1. lower-*.f64 37.4

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

   5. Applied rewrites 37.4%

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

   6. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

   8. Applied rewrites 94.7%

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

   if -2.0999999999999999e-24 < z < 1.90000000000000006e65

   1. Initial program 96.9%

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

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{x + \frac{y \cdot \left(b + z \cdot \left(a + {z}^{2} \cdot \left(\frac{55833770631}{5000000000} + \frac{313060547623}{100000000000} \cdot z\right)\right)\right)}{\frac{607771387771}{1000000000000} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)}} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\frac{y \cdot \left(b + z \cdot \left(a + {z}^{2} \cdot \left(\frac{55833770631}{5000000000} + \frac{313060547623}{100000000000} \cdot z\right)\right)\right)}{\frac{607771387771}{1000000000000} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)} + x} \]

      2. *-commutative N/A

         \[\leadsto \frac{\color{blue}{\left(b + z \cdot \left(a + {z}^{2} \cdot \left(\frac{55833770631}{5000000000} + \frac{313060547623}{100000000000} \cdot z\right)\right)\right) \cdot y}}{\frac{607771387771}{1000000000000} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)} + x \]

      3. associate-/l* N/A

         \[\leadsto \color{blue}{\left(b + z \cdot \left(a + {z}^{2} \cdot \left(\frac{55833770631}{5000000000} + \frac{313060547623}{100000000000} \cdot z\right)\right)\right) \cdot \frac{y}{\frac{607771387771}{1000000000000} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)}} + x \]

      4. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(b + z \cdot \left(a + {z}^{2} \cdot \left(\frac{55833770631}{5000000000} + \frac{313060547623}{100000000000} \cdot z\right)\right), \frac{y}{\frac{607771387771}{1000000000000} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)}, x\right)} \]

   5. Applied rewrites 96.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z \cdot z, \mathsf{fma}\left(3.13060547623, z, 11.1667541262\right), a\right), z, b\right), \frac{y}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(15.234687407 + z, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}, x\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 94.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.22 \cdot 10^{+45}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-24}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(3.13060547623, z, 11.1667541262\right), z, t\right), z, a\right) \cdot z}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(15.234687407 + z, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}, x\right)\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+65}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z \cdot z, \mathsf{fma}\left(3.13060547623, z, 11.1667541262\right), a\right), z, b\right), \frac{y}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(15.234687407 + z, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 94.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.22 \cdot 10^{+45}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \mathbf{elif}\;z \leq -40:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(3.13060547623, z, 11.1667541262\right), z, t\right), z, a\right) \cdot z}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(15.234687407 + z, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}, x\right)\\ \mathbf{elif}\;z \leq 165000000:\\ \;\;\;\;x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{11.9400905721 \cdot z + 0.607771387771}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.22e+45)
   (fma 3.13060547623 y x)
   (if (<= z -40.0)
     (fma
      y
      (/
       (* (fma (fma (fma 3.13060547623 z 11.1667541262) z t) z a) z)
       (fma
        (fma (fma (+ 15.234687407 z) z 31.4690115749) z 11.9400905721)
        z
        0.607771387771))
      x)
     (if (<= z 165000000.0)
       (+
        x
        (/
         (*
          y
          (+
           (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z)
           b))
         (+ (* 11.9400905721 z) 0.607771387771)))
       (fma 3.13060547623 y x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.22e+45) {
		tmp = fma(3.13060547623, y, x);
	} else if (z <= -40.0) {
		tmp = fma(y, ((fma(fma(fma(3.13060547623, z, 11.1667541262), z, t), z, a) * z) / fma(fma(fma((15.234687407 + z), z, 31.4690115749), z, 11.9400905721), z, 0.607771387771)), x);
	} else if (z <= 165000000.0) {
		tmp = x + ((y * ((((((((z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b)) / ((11.9400905721 * z) + 0.607771387771));
	} else {
		tmp = fma(3.13060547623, y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.22e+45)
		tmp = fma(3.13060547623, y, x);
	elseif (z <= -40.0)
		tmp = fma(y, Float64(Float64(fma(fma(fma(3.13060547623, z, 11.1667541262), z, t), z, a) * z) / fma(fma(fma(Float64(15.234687407 + z), z, 31.4690115749), z, 11.9400905721), z, 0.607771387771)), x);
	elseif (z <= 165000000.0)
		tmp = 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(11.9400905721 * z) + 0.607771387771)));
	else
		tmp = fma(3.13060547623, y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.22e+45], N[(3.13060547623 * y + x), $MachinePrecision], If[LessEqual[z, -40.0], N[(y * N[(N[(N[(N[(N[(3.13060547623 * z + 11.1667541262), $MachinePrecision] * z + t), $MachinePrecision] * z + a), $MachinePrecision] * z), $MachinePrecision] / N[(N[(N[(N[(15.234687407 + z), $MachinePrecision] * z + 31.4690115749), $MachinePrecision] * z + 11.9400905721), $MachinePrecision] * z + 0.607771387771), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[z, 165000000.0], 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[(11.9400905721 * z), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(3.13060547623 * y + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.21999999999999997e45 or 1.65e8 < z

   1. Initial program 12.3%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-fma.f64 90.0

         \[\leadsto \color{blue}{\mathsf{fma}\left(3.13060547623, y, x\right)} \]

   5. Applied rewrites 90.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(3.13060547623, y, x\right)} \]

   if -1.21999999999999997e45 < z < -40

   1. Initial program 72.0%

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

   3. Taylor expanded in z around 0

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

      1. lower-*.f64 22.5

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

   5. Applied rewrites 22.5%

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

   6. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

   8. Applied rewrites 99.1%

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

   if -40 < z < 1.65e8

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0

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

      1. lower-*.f64 96.5

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

   5. Applied rewrites 96.5%

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

4. Final simplification 93.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.22 \cdot 10^{+45}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \mathbf{elif}\;z \leq -40:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(3.13060547623, z, 11.1667541262\right), z, t\right), z, a\right) \cdot z}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(15.234687407 + z, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}, x\right)\\ \mathbf{elif}\;z \leq 165000000:\\ \;\;\;\;x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{11.9400905721 \cdot z + 0.607771387771}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 93.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -40:\\ \;\;\;\;x + \left(3.13060547623 - \frac{36.52704169880642}{z}\right) \cdot y\\ \mathbf{elif}\;z \leq 165000000:\\ \;\;\;\;x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{11.9400905721 \cdot z + 0.607771387771}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -40.0)
   (+ x (* (- 3.13060547623 (/ 36.52704169880642 z)) y))
   (if (<= z 165000000.0)
     (+
      x
      (/
       (*
        y
        (+
         (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z)
         b))
       (+ (* 11.9400905721 z) 0.607771387771)))
     (fma 3.13060547623 y x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -40.0) {
		tmp = x + ((3.13060547623 - (36.52704169880642 / z)) * y);
	} else if (z <= 165000000.0) {
		tmp = x + ((y * ((((((((z * 3.13060547623) + 11.1667541262) * z) + t) * z) + a) * z) + b)) / ((11.9400905721 * z) + 0.607771387771));
	} else {
		tmp = fma(3.13060547623, y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -40.0)
		tmp = Float64(x + Float64(Float64(3.13060547623 - Float64(36.52704169880642 / z)) * y));
	elseif (z <= 165000000.0)
		tmp = 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(11.9400905721 * z) + 0.607771387771)));
	else
		tmp = fma(3.13060547623, y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -40.0], N[(x + N[(N[(3.13060547623 - N[(36.52704169880642 / z), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 165000000.0], 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[(11.9400905721 * z), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(3.13060547623 * y + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -40

   1. Initial program 20.1%

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

   3. Taylor expanded in z around -inf

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. mul-1-neg N/A

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

      4. distribute-neg-frac N/A

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

      5. lower-/.f64 N/A

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

      6. mul-1-neg N/A

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

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

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

      8. associate-*r* N/A

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

      9. lower-*.f64 N/A

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

      10. mul-1-neg N/A

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

      11. lower-neg.f64 N/A

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

      12. metadata-eval 83.8

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

   5. Applied rewrites 83.8%

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

   6. Taylor expanded in y around 0

      \[\leadsto x + y \cdot \color{blue}{\left(\frac{313060547623}{100000000000} - \frac{3652704169880641883561}{100000000000000000000} \cdot \frac{1}{z}\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 83.8%

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

   if -40 < z < 1.65e8

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0

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

      1. lower-*.f64 96.5

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

   5. Applied rewrites 96.5%

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

   if 1.65e8 < z

   1. Initial program 13.6%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-fma.f64 88.8

         \[\leadsto \color{blue}{\mathsf{fma}\left(3.13060547623, y, x\right)} \]

   5. Applied rewrites 88.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(3.13060547623, y, x\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -40:\\ \;\;\;\;x + \left(3.13060547623 - \frac{36.52704169880642}{z}\right) \cdot y\\ \mathbf{elif}\;z \leq 165000000:\\ \;\;\;\;x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{11.9400905721 \cdot z + 0.607771387771}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 87.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+30} \lor \neg \left(z \leq 165000000\right):\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(z \cdot z, \mathsf{fma}\left(\mathsf{fma}\left(3.13060547623, z, 11.1667541262\right), z, t\right), b\right) \cdot y}{\mathsf{fma}\left(\mathsf{fma}\left(31.4690115749, z, 11.9400905721\right), z, 0.607771387771\right)} + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -4.5e+30) (not (<= z 165000000.0)))
   (fma 3.13060547623 y x)
   (+
    (/
     (* (fma (* z z) (fma (fma 3.13060547623 z 11.1667541262) z t) b) y)
     (fma (fma 31.4690115749 z 11.9400905721) z 0.607771387771))
    x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -4.5e+30) || !(z <= 165000000.0)) {
		tmp = fma(3.13060547623, y, x);
	} else {
		tmp = ((fma((z * z), fma(fma(3.13060547623, z, 11.1667541262), z, t), b) * y) / fma(fma(31.4690115749, z, 11.9400905721), z, 0.607771387771)) + x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -4.5e+30) || !(z <= 165000000.0))
		tmp = fma(3.13060547623, y, x);
	else
		tmp = Float64(Float64(Float64(fma(Float64(z * z), fma(fma(3.13060547623, z, 11.1667541262), z, t), b) * y) / fma(fma(31.4690115749, z, 11.9400905721), z, 0.607771387771)) + x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -4.5e+30], N[Not[LessEqual[z, 165000000.0]], $MachinePrecision]], N[(3.13060547623 * y + x), $MachinePrecision], N[(N[(N[(N[(N[(z * z), $MachinePrecision] * N[(N[(3.13060547623 * z + 11.1667541262), $MachinePrecision] * z + t), $MachinePrecision] + b), $MachinePrecision] * y), $MachinePrecision] / N[(N[(31.4690115749 * z + 11.9400905721), $MachinePrecision] * z + 0.607771387771), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.49999999999999995e30 or 1.65e8 < z

   1. Initial program 12.9%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-fma.f64 88.6

         \[\leadsto \color{blue}{\mathsf{fma}\left(3.13060547623, y, x\right)} \]

   5. Applied rewrites 88.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(3.13060547623, y, x\right)} \]

   if -4.49999999999999995e30 < z < 1.65e8

   1. Initial program 99.0%

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

   3. Taylor expanded in z around 0

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

      1. lower-*.f64 79.6

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

   5. Applied rewrites 79.6%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 79.6

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

   7. Applied rewrites 79.6%

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

   8. Taylor expanded in z around 0

      \[\leadsto \frac{b \cdot y}{\mathsf{fma}\left(\color{blue}{\frac{119400905721}{10000000000} + \frac{314690115749}{10000000000} \cdot z}, z, \frac{607771387771}{1000000000000}\right)} + x \]
   9. Step-by-step derivation

      1. +-commutative N/A

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

      2. lower-fma.f64 78.2

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

   10. Applied rewrites 78.2%

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

   11. Taylor expanded in a around 0

       \[\leadsto \frac{\color{blue}{y \cdot \left(b + {z}^{2} \cdot \left(t + z \cdot \left(\frac{55833770631}{5000000000} + \frac{313060547623}{100000000000} \cdot z\right)\right)\right)}}{\mathsf{fma}\left(\mathsf{fma}\left(\frac{314690115749}{10000000000}, z, \frac{119400905721}{10000000000}\right), z, \frac{607771387771}{1000000000000}\right)} + x \]
   12. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \frac{\color{blue}{\left(b + {z}^{2} \cdot \left(t + z \cdot \left(\frac{55833770631}{5000000000} + \frac{313060547623}{100000000000} \cdot z\right)\right)\right) \cdot y}}{\mathsf{fma}\left(\mathsf{fma}\left(\frac{314690115749}{10000000000}, z, \frac{119400905721}{10000000000}\right), z, \frac{607771387771}{1000000000000}\right)} + x \]

       2. lower-*.f64 N/A

          \[\leadsto \frac{\color{blue}{\left(b + {z}^{2} \cdot \left(t + z \cdot \left(\frac{55833770631}{5000000000} + \frac{313060547623}{100000000000} \cdot z\right)\right)\right) \cdot y}}{\mathsf{fma}\left(\mathsf{fma}\left(\frac{314690115749}{10000000000}, z, \frac{119400905721}{10000000000}\right), z, \frac{607771387771}{1000000000000}\right)} + x \]

       3. +-commutative N/A

          \[\leadsto \frac{\color{blue}{\left({z}^{2} \cdot \left(t + z \cdot \left(\frac{55833770631}{5000000000} + \frac{313060547623}{100000000000} \cdot z\right)\right) + b\right)} \cdot y}{\mathsf{fma}\left(\mathsf{fma}\left(\frac{314690115749}{10000000000}, z, \frac{119400905721}{10000000000}\right), z, \frac{607771387771}{1000000000000}\right)} + x \]

       4. lower-fma.f64 N/A

          \[\leadsto \frac{\color{blue}{\mathsf{fma}\left({z}^{2}, t + z \cdot \left(\frac{55833770631}{5000000000} + \frac{313060547623}{100000000000} \cdot z\right), b\right)} \cdot y}{\mathsf{fma}\left(\mathsf{fma}\left(\frac{314690115749}{10000000000}, z, \frac{119400905721}{10000000000}\right), z, \frac{607771387771}{1000000000000}\right)} + x \]

       5. unpow2 N/A

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

       6. lower-*.f64 N/A

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

       7. +-commutative N/A

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

       8. *-commutative N/A

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

       9. lower-fma.f64 N/A

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

       10. +-commutative N/A

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

       11. lower-fma.f64 86.4

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

   13. Applied rewrites 86.4%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+30} \lor \neg \left(z \leq 165000000\right):\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(z \cdot z, \mathsf{fma}\left(\mathsf{fma}\left(3.13060547623, z, 11.1667541262\right), z, t\right), b\right) \cdot y}{\mathsf{fma}\left(\mathsf{fma}\left(31.4690115749, z, 11.9400905721\right), z, 0.607771387771\right)} + x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 86.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.16 \cdot 10^{+24} \lor \neg \left(z \leq 3400000\right):\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(z \cdot z, \mathsf{fma}\left(\mathsf{fma}\left(3.13060547623, z, 11.1667541262\right), z, t\right), b\right), \mathsf{fma}\left(\left(549.8376187179895 \cdot z - 32.324150453290734\right) \cdot y, z, 1.6453555072203998 \cdot y\right), x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.16e+24) (not (<= z 3400000.0)))
   (fma 3.13060547623 y x)
   (fma
    (fma (* z z) (fma (fma 3.13060547623 z 11.1667541262) z t) b)
    (fma
     (* (- (* 549.8376187179895 z) 32.324150453290734) y)
     z
     (* 1.6453555072203998 y))
    x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.16e+24) || !(z <= 3400000.0)) {
		tmp = fma(3.13060547623, y, x);
	} else {
		tmp = fma(fma((z * z), fma(fma(3.13060547623, z, 11.1667541262), z, t), b), fma((((549.8376187179895 * z) - 32.324150453290734) * y), z, (1.6453555072203998 * y)), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.16e+24) || !(z <= 3400000.0))
		tmp = fma(3.13060547623, y, x);
	else
		tmp = fma(fma(Float64(z * z), fma(fma(3.13060547623, z, 11.1667541262), z, t), b), fma(Float64(Float64(Float64(549.8376187179895 * z) - 32.324150453290734) * y), z, Float64(1.6453555072203998 * y)), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.16e+24], N[Not[LessEqual[z, 3400000.0]], $MachinePrecision]], N[(3.13060547623 * y + x), $MachinePrecision], N[(N[(N[(z * z), $MachinePrecision] * N[(N[(3.13060547623 * z + 11.1667541262), $MachinePrecision] * z + t), $MachinePrecision] + b), $MachinePrecision] * N[(N[(N[(N[(549.8376187179895 * z), $MachinePrecision] - 32.324150453290734), $MachinePrecision] * y), $MachinePrecision] * z + N[(1.6453555072203998 * y), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.16000000000000005e24 or 3.4e6 < z

   1. Initial program 13.6%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-fma.f64 88.0

         \[\leadsto \color{blue}{\mathsf{fma}\left(3.13060547623, y, x\right)} \]

   5. Applied rewrites 88.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(3.13060547623, y, x\right)} \]

   if -1.16000000000000005e24 < z < 3.4e6

   1. Initial program 99.0%

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

   3. Taylor expanded in a around 0

      \[\leadsto \color{blue}{x + \frac{y \cdot \left(b + {z}^{2} \cdot \left(t + z \cdot \left(\frac{55833770631}{5000000000} + \frac{313060547623}{100000000000} \cdot z\right)\right)\right)}{\frac{607771387771}{1000000000000} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)}} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\frac{y \cdot \left(b + {z}^{2} \cdot \left(t + z \cdot \left(\frac{55833770631}{5000000000} + \frac{313060547623}{100000000000} \cdot z\right)\right)\right)}{\frac{607771387771}{1000000000000} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)} + x} \]

      2. *-commutative N/A

         \[\leadsto \frac{\color{blue}{\left(b + {z}^{2} \cdot \left(t + z \cdot \left(\frac{55833770631}{5000000000} + \frac{313060547623}{100000000000} \cdot z\right)\right)\right) \cdot y}}{\frac{607771387771}{1000000000000} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)} + x \]

      3. associate-/l* N/A

         \[\leadsto \color{blue}{\left(b + {z}^{2} \cdot \left(t + z \cdot \left(\frac{55833770631}{5000000000} + \frac{313060547623}{100000000000} \cdot z\right)\right)\right) \cdot \frac{y}{\frac{607771387771}{1000000000000} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)}} + x \]

      4. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(b + {z}^{2} \cdot \left(t + z \cdot \left(\frac{55833770631}{5000000000} + \frac{313060547623}{100000000000} \cdot z\right)\right), \frac{y}{\frac{607771387771}{1000000000000} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)}, x\right)} \]

   5. Applied rewrites 89.0%

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

   6. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(z \cdot z, \mathsf{fma}\left(\mathsf{fma}\left(\frac{313060547623}{100000000000}, z, \frac{55833770631}{5000000000}\right), z, t\right), b\right), \frac{1000000000000}{607771387771} \cdot y + \color{blue}{z \cdot \left(-1 \cdot \left(z \cdot \left(\frac{-142565762869951305298410000000000000000}{224502278183706222041215714334315011} \cdot y + \frac{31469011574900000000000000}{369386059793087248348441} \cdot y\right)\right) - \frac{11940090572100000000000000}{369386059793087248348441} \cdot y\right)}, x\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 86.7%

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(z \cdot z, \mathsf{fma}\left(\mathsf{fma}\left(3.13060547623, z, 11.1667541262\right), z, t\right), b\right), \mathsf{fma}\left(\mathsf{fma}\left(-z, y \cdot -549.8376187179895, -32.324150453290734 \cdot y\right), \color{blue}{z}, 1.6453555072203998 \cdot y\right), x\right) \]

   9. Taylor expanded in y around 0

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(z \cdot z, \mathsf{fma}\left(\mathsf{fma}\left(\frac{313060547623}{100000000000}, z, \frac{55833770631}{5000000000}\right), z, t\right), b\right), \mathsf{fma}\left(y \cdot \left(\frac{123439798033292669987862100000000000000}{224502278183706222041215714334315011} \cdot z - \frac{11940090572100000000000000}{369386059793087248348441}\right), z, \frac{1000000000000}{607771387771} \cdot y\right), x\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 86.7%

       \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(z \cdot z, \mathsf{fma}\left(\mathsf{fma}\left(3.13060547623, z, 11.1667541262\right), z, t\right), b\right), \mathsf{fma}\left(\left(549.8376187179895 \cdot z - 32.324150453290734\right) \cdot y, z, 1.6453555072203998 \cdot y\right), x\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.16 \cdot 10^{+24} \lor \neg \left(z \leq 3400000\right):\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(z \cdot z, \mathsf{fma}\left(\mathsf{fma}\left(3.13060547623, z, 11.1667541262\right), z, t\right), b\right), \mathsf{fma}\left(\left(549.8376187179895 \cdot z - 32.324150453290734\right) \cdot y, z, 1.6453555072203998 \cdot y\right), x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 86.7% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+30} \lor \neg \left(z \leq 3400000\right):\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(z \cdot z, \mathsf{fma}\left(\mathsf{fma}\left(3.13060547623, z, 11.1667541262\right), z, t\right), b\right), 1.6453555072203998 \cdot y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -4.5e+30) (not (<= z 3400000.0)))
   (fma 3.13060547623 y x)
   (fma
    (fma (* z z) (fma (fma 3.13060547623 z 11.1667541262) z t) b)
    (* 1.6453555072203998 y)
    x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -4.5e+30) || !(z <= 3400000.0)) {
		tmp = fma(3.13060547623, y, x);
	} else {
		tmp = fma(fma((z * z), fma(fma(3.13060547623, z, 11.1667541262), z, t), b), (1.6453555072203998 * y), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -4.5e+30) || !(z <= 3400000.0))
		tmp = fma(3.13060547623, y, x);
	else
		tmp = fma(fma(Float64(z * z), fma(fma(3.13060547623, z, 11.1667541262), z, t), b), Float64(1.6453555072203998 * y), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -4.5e+30], N[Not[LessEqual[z, 3400000.0]], $MachinePrecision]], N[(3.13060547623 * y + x), $MachinePrecision], N[(N[(N[(z * z), $MachinePrecision] * N[(N[(3.13060547623 * z + 11.1667541262), $MachinePrecision] * z + t), $MachinePrecision] + b), $MachinePrecision] * N[(1.6453555072203998 * y), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.49999999999999995e30 or 3.4e6 < z

   1. Initial program 12.9%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-fma.f64 88.6

         \[\leadsto \color{blue}{\mathsf{fma}\left(3.13060547623, y, x\right)} \]

   5. Applied rewrites 88.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(3.13060547623, y, x\right)} \]

   if -4.49999999999999995e30 < z < 3.4e6

   1. Initial program 99.0%

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

   3. Taylor expanded in a around 0

      \[\leadsto \color{blue}{x + \frac{y \cdot \left(b + {z}^{2} \cdot \left(t + z \cdot \left(\frac{55833770631}{5000000000} + \frac{313060547623}{100000000000} \cdot z\right)\right)\right)}{\frac{607771387771}{1000000000000} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)}} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{\frac{y \cdot \left(b + {z}^{2} \cdot \left(t + z \cdot \left(\frac{55833770631}{5000000000} + \frac{313060547623}{100000000000} \cdot z\right)\right)\right)}{\frac{607771387771}{1000000000000} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)} + x} \]

      2. *-commutative N/A

         \[\leadsto \frac{\color{blue}{\left(b + {z}^{2} \cdot \left(t + z \cdot \left(\frac{55833770631}{5000000000} + \frac{313060547623}{100000000000} \cdot z\right)\right)\right) \cdot y}}{\frac{607771387771}{1000000000000} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)} + x \]

      3. associate-/l* N/A

         \[\leadsto \color{blue}{\left(b + {z}^{2} \cdot \left(t + z \cdot \left(\frac{55833770631}{5000000000} + \frac{313060547623}{100000000000} \cdot z\right)\right)\right) \cdot \frac{y}{\frac{607771387771}{1000000000000} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)}} + x \]

      4. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(b + {z}^{2} \cdot \left(t + z \cdot \left(\frac{55833770631}{5000000000} + \frac{313060547623}{100000000000} \cdot z\right)\right), \frac{y}{\frac{607771387771}{1000000000000} + z \cdot \left(\frac{119400905721}{10000000000} + z \cdot \left(\frac{314690115749}{10000000000} + z \cdot \left(\frac{15234687407}{1000000000} + z\right)\right)\right)}, x\right)} \]

   5. Applied rewrites 88.4%

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

   6. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(z \cdot z, \mathsf{fma}\left(\mathsf{fma}\left(\frac{313060547623}{100000000000}, z, \frac{55833770631}{5000000000}\right), z, t\right), b\right), \frac{1000000000000}{607771387771} \cdot \color{blue}{y}, x\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 85.0%

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(z \cdot z, \mathsf{fma}\left(\mathsf{fma}\left(3.13060547623, z, 11.1667541262\right), z, t\right), b\right), 1.6453555072203998 \cdot \color{blue}{y}, x\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+30} \lor \neg \left(z \leq 3400000\right):\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(z \cdot z, \mathsf{fma}\left(\mathsf{fma}\left(3.13060547623, z, 11.1667541262\right), z, t\right), b\right), 1.6453555072203998 \cdot y, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 86.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -115000000 \lor \neg \left(z \leq 92000\right):\\ \;\;\;\;x + \left(3.13060547623 - \frac{36.52704169880642}{z}\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1.6453555072203998 \cdot b, y, \left(y \cdot \left(1.6453555072203998 \cdot a\right)\right) \cdot z\right) + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -115000000.0) (not (<= z 92000.0)))
   (+ x (* (- 3.13060547623 (/ 36.52704169880642 z)) y))
   (+
    (fma (* 1.6453555072203998 b) y (* (* y (* 1.6453555072203998 a)) z))
    x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -115000000.0) || !(z <= 92000.0)) {
		tmp = x + ((3.13060547623 - (36.52704169880642 / z)) * y);
	} else {
		tmp = fma((1.6453555072203998 * b), y, ((y * (1.6453555072203998 * a)) * z)) + x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -115000000.0) || !(z <= 92000.0))
		tmp = Float64(x + Float64(Float64(3.13060547623 - Float64(36.52704169880642 / z)) * y));
	else
		tmp = Float64(fma(Float64(1.6453555072203998 * b), y, Float64(Float64(y * Float64(1.6453555072203998 * a)) * z)) + x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -115000000.0], N[Not[LessEqual[z, 92000.0]], $MachinePrecision]], N[(x + N[(N[(3.13060547623 - N[(36.52704169880642 / z), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], N[(N[(N[(1.6453555072203998 * b), $MachinePrecision] * y + N[(N[(y * N[(1.6453555072203998 * a), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.15e8 or 92000 < z

   1. Initial program 17.0%

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

   3. Taylor expanded in z around -inf

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. mul-1-neg N/A

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

      4. distribute-neg-frac N/A

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

      5. lower-/.f64 N/A

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

      6. mul-1-neg N/A

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

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

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

      8. associate-*r* N/A

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

      9. lower-*.f64 N/A

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

      10. mul-1-neg N/A

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

      11. lower-neg.f64 N/A

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

      12. metadata-eval 86.2

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

   5. Applied rewrites 86.2%

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

   6. Taylor expanded in y around 0

      \[\leadsto x + y \cdot \color{blue}{\left(\frac{313060547623}{100000000000} - \frac{3652704169880641883561}{100000000000000000000} \cdot \frac{1}{z}\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 86.2%

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

   if -1.15e8 < z < 92000

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0

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

      1. lower-*.f64 82.2

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

   5. Applied rewrites 82.2%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 82.2

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

   7. Applied rewrites 82.2%

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

   8. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\left(\frac{1000000000000}{607771387771} \cdot \left(b \cdot y\right) + z \cdot \left(\frac{1000000000000}{607771387771} \cdot \left(a \cdot y\right) - \frac{11940090572100000000000000}{369386059793087248348441} \cdot \left(b \cdot y\right)\right)\right)} + x \]
   9. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(\color{blue}{\left(\frac{1000000000000}{607771387771} \cdot b\right) \cdot y} + z \cdot \left(\frac{1000000000000}{607771387771} \cdot \left(a \cdot y\right) - \frac{11940090572100000000000000}{369386059793087248348441} \cdot \left(b \cdot y\right)\right)\right) + x \]

      2. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{1000000000000}{607771387771} \cdot b, y, z \cdot \left(\frac{1000000000000}{607771387771} \cdot \left(a \cdot y\right) - \frac{11940090572100000000000000}{369386059793087248348441} \cdot \left(b \cdot y\right)\right)\right)} + x \]

      3. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{1000000000000}{607771387771} \cdot b}, y, z \cdot \left(\frac{1000000000000}{607771387771} \cdot \left(a \cdot y\right) - \frac{11940090572100000000000000}{369386059793087248348441} \cdot \left(b \cdot y\right)\right)\right) + x \]

      4. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\frac{1000000000000}{607771387771} \cdot b, y, \color{blue}{\left(\frac{1000000000000}{607771387771} \cdot \left(a \cdot y\right) - \frac{11940090572100000000000000}{369386059793087248348441} \cdot \left(b \cdot y\right)\right) \cdot z}\right) + x \]

      5. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{1000000000000}{607771387771} \cdot b, y, \color{blue}{\left(\frac{1000000000000}{607771387771} \cdot \left(a \cdot y\right) - \frac{11940090572100000000000000}{369386059793087248348441} \cdot \left(b \cdot y\right)\right) \cdot z}\right) + x \]

      6. associate-*r* N/A

         \[\leadsto \mathsf{fma}\left(\frac{1000000000000}{607771387771} \cdot b, y, \left(\color{blue}{\left(\frac{1000000000000}{607771387771} \cdot a\right) \cdot y} - \frac{11940090572100000000000000}{369386059793087248348441} \cdot \left(b \cdot y\right)\right) \cdot z\right) + x \]

      7. associate-*r* N/A

         \[\leadsto \mathsf{fma}\left(\frac{1000000000000}{607771387771} \cdot b, y, \left(\left(\frac{1000000000000}{607771387771} \cdot a\right) \cdot y - \color{blue}{\left(\frac{11940090572100000000000000}{369386059793087248348441} \cdot b\right) \cdot y}\right) \cdot z\right) + x \]

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

         \[\leadsto \mathsf{fma}\left(\frac{1000000000000}{607771387771} \cdot b, y, \color{blue}{\left(y \cdot \left(\frac{1000000000000}{607771387771} \cdot a - \frac{11940090572100000000000000}{369386059793087248348441} \cdot b\right)\right)} \cdot z\right) + x \]

      9. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{1000000000000}{607771387771} \cdot b, y, \color{blue}{\left(y \cdot \left(\frac{1000000000000}{607771387771} \cdot a - \frac{11940090572100000000000000}{369386059793087248348441} \cdot b\right)\right)} \cdot z\right) + x \]

      10. lower--.f64 N/A

          \[\leadsto \mathsf{fma}\left(\frac{1000000000000}{607771387771} \cdot b, y, \left(y \cdot \color{blue}{\left(\frac{1000000000000}{607771387771} \cdot a - \frac{11940090572100000000000000}{369386059793087248348441} \cdot b\right)}\right) \cdot z\right) + x \]

      11. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\frac{1000000000000}{607771387771} \cdot b, y, \left(y \cdot \left(\color{blue}{\frac{1000000000000}{607771387771} \cdot a} - \frac{11940090572100000000000000}{369386059793087248348441} \cdot b\right)\right) \cdot z\right) + x \]

      12. lower-*.f64 84.2

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

   10. Applied rewrites 84.2%

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

   11. Taylor expanded in a around inf

       \[\leadsto \mathsf{fma}\left(\frac{1000000000000}{607771387771} \cdot b, y, \left(y \cdot \left(\frac{1000000000000}{607771387771} \cdot a\right)\right) \cdot z\right) + x \]
   12. Step-by-step derivation

   13. Applied rewrites 86.5%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -115000000 \lor \neg \left(z \leq 92000\right):\\ \;\;\;\;x + \left(3.13060547623 - \frac{36.52704169880642}{z}\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(1.6453555072203998 \cdot b, y, \left(y \cdot \left(1.6453555072203998 \cdot a\right)\right) \cdot z\right) + x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 83.5% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-25}:\\ \;\;\;\;x + \left(3.13060547623 - \frac{36.52704169880642}{z}\right) \cdot y\\ \mathbf{elif}\;z \leq 3400000:\\ \;\;\;\;x + \frac{b \cdot y}{\mathsf{fma}\left(11.9400905721, z, 0.607771387771\right)}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.6e-25)
   (+ x (* (- 3.13060547623 (/ 36.52704169880642 z)) y))
   (if (<= z 3400000.0)
     (+ x (/ (* b y) (fma 11.9400905721 z 0.607771387771)))
     (fma 3.13060547623 y x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.6e-25) {
		tmp = x + ((3.13060547623 - (36.52704169880642 / z)) * y);
	} else if (z <= 3400000.0) {
		tmp = x + ((b * y) / fma(11.9400905721, z, 0.607771387771));
	} else {
		tmp = fma(3.13060547623, y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.6e-25)
		tmp = Float64(x + Float64(Float64(3.13060547623 - Float64(36.52704169880642 / z)) * y));
	elseif (z <= 3400000.0)
		tmp = Float64(x + Float64(Float64(b * y) / fma(11.9400905721, z, 0.607771387771)));
	else
		tmp = fma(3.13060547623, y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.6e-25], N[(x + N[(N[(3.13060547623 - N[(36.52704169880642 / z), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3400000.0], N[(x + N[(N[(b * y), $MachinePrecision] / N[(11.9400905721 * z + 0.607771387771), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(3.13060547623 * y + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.6000000000000001e-25

   1. Initial program 31.4%

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

   3. Taylor expanded in z around -inf

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. mul-1-neg N/A

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

      4. distribute-neg-frac N/A

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

      5. lower-/.f64 N/A

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

      6. mul-1-neg N/A

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

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

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

      8. associate-*r* N/A

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

      9. lower-*.f64 N/A

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

      10. mul-1-neg N/A

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

      11. lower-neg.f64 N/A

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

      12. metadata-eval 78.7

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

   5. Applied rewrites 78.7%

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

   6. Taylor expanded in y around 0

      \[\leadsto x + y \cdot \color{blue}{\left(\frac{313060547623}{100000000000} - \frac{3652704169880641883561}{100000000000000000000} \cdot \frac{1}{z}\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 78.7%

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

   if -1.6000000000000001e-25 < z < 3.4e6

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0

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

      1. lower-*.f64 85.5

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

   5. Applied rewrites 85.5%

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

   6. Taylor expanded in z around 0

      \[\leadsto x + \frac{b \cdot y}{\color{blue}{\frac{607771387771}{1000000000000} + \frac{119400905721}{10000000000} \cdot z}} \]
   7. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto x + \frac{b \cdot y}{\color{blue}{\frac{119400905721}{10000000000} \cdot z + \frac{607771387771}{1000000000000}}} \]

      2. lower-fma.f64 84.2

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

   8. Applied rewrites 84.2%

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

   if 3.4e6 < z

   1. Initial program 13.6%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-fma.f64 88.8

         \[\leadsto \color{blue}{\mathsf{fma}\left(3.13060547623, y, x\right)} \]

   5. Applied rewrites 88.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(3.13060547623, y, x\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-25}:\\ \;\;\;\;x + \left(3.13060547623 - \frac{36.52704169880642}{z}\right) \cdot y\\ \mathbf{elif}\;z \leq 3400000:\\ \;\;\;\;x + \frac{b \cdot y}{\mathsf{fma}\left(11.9400905721, z, 0.607771387771\right)}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 83.5% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-25}:\\ \;\;\;\;x + \left(3.13060547623 - \frac{36.52704169880642}{z}\right) \cdot y\\ \mathbf{elif}\;z \leq 3400000:\\ \;\;\;\;\mathsf{fma}\left(b \cdot y, 1.6453555072203998, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.6e-25)
   (+ x (* (- 3.13060547623 (/ 36.52704169880642 z)) y))
   (if (<= z 3400000.0)
     (fma (* b y) 1.6453555072203998 x)
     (fma 3.13060547623 y x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.6e-25) {
		tmp = x + ((3.13060547623 - (36.52704169880642 / z)) * y);
	} else if (z <= 3400000.0) {
		tmp = fma((b * y), 1.6453555072203998, x);
	} else {
		tmp = fma(3.13060547623, y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.6e-25)
		tmp = Float64(x + Float64(Float64(3.13060547623 - Float64(36.52704169880642 / z)) * y));
	elseif (z <= 3400000.0)
		tmp = fma(Float64(b * y), 1.6453555072203998, x);
	else
		tmp = fma(3.13060547623, y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.6e-25], N[(x + N[(N[(3.13060547623 - N[(36.52704169880642 / z), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3400000.0], N[(N[(b * y), $MachinePrecision] * 1.6453555072203998 + x), $MachinePrecision], N[(3.13060547623 * y + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.6000000000000001e-25

   1. Initial program 31.4%

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

   3. Taylor expanded in z around -inf

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

      1. +-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. mul-1-neg N/A

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

      4. distribute-neg-frac N/A

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

      5. lower-/.f64 N/A

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

      6. mul-1-neg N/A

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

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

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

      8. associate-*r* N/A

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

      9. lower-*.f64 N/A

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

      10. mul-1-neg N/A

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

      11. lower-neg.f64 N/A

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

      12. metadata-eval 78.7

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

   5. Applied rewrites 78.7%

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

   6. Taylor expanded in y around 0

      \[\leadsto x + y \cdot \color{blue}{\left(\frac{313060547623}{100000000000} - \frac{3652704169880641883561}{100000000000000000000} \cdot \frac{1}{z}\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 78.7%

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

   if -1.6000000000000001e-25 < z < 3.4e6

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 84.1

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

   5. Applied rewrites 84.1%

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

   if 3.4e6 < z

   1. Initial program 13.6%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-fma.f64 88.8

         \[\leadsto \color{blue}{\mathsf{fma}\left(3.13060547623, y, x\right)} \]

   5. Applied rewrites 88.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(3.13060547623, y, x\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-25}:\\ \;\;\;\;x + \left(3.13060547623 - \frac{36.52704169880642}{z}\right) \cdot y\\ \mathbf{elif}\;z \leq 3400000:\\ \;\;\;\;\mathsf{fma}\left(b \cdot y, 1.6453555072203998, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 83.8% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -150000000 \lor \neg \left(z \leq 3400000\right):\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b \cdot y, 1.6453555072203998, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -150000000.0) (not (<= z 3400000.0)))
   (fma 3.13060547623 y x)
   (fma (* b y) 1.6453555072203998 x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -150000000.0) || !(z <= 3400000.0)) {
		tmp = fma(3.13060547623, y, x);
	} else {
		tmp = fma((b * y), 1.6453555072203998, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -150000000.0) || !(z <= 3400000.0))
		tmp = fma(3.13060547623, y, x);
	else
		tmp = fma(Float64(b * y), 1.6453555072203998, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -150000000.0], N[Not[LessEqual[z, 3400000.0]], $MachinePrecision]], N[(3.13060547623 * y + x), $MachinePrecision], N[(N[(b * y), $MachinePrecision] * 1.6453555072203998 + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.5e8 or 3.4e6 < z

   1. Initial program 16.3%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-fma.f64 86.6

         \[\leadsto \color{blue}{\mathsf{fma}\left(3.13060547623, y, x\right)} \]

   5. Applied rewrites 86.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(3.13060547623, y, x\right)} \]

   if -1.5e8 < z < 3.4e6

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-*.f64 79.9

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

   5. Applied rewrites 79.9%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -150000000 \lor \neg \left(z \leq 3400000\right):\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(b \cdot y, 1.6453555072203998, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 62.1% accurate, 11.3× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(3.13060547623, y, x\right) \end{array} \]

FPCore

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

C

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

Julia

function code(x, y, z, t, a, b)
	return fma(3.13060547623, y, x)
end

Wolfram

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

Derivation

1. Initial program 58.7%

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

3. Taylor expanded in z around inf

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

   1. +-commutative N/A

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

   2. lower-fma.f64 63.8

      \[\leadsto \color{blue}{\mathsf{fma}\left(3.13060547623, y, x\right)} \]

5. Applied rewrites 63.8%

   \[\leadsto \color{blue}{\mathsf{fma}\left(3.13060547623, y, x\right)} \]

6. Final simplification 63.8%

   \[\leadsto \mathsf{fma}\left(3.13060547623, y, x\right) \]
7. Add Preprocessing

Alternative 18: 22.5% accurate, 13.2× speedup

Math

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

FPCore

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

C

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

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 = 3.13060547623d0 * y
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 58.7%

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

3. Taylor expanded in z around inf

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

   1. +-commutative N/A

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

   2. lower-fma.f64 63.8

      \[\leadsto \color{blue}{\mathsf{fma}\left(3.13060547623, y, x\right)} \]

5. Applied rewrites 63.8%

   \[\leadsto \color{blue}{\mathsf{fma}\left(3.13060547623, y, x\right)} \]

6. Taylor expanded in x around 0

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

8. Applied rewrites 21.4%

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

9. Final simplification 21.4%

   \[\leadsto 3.13060547623 \cdot y \]
10. Add Preprocessing

Developer Target 1: 98.5% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024339 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, D"
  :precision binary64

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

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