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

Percentage Accurate: 58.2% → 97.0%

Time: 16.9s

Alternatives: 14

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: 97.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y, 3.13060547623, x\right) + \left(\mathsf{fma}\left(y, \frac{t}{z \cdot z}, 11.1667541262 \cdot \frac{y}{z}\right) - \mathsf{fma}\left(y, \frac{98.5170599679272}{z \cdot z}, \mathsf{fma}\left(y, \frac{47.69379582500642}{z}, \frac{y \cdot -556.47806218377}{z \cdot z}\right)\right)\right)\\ \mathbf{if}\;z \leq -7.4 \cdot 10^{+21}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 8500000000000:\\ \;\;\;\;\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}, y \cdot \mathsf{fma}\left(z, \mathsf{fma}\left(z, t, a\right), b\right), x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+
          (fma y 3.13060547623 x)
          (-
           (fma y (/ t (* z z)) (* 11.1667541262 (/ y z)))
           (fma
            y
            (/ 98.5170599679272 (* z z))
            (fma
             y
             (/ 47.69379582500642 z)
             (/ (* y -556.47806218377) (* z z))))))))
   (if (<= z -7.4e+21)
     t_1
     (if (<= z 8500000000000.0)
       (fma
        (/
         1.0
         (fma
          z
          (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721)
          0.607771387771))
        (* y (fma z (fma z t a) b))
        x)
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = fma(y, 3.13060547623, x) + (fma(y, (t / (z * z)), (11.1667541262 * (y / z))) - fma(y, (98.5170599679272 / (z * z)), fma(y, (47.69379582500642 / z), ((y * -556.47806218377) / (z * z)))));
	double tmp;
	if (z <= -7.4e+21) {
		tmp = t_1;
	} else if (z <= 8500000000000.0) {
		tmp = fma((1.0 / fma(z, fma(z, fma(z, (z + 15.234687407), 31.4690115749), 11.9400905721), 0.607771387771)), (y * fma(z, fma(z, t, a), b)), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(fma(y, 3.13060547623, x) + Float64(fma(y, Float64(t / Float64(z * z)), Float64(11.1667541262 * Float64(y / z))) - fma(y, Float64(98.5170599679272 / Float64(z * z)), fma(y, Float64(47.69379582500642 / z), Float64(Float64(y * -556.47806218377) / Float64(z * z))))))
	tmp = 0.0
	if (z <= -7.4e+21)
		tmp = t_1;
	elseif (z <= 8500000000000.0)
		tmp = fma(Float64(1.0 / fma(z, fma(z, fma(z, Float64(z + 15.234687407), 31.4690115749), 11.9400905721), 0.607771387771)), Float64(y * fma(z, fma(z, t, a), b)), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y * 3.13060547623 + x), $MachinePrecision] + N[(N[(y * N[(t / N[(z * z), $MachinePrecision]), $MachinePrecision] + N[(11.1667541262 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * N[(98.5170599679272 / N[(z * z), $MachinePrecision]), $MachinePrecision] + N[(y * N[(47.69379582500642 / z), $MachinePrecision] + N[(N[(y * -556.47806218377), $MachinePrecision] / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.4e+21], t$95$1, If[LessEqual[z, 8500000000000.0], N[(N[(1.0 / N[(z * N[(z * N[(z * N[(z + 15.234687407), $MachinePrecision] + 31.4690115749), $MachinePrecision] + 11.9400905721), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision] * N[(y * N[(z * N[(z * t + a), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -7.4e21 or 8.5e12 < z

   1. Initial program 12.7%

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

   3. Taylor expanded in z around inf

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

   5. Simplified 96.6%

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

   if -7.4e21 < z < 8.5e12

   1. Initial program 99.6%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. accelerator-lowering-fma.f64 99.6

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

   5. Simplified 99.6%

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

      1. +-commutative N/A

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

      2. clear-num N/A

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

      3. associate-/r/ N/A

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

      4. distribute-lft-in N/A

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

      5. *-commutative N/A

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

      6. associate-*r* N/A

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

      7. +-commutative N/A

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

      8. distribute-lft-out N/A

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

      9. *-commutative N/A

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

      10. accelerator-lowering-fma.f64 N/A

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

   7. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}, y \cdot \mathsf{fma}\left(z, \mathsf{fma}\left(z, t, a\right), b\right), x\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 67.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)} \leq -5 \cdot 10^{+37}:\\ \;\;\;\;b \cdot \left(y \cdot 1.6453555072203998\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<=
      (/
       (*
        y
        (+
         b
         (* z (+ a (* z (+ t (* z (+ 11.1667541262 (* z 3.13060547623)))))))))
       (+
        0.607771387771
        (*
         z
         (+ 11.9400905721 (* z (+ 31.4690115749 (* z (+ z 15.234687407))))))))
      -5e+37)
   (* b (* y 1.6453555072203998))
   (fma y 3.13060547623 x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((y * (b + (z * (a + (z * (t + (z * (11.1667541262 + (z * 3.13060547623))))))))) / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * (z + 15.234687407)))))))) <= -5e+37) {
		tmp = b * (y * 1.6453555072203998);
	} else {
		tmp = fma(y, 3.13060547623, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(Float64(y * Float64(b + Float64(z * Float64(a + Float64(z * Float64(t + Float64(z * Float64(11.1667541262 + Float64(z * 3.13060547623))))))))) / Float64(0.607771387771 + Float64(z * Float64(11.9400905721 + Float64(z * Float64(31.4690115749 + Float64(z * Float64(z + 15.234687407)))))))) <= -5e+37)
		tmp = Float64(b * Float64(y * 1.6453555072203998));
	else
		tmp = fma(y, 3.13060547623, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(N[(y * N[(b + N[(z * N[(a + N[(z * N[(t + N[(z * N[(11.1667541262 + N[(z * 3.13060547623), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(0.607771387771 + N[(z * N[(11.9400905721 + N[(z * N[(31.4690115749 + N[(z * N[(z + 15.234687407), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], -5e+37], N[(b * N[(y * 1.6453555072203998), $MachinePrecision]), $MachinePrecision], N[(y * 3.13060547623 + 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))) < -4.99999999999999989e37

   1. Initial program 85.3%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. accelerator-lowering-fma.f64 85.2

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

   5. Simplified 85.2%

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

   6. Taylor expanded in z around 0

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

   8. Simplified 81.6%

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

   9. Taylor expanded in b around inf

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

       1. *-commutative N/A

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

       2. associate-*r* N/A

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

       3. *-commutative N/A

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

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

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

       5. *-commutative N/A

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

       6. *-lowering-*.f64 52.0

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

   11. Simplified 52.0%

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

   if -4.99999999999999989e37 < (/.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 49.2%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   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. *-commutative N/A

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

      3. accelerator-lowering-fma.f64 72.9

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

   5. Simplified 72.9%

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

4. Final simplification 69.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)} \leq -5 \cdot 10^{+37}:\\ \;\;\;\;b \cdot \left(y \cdot 1.6453555072203998\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 96.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+52}:\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623, x\right)\\ \mathbf{elif}\;z \leq 9000000000000:\\ \;\;\;\;\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}, y \cdot \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right), x\right)\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+124}:\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623, x\right) + \frac{\frac{\mathsf{fma}\left(y, t, \mathsf{fma}\left(y, -98.5170599679272, y \cdot 556.47806218377\right)\right)}{z} - y \cdot 36.52704169880642}{z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -6e+52)
   (fma y 3.13060547623 x)
   (if (<= z 9000000000000.0)
     (fma
      (/
       1.0
       (fma
        z
        (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721)
        0.607771387771))
      (* y (fma z (fma z (fma z (fma z 3.13060547623 11.1667541262) t) a) b))
      x)
     (if (<= z 4e+124)
       (+
        (fma y 3.13060547623 x)
        (/
         (-
          (/ (fma y t (fma y -98.5170599679272 (* y 556.47806218377))) z)
          (* y 36.52704169880642))
         z))
       (fma y 3.13060547623 x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -6e+52) {
		tmp = fma(y, 3.13060547623, x);
	} else if (z <= 9000000000000.0) {
		tmp = fma((1.0 / fma(z, fma(z, fma(z, (z + 15.234687407), 31.4690115749), 11.9400905721), 0.607771387771)), (y * fma(z, fma(z, fma(z, fma(z, 3.13060547623, 11.1667541262), t), a), b)), x);
	} else if (z <= 4e+124) {
		tmp = fma(y, 3.13060547623, x) + (((fma(y, t, fma(y, -98.5170599679272, (y * 556.47806218377))) / z) - (y * 36.52704169880642)) / z);
	} else {
		tmp = fma(y, 3.13060547623, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -6e+52)
		tmp = fma(y, 3.13060547623, x);
	elseif (z <= 9000000000000.0)
		tmp = fma(Float64(1.0 / fma(z, fma(z, fma(z, Float64(z + 15.234687407), 31.4690115749), 11.9400905721), 0.607771387771)), Float64(y * fma(z, fma(z, fma(z, fma(z, 3.13060547623, 11.1667541262), t), a), b)), x);
	elseif (z <= 4e+124)
		tmp = Float64(fma(y, 3.13060547623, x) + Float64(Float64(Float64(fma(y, t, fma(y, -98.5170599679272, Float64(y * 556.47806218377))) / z) - Float64(y * 36.52704169880642)) / z));
	else
		tmp = fma(y, 3.13060547623, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -6e+52], N[(y * 3.13060547623 + x), $MachinePrecision], If[LessEqual[z, 9000000000000.0], N[(N[(1.0 / N[(z * N[(z * N[(z * N[(z + 15.234687407), $MachinePrecision] + 31.4690115749), $MachinePrecision] + 11.9400905721), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision] * N[(y * N[(z * N[(z * N[(z * N[(z * 3.13060547623 + 11.1667541262), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[z, 4e+124], N[(N[(y * 3.13060547623 + x), $MachinePrecision] + N[(N[(N[(N[(y * t + N[(y * -98.5170599679272 + N[(y * 556.47806218377), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] - N[(y * 36.52704169880642), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(y * 3.13060547623 + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6e52 or 3.99999999999999979e124 < z

   1. Initial program 3.4%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. accelerator-lowering-fma.f64 96.8

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

   5. Simplified 96.8%

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

   if -6e52 < z < 9e12

   1. Initial program 98.9%

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

      1. +-commutative N/A

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

      2. clear-num N/A

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

      3. associate-/r/ N/A

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

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

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

   4. Applied egg-rr 99.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}, y \cdot \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right), x\right)} \]

   if 9e12 < z < 3.99999999999999979e124

   1. Initial program 29.2%

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

   3. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{x + \left(-1 \cdot \frac{\left(\frac{-55833770631}{5000000000} \cdot y + -1 \cdot \frac{t \cdot y - \left(\frac{-15234687407}{1000000000} \cdot \left(\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y\right) + \frac{98517059967927196814627}{1000000000000000000000} \cdot y\right)}{z}\right) - \frac{-4769379582500641883561}{100000000000000000000} \cdot y}{z} + \frac{313060547623}{100000000000} \cdot y\right)} \]

   5. Simplified 95.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, 3.13060547623, x\right) - \frac{\left(-\frac{\mathsf{fma}\left(y, t, \mathsf{fma}\left(y, -98.5170599679272, y \cdot 556.47806218377\right)\right)}{z}\right) + y \cdot 36.52704169880642}{z}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 97.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+52}:\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623, x\right)\\ \mathbf{elif}\;z \leq 9000000000000:\\ \;\;\;\;\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}, y \cdot \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right), x\right)\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+124}:\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623, x\right) + \frac{\frac{\mathsf{fma}\left(y, t, \mathsf{fma}\left(y, -98.5170599679272, y \cdot 556.47806218377\right)\right)}{z} - y \cdot 36.52704169880642}{z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 96.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+63}:\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623, x\right)\\ \mathbf{elif}\;z \leq 9500000000000:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right), \frac{y}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}, x\right)\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+124}:\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623, x\right) + \frac{\frac{\mathsf{fma}\left(y, t, \mathsf{fma}\left(y, -98.5170599679272, y \cdot 556.47806218377\right)\right)}{z} - y \cdot 36.52704169880642}{z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -4.8e+63)
   (fma y 3.13060547623 x)
   (if (<= z 9500000000000.0)
     (fma
      (fma z (fma z (fma z (fma z 3.13060547623 11.1667541262) t) a) b)
      (/
       y
       (fma
        z
        (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721)
        0.607771387771))
      x)
     (if (<= z 5e+124)
       (+
        (fma y 3.13060547623 x)
        (/
         (-
          (/ (fma y t (fma y -98.5170599679272 (* y 556.47806218377))) z)
          (* y 36.52704169880642))
         z))
       (fma y 3.13060547623 x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -4.8e+63) {
		tmp = fma(y, 3.13060547623, x);
	} else if (z <= 9500000000000.0) {
		tmp = fma(fma(z, fma(z, fma(z, fma(z, 3.13060547623, 11.1667541262), t), a), b), (y / fma(z, fma(z, fma(z, (z + 15.234687407), 31.4690115749), 11.9400905721), 0.607771387771)), x);
	} else if (z <= 5e+124) {
		tmp = fma(y, 3.13060547623, x) + (((fma(y, t, fma(y, -98.5170599679272, (y * 556.47806218377))) / z) - (y * 36.52704169880642)) / z);
	} else {
		tmp = fma(y, 3.13060547623, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -4.8e+63)
		tmp = fma(y, 3.13060547623, x);
	elseif (z <= 9500000000000.0)
		tmp = fma(fma(z, fma(z, fma(z, fma(z, 3.13060547623, 11.1667541262), t), a), b), Float64(y / fma(z, fma(z, fma(z, Float64(z + 15.234687407), 31.4690115749), 11.9400905721), 0.607771387771)), x);
	elseif (z <= 5e+124)
		tmp = Float64(fma(y, 3.13060547623, x) + Float64(Float64(Float64(fma(y, t, fma(y, -98.5170599679272, Float64(y * 556.47806218377))) / z) - Float64(y * 36.52704169880642)) / z));
	else
		tmp = fma(y, 3.13060547623, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -4.8e+63], N[(y * 3.13060547623 + x), $MachinePrecision], If[LessEqual[z, 9500000000000.0], N[(N[(z * N[(z * N[(z * N[(z * 3.13060547623 + 11.1667541262), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision] + b), $MachinePrecision] * N[(y / N[(z * N[(z * N[(z * N[(z + 15.234687407), $MachinePrecision] + 31.4690115749), $MachinePrecision] + 11.9400905721), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[z, 5e+124], N[(N[(y * 3.13060547623 + x), $MachinePrecision] + N[(N[(N[(N[(y * t + N[(y * -98.5170599679272 + N[(y * 556.47806218377), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] - N[(y * 36.52704169880642), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(y * 3.13060547623 + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.8e63 or 4.9999999999999996e124 < z

   1. Initial program 3.3%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   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. *-commutative N/A

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

      3. accelerator-lowering-fma.f64 97.8

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

   5. Simplified 97.8%

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

   if -4.8e63 < z < 9.5e12

   1. Initial program 96.8%

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

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

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

   4. Applied egg-rr 98.2%

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

   if 9.5e12 < z < 4.9999999999999996e124

   1. Initial program 29.2%

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

   3. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{x + \left(-1 \cdot \frac{\left(\frac{-55833770631}{5000000000} \cdot y + -1 \cdot \frac{t \cdot y - \left(\frac{-15234687407}{1000000000} \cdot \left(\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y\right) + \frac{98517059967927196814627}{1000000000000000000000} \cdot y\right)}{z}\right) - \frac{-4769379582500641883561}{100000000000000000000} \cdot y}{z} + \frac{313060547623}{100000000000} \cdot y\right)} \]

   5. Simplified 95.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, 3.13060547623, x\right) - \frac{\left(-\frac{\mathsf{fma}\left(y, t, \mathsf{fma}\left(y, -98.5170599679272, y \cdot 556.47806218377\right)\right)}{z}\right) + y \cdot 36.52704169880642}{z}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 97.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+63}:\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623, x\right)\\ \mathbf{elif}\;z \leq 9500000000000:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right), \frac{y}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}, x\right)\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+124}:\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623, x\right) + \frac{\frac{\mathsf{fma}\left(y, t, \mathsf{fma}\left(y, -98.5170599679272, y \cdot 556.47806218377\right)\right)}{z} - y \cdot 36.52704169880642}{z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 95.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+22}:\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623, x\right)\\ \mathbf{elif}\;z \leq 9500000000000:\\ \;\;\;\;\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}, y \cdot \mathsf{fma}\left(z, \mathsf{fma}\left(z, t, a\right), b\right), x\right)\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+124}:\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623, x\right) + \frac{\frac{\mathsf{fma}\left(y, t, \mathsf{fma}\left(y, -98.5170599679272, y \cdot 556.47806218377\right)\right)}{z} - y \cdot 36.52704169880642}{z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.15e+22)
   (fma y 3.13060547623 x)
   (if (<= z 9500000000000.0)
     (fma
      (/
       1.0
       (fma
        z
        (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721)
        0.607771387771))
      (* y (fma z (fma z t a) b))
      x)
     (if (<= z 6.5e+124)
       (+
        (fma y 3.13060547623 x)
        (/
         (-
          (/ (fma y t (fma y -98.5170599679272 (* y 556.47806218377))) z)
          (* y 36.52704169880642))
         z))
       (fma y 3.13060547623 x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.15e+22) {
		tmp = fma(y, 3.13060547623, x);
	} else if (z <= 9500000000000.0) {
		tmp = fma((1.0 / fma(z, fma(z, fma(z, (z + 15.234687407), 31.4690115749), 11.9400905721), 0.607771387771)), (y * fma(z, fma(z, t, a), b)), x);
	} else if (z <= 6.5e+124) {
		tmp = fma(y, 3.13060547623, x) + (((fma(y, t, fma(y, -98.5170599679272, (y * 556.47806218377))) / z) - (y * 36.52704169880642)) / z);
	} else {
		tmp = fma(y, 3.13060547623, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.15e+22)
		tmp = fma(y, 3.13060547623, x);
	elseif (z <= 9500000000000.0)
		tmp = fma(Float64(1.0 / fma(z, fma(z, fma(z, Float64(z + 15.234687407), 31.4690115749), 11.9400905721), 0.607771387771)), Float64(y * fma(z, fma(z, t, a), b)), x);
	elseif (z <= 6.5e+124)
		tmp = Float64(fma(y, 3.13060547623, x) + Float64(Float64(Float64(fma(y, t, fma(y, -98.5170599679272, Float64(y * 556.47806218377))) / z) - Float64(y * 36.52704169880642)) / z));
	else
		tmp = fma(y, 3.13060547623, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.15e+22], N[(y * 3.13060547623 + x), $MachinePrecision], If[LessEqual[z, 9500000000000.0], N[(N[(1.0 / N[(z * N[(z * N[(z * N[(z + 15.234687407), $MachinePrecision] + 31.4690115749), $MachinePrecision] + 11.9400905721), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision] * N[(y * N[(z * N[(z * t + a), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[z, 6.5e+124], N[(N[(y * 3.13060547623 + x), $MachinePrecision] + N[(N[(N[(N[(y * t + N[(y * -98.5170599679272 + N[(y * 556.47806218377), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] - N[(y * 36.52704169880642), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(y * 3.13060547623 + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.1500000000000001e22 or 6.50000000000000008e124 < z

   1. Initial program 8.2%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   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. *-commutative N/A

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

      3. accelerator-lowering-fma.f64 95.1

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

   5. Simplified 95.1%

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

   if -1.1500000000000001e22 < z < 9.5e12

   1. Initial program 99.6%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. accelerator-lowering-fma.f64 99.6

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

   5. Simplified 99.6%

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

      1. +-commutative N/A

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

      2. clear-num N/A

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

      3. associate-/r/ N/A

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

      4. distribute-lft-in N/A

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

      5. *-commutative N/A

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

      6. associate-*r* N/A

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

      7. +-commutative N/A

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

      8. distribute-lft-out N/A

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

      9. *-commutative N/A

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

      10. accelerator-lowering-fma.f64 N/A

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

   7. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}, y \cdot \mathsf{fma}\left(z, \mathsf{fma}\left(z, t, a\right), b\right), x\right)} \]

   if 9.5e12 < z < 6.50000000000000008e124

   1. Initial program 29.2%

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

   3. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{x + \left(-1 \cdot \frac{\left(\frac{-55833770631}{5000000000} \cdot y + -1 \cdot \frac{t \cdot y - \left(\frac{-15234687407}{1000000000} \cdot \left(\frac{-55833770631}{5000000000} \cdot y - \frac{-4769379582500641883561}{100000000000000000000} \cdot y\right) + \frac{98517059967927196814627}{1000000000000000000000} \cdot y\right)}{z}\right) - \frac{-4769379582500641883561}{100000000000000000000} \cdot y}{z} + \frac{313060547623}{100000000000} \cdot y\right)} \]

   5. Simplified 95.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, 3.13060547623, x\right) - \frac{\left(-\frac{\mathsf{fma}\left(y, t, \mathsf{fma}\left(y, -98.5170599679272, y \cdot 556.47806218377\right)\right)}{z}\right) + y \cdot 36.52704169880642}{z}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 97.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+22}:\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623, x\right)\\ \mathbf{elif}\;z \leq 9500000000000:\\ \;\;\;\;\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}, y \cdot \mathsf{fma}\left(z, \mathsf{fma}\left(z, t, a\right), b\right), x\right)\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+124}:\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623, x\right) + \frac{\frac{\mathsf{fma}\left(y, t, \mathsf{fma}\left(y, -98.5170599679272, y \cdot 556.47806218377\right)\right)}{z} - y \cdot 36.52704169880642}{z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 94.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+22}:\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623, x\right)\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+49}:\\ \;\;\;\;\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}, y \cdot \mathsf{fma}\left(z, \mathsf{fma}\left(z, t, a\right), b\right), x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.15e+22)
   (fma y 3.13060547623 x)
   (if (<= z 6.5e+49)
     (fma
      (/
       1.0
       (fma
        z
        (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721)
        0.607771387771))
      (* y (fma z (fma z t a) b))
      x)
     (fma y 3.13060547623 x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.15e+22) {
		tmp = fma(y, 3.13060547623, x);
	} else if (z <= 6.5e+49) {
		tmp = fma((1.0 / fma(z, fma(z, fma(z, (z + 15.234687407), 31.4690115749), 11.9400905721), 0.607771387771)), (y * fma(z, fma(z, t, a), b)), x);
	} else {
		tmp = fma(y, 3.13060547623, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.15e+22)
		tmp = fma(y, 3.13060547623, x);
	elseif (z <= 6.5e+49)
		tmp = fma(Float64(1.0 / fma(z, fma(z, fma(z, Float64(z + 15.234687407), 31.4690115749), 11.9400905721), 0.607771387771)), Float64(y * fma(z, fma(z, t, a), b)), x);
	else
		tmp = fma(y, 3.13060547623, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.15e+22], N[(y * 3.13060547623 + x), $MachinePrecision], If[LessEqual[z, 6.5e+49], N[(N[(1.0 / N[(z * N[(z * N[(z * N[(z + 15.234687407), $MachinePrecision] + 31.4690115749), $MachinePrecision] + 11.9400905721), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision] * N[(y * N[(z * N[(z * t + a), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(y * 3.13060547623 + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.1500000000000001e22 or 6.5000000000000005e49 < z

   1. Initial program 8.6%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   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. *-commutative N/A

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

      3. accelerator-lowering-fma.f64 92.2

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

   5. Simplified 92.2%

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

   if -1.1500000000000001e22 < z < 6.5000000000000005e49

   1. Initial program 98.2%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. accelerator-lowering-fma.f64 97.0

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

   5. Simplified 97.0%

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

      1. +-commutative N/A

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

      2. clear-num N/A

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

      3. associate-/r/ N/A

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

      4. distribute-lft-in N/A

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

      5. *-commutative N/A

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

      6. associate-*r* N/A

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

      7. +-commutative N/A

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

      8. distribute-lft-out N/A

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

      9. *-commutative N/A

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

      10. accelerator-lowering-fma.f64 N/A

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

   7. Applied egg-rr 97.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{1}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}, y \cdot \mathsf{fma}\left(z, \mathsf{fma}\left(z, t, a\right), b\right), x\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 95.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+22}:\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623, x\right)\\ \mathbf{elif}\;z \leq 1.16 \cdot 10^{+53}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(z, \mathsf{fma}\left(z, t, a\right), b\right), \frac{y}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.05e+22)
   (fma y 3.13060547623 x)
   (if (<= z 1.16e+53)
     (fma
      (fma z (fma z t a) b)
      (/
       y
       (fma
        z
        (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721)
        0.607771387771))
      x)
     (fma y 3.13060547623 x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.05e+22) {
		tmp = fma(y, 3.13060547623, x);
	} else if (z <= 1.16e+53) {
		tmp = fma(fma(z, fma(z, t, a), b), (y / fma(z, fma(z, fma(z, (z + 15.234687407), 31.4690115749), 11.9400905721), 0.607771387771)), x);
	} else {
		tmp = fma(y, 3.13060547623, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.05e+22)
		tmp = fma(y, 3.13060547623, x);
	elseif (z <= 1.16e+53)
		tmp = fma(fma(z, fma(z, t, a), b), Float64(y / fma(z, fma(z, fma(z, Float64(z + 15.234687407), 31.4690115749), 11.9400905721), 0.607771387771)), x);
	else
		tmp = fma(y, 3.13060547623, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.05e+22], N[(y * 3.13060547623 + x), $MachinePrecision], If[LessEqual[z, 1.16e+53], N[(N[(z * N[(z * t + a), $MachinePrecision] + b), $MachinePrecision] * N[(y / N[(z * N[(z * N[(z * N[(z + 15.234687407), $MachinePrecision] + 31.4690115749), $MachinePrecision] + 11.9400905721), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(y * 3.13060547623 + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.0499999999999999e22 or 1.16e53 < z

   1. Initial program 8.6%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   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. *-commutative N/A

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

      3. accelerator-lowering-fma.f64 92.2

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

   5. Simplified 92.2%

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

   if -1.0499999999999999e22 < z < 1.16e53

   1. Initial program 98.2%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. accelerator-lowering-fma.f64 97.0

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

   5. Simplified 97.0%

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

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

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

   7. Applied egg-rr 97.0%

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

Alternative 8: 93.1% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+21}:\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623, x\right)\\ \mathbf{elif}\;z \leq 950000000:\\ \;\;\;\;\mathsf{fma}\left(y \cdot \mathsf{fma}\left(z, \mathsf{fma}\left(z, t, a\right), b\right), 1.6453555072203998, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{z}, -36.52704169880642, \mathsf{fma}\left(y, 3.13060547623, x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.9e+21)
   (fma y 3.13060547623 x)
   (if (<= z 950000000.0)
     (fma (* y (fma z (fma z t a) b)) 1.6453555072203998 x)
     (fma (/ y z) -36.52704169880642 (fma y 3.13060547623 x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.9e+21) {
		tmp = fma(y, 3.13060547623, x);
	} else if (z <= 950000000.0) {
		tmp = fma((y * fma(z, fma(z, t, a), b)), 1.6453555072203998, x);
	} else {
		tmp = fma((y / z), -36.52704169880642, fma(y, 3.13060547623, x));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.9e+21)
		tmp = fma(y, 3.13060547623, x);
	elseif (z <= 950000000.0)
		tmp = fma(Float64(y * fma(z, fma(z, t, a), b)), 1.6453555072203998, x);
	else
		tmp = fma(Float64(y / z), -36.52704169880642, fma(y, 3.13060547623, x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.9e+21], N[(y * 3.13060547623 + x), $MachinePrecision], If[LessEqual[z, 950000000.0], N[(N[(y * N[(z * N[(z * t + a), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] * 1.6453555072203998 + x), $MachinePrecision], N[(N[(y / z), $MachinePrecision] * -36.52704169880642 + N[(y * 3.13060547623 + x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.9e21

   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. *-commutative N/A

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

      3. accelerator-lowering-fma.f64 92.7

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

   5. Simplified 92.7%

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

   if -1.9e21 < z < 9.5e8

   1. Initial program 99.6%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. accelerator-lowering-fma.f64 99.6

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

   5. Simplified 99.6%

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

   6. Taylor expanded in z around 0

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

   8. Simplified 96.5%

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

      1. +-commutative N/A

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

      2. div-inv N/A

         \[\leadsto \color{blue}{\left(y \cdot \left(z \cdot \left(z \cdot t + a\right) + b\right)\right) \cdot \frac{1}{\frac{607771387771}{1000000000000}}} + x \]

      3. metadata-eval N/A

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

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

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

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

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

      6. accelerator-lowering-fma.f64 N/A

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

      7. accelerator-lowering-fma.f64 96.6

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

   10. Applied egg-rr 96.6%

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

   if 9.5e8 < z

   1. Initial program 13.2%

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

   3. Taylor expanded in z around inf

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

      1. associate--l+ N/A

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

      2. +-commutative N/A

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

      3. associate--l+ N/A

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

      4. +-commutative N/A

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

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

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

      6. metadata-eval N/A

         \[\leadsto \left(\frac{y}{z} \cdot \color{blue}{\frac{-3652704169880641883561}{100000000000000000000}} + \frac{313060547623}{100000000000} \cdot y\right) + x \]

      7. metadata-eval N/A

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

      8. metadata-eval N/A

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

      9. times-frac N/A

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

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

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

      11. *-commutative N/A

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

      12. mul-1-neg N/A

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

      13. distribute-neg-frac2 N/A

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

      14. mul-1-neg N/A

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

      15. associate-+l+ N/A

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

   5. Simplified 85.1%

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

Alternative 9: 93.1% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+21}:\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623, x\right)\\ \mathbf{elif}\;z \leq 650000000:\\ \;\;\;\;\mathsf{fma}\left(y \cdot \mathsf{fma}\left(z, \mathsf{fma}\left(z, t, a\right), b\right), 1.6453555072203998, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -5.5e+21)
   (fma y 3.13060547623 x)
   (if (<= z 650000000.0)
     (fma (* y (fma z (fma z t a) b)) 1.6453555072203998 x)
     (fma y 3.13060547623 x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -5.5e+21) {
		tmp = fma(y, 3.13060547623, x);
	} else if (z <= 650000000.0) {
		tmp = fma((y * fma(z, fma(z, t, a), b)), 1.6453555072203998, x);
	} else {
		tmp = fma(y, 3.13060547623, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -5.5e+21)
		tmp = fma(y, 3.13060547623, x);
	elseif (z <= 650000000.0)
		tmp = fma(Float64(y * fma(z, fma(z, t, a), b)), 1.6453555072203998, x);
	else
		tmp = fma(y, 3.13060547623, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -5.5e+21], N[(y * 3.13060547623 + x), $MachinePrecision], If[LessEqual[z, 650000000.0], N[(N[(y * N[(z * N[(z * t + a), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] * 1.6453555072203998 + x), $MachinePrecision], N[(y * 3.13060547623 + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.5e21 or 6.5e8 < z

   1. Initial program 12.7%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   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. *-commutative N/A

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

      3. accelerator-lowering-fma.f64 88.9

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

   5. Simplified 88.9%

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

   if -5.5e21 < z < 6.5e8

   1. Initial program 99.6%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. accelerator-lowering-fma.f64 99.6

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

   5. Simplified 99.6%

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

   6. Taylor expanded in z around 0

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

   8. Simplified 96.5%

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

      1. +-commutative N/A

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

      2. div-inv N/A

         \[\leadsto \color{blue}{\left(y \cdot \left(z \cdot \left(z \cdot t + a\right) + b\right)\right) \cdot \frac{1}{\frac{607771387771}{1000000000000}}} + x \]

      3. metadata-eval N/A

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

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

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

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

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

      6. accelerator-lowering-fma.f64 N/A

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

      7. accelerator-lowering-fma.f64 96.6

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

   10. Applied egg-rr 96.6%

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

Alternative 10: 90.3% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+21}:\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623, x\right)\\ \mathbf{elif}\;z \leq 95000000000:\\ \;\;\;\;\mathsf{fma}\left(y \cdot 1.6453555072203998, \mathsf{fma}\left(z, a, b\right), x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -6.8e+21)
   (fma y 3.13060547623 x)
   (if (<= z 95000000000.0)
     (fma (* y 1.6453555072203998) (fma z a b) x)
     (fma y 3.13060547623 x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -6.8e+21) {
		tmp = fma(y, 3.13060547623, x);
	} else if (z <= 95000000000.0) {
		tmp = fma((y * 1.6453555072203998), fma(z, a, b), x);
	} else {
		tmp = fma(y, 3.13060547623, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -6.8e+21)
		tmp = fma(y, 3.13060547623, x);
	elseif (z <= 95000000000.0)
		tmp = fma(Float64(y * 1.6453555072203998), fma(z, a, b), x);
	else
		tmp = fma(y, 3.13060547623, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -6.8e+21], N[(y * 3.13060547623 + x), $MachinePrecision], If[LessEqual[z, 95000000000.0], N[(N[(y * 1.6453555072203998), $MachinePrecision] * N[(z * a + b), $MachinePrecision] + x), $MachinePrecision], N[(y * 3.13060547623 + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -6.8e21 or 9.5e10 < z

   1. Initial program 12.7%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   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. *-commutative N/A

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

      3. accelerator-lowering-fma.f64 88.9

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

   5. Simplified 88.9%

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

   if -6.8e21 < z < 9.5e10

   1. Initial program 99.6%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. accelerator-lowering-fma.f64 N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. accelerator-lowering-fma.f64 99.6

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

   5. Simplified 99.6%

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

   6. Taylor expanded in z around 0

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

   8. Simplified 96.5%

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

   9. Taylor expanded in z around 0

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

       1. +-commutative N/A

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

       2. *-commutative N/A

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

       3. associate-*r* N/A

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

       4. associate-*r* N/A

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

       5. associate-*l* N/A

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

       6. *-commutative N/A

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

       7. *-commutative N/A

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

       8. associate-*r* N/A

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

       9. distribute-lft-in N/A

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

       10. +-commutative N/A

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

       11. accelerator-lowering-fma.f64 N/A

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

       12. *-commutative N/A

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

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

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

       14. +-commutative N/A

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

       15. *-commutative N/A

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

       16. accelerator-lowering-fma.f64 91.7

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

   11. Simplified 91.7%

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

Alternative 11: 83.6% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+19}:\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623, x\right)\\ \mathbf{elif}\;z \leq 230000000000:\\ \;\;\;\;\mathsf{fma}\left(y, b \cdot 1.6453555072203998, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -8.5e+19)
   (fma y 3.13060547623 x)
   (if (<= z 230000000000.0)
     (fma y (* b 1.6453555072203998) x)
     (fma y 3.13060547623 x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -8.5e+19) {
		tmp = fma(y, 3.13060547623, x);
	} else if (z <= 230000000000.0) {
		tmp = fma(y, (b * 1.6453555072203998), x);
	} else {
		tmp = fma(y, 3.13060547623, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -8.5e+19)
		tmp = fma(y, 3.13060547623, x);
	elseif (z <= 230000000000.0)
		tmp = fma(y, Float64(b * 1.6453555072203998), x);
	else
		tmp = fma(y, 3.13060547623, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -8.5e+19], N[(y * 3.13060547623 + x), $MachinePrecision], If[LessEqual[z, 230000000000.0], N[(y * N[(b * 1.6453555072203998), $MachinePrecision] + x), $MachinePrecision], N[(y * 3.13060547623 + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -8.5e19 or 2.3e11 < z

   1. Initial program 13.4%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. accelerator-lowering-fma.f64 88.3

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

   5. Simplified 88.3%

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

   if -8.5e19 < z < 2.3e11

   1. Initial program 99.6%

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   2. 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. associate-*r* N/A

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

      3. *-commutative N/A

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

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

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 75.5

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

   5. Simplified 75.5%

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

Alternative 12: 52.0% accurate, 4.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{-31}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-114}:\\ \;\;\;\;y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -2.1e-31) x (if (<= x 9e-114) (* y 3.13060547623) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -2.1e-31) {
		tmp = x;
	} else if (x <= 9e-114) {
		tmp = y * 3.13060547623;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-2.1d-31)) then
        tmp = x
    else if (x <= 9d-114) then
        tmp = y * 3.13060547623d0
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -2.1e-31) {
		tmp = x;
	} else if (x <= 9e-114) {
		tmp = y * 3.13060547623;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -2.1e-31:
		tmp = x
	elif x <= 9e-114:
		tmp = y * 3.13060547623
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -2.1e-31)
		tmp = x;
	elseif (x <= 9e-114)
		tmp = Float64(y * 3.13060547623);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -2.1e-31)
		tmp = x;
	elseif (x <= 9e-114)
		tmp = y * 3.13060547623;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -2.1e-31], x, If[LessEqual[x, 9e-114], N[(y * 3.13060547623), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -2.09999999999999991e-31 or 8.99999999999999937e-114 < x

   1. Initial program 58.4%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 59.8%

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

   if -2.09999999999999991e-31 < x < 8.99999999999999937e-114

   1. Initial program 51.9%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 50.8

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

   5. Simplified 50.8%

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

   6. Taylor expanded in x around 0

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

      1. *-lowering-*.f64 42.1

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

   8. Simplified 42.1%

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

4. Final simplification 52.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{-31}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-114}:\\ \;\;\;\;y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 63.1% accurate, 11.3× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 55.8%

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

3. Taylor expanded in z around 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. *-commutative N/A

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

   3. accelerator-lowering-fma.f64 61.7

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

5. Simplified 61.7%

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

Alternative 14: 45.8% accurate, 79.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 55.8%

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

3. Taylor expanded in x around inf

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

5. Simplified 42.1%

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

Developer Target 1: 98.5% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024204 
(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))))