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

Percentage Accurate: 57.7% → 97.7%

Time: 19.2s

Alternatives: 16

Speedup: 2.2×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 57.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+18}:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 - y \cdot \frac{36.52704169880642 - \frac{\left(t + 457.9610022158428\right) + \frac{\left(-6976.8927133548 + t \cdot -15.234687407\right) + \left(a + 1112.0901850848957\right)}{z}}{z}}{z}\right)\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+24}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot t\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z \cdot \left(\frac{15.234687407}{z} + 1\right)\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623 + \frac{\frac{t + 457.9610022158428}{z} - 36.52704169880642}{z}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -3.4e+18)
   (+
    x
    (-
     (* y 3.13060547623)
     (*
      y
      (/
       (-
        36.52704169880642
        (/
         (+
          (+ t 457.9610022158428)
          (/
           (+
            (+ -6976.8927133548 (* t -15.234687407))
            (+ a 1112.0901850848957))
           z))
         z))
       z))))
   (if (<= z 1.25e+24)
     (+
      x
      (/
       (* y (+ b (* z (+ a (* z t)))))
       (+
        0.607771387771
        (*
         z
         (+
          11.9400905721
          (* z (+ 31.4690115749 (* z (* z (+ (/ 15.234687407 z) 1.0))))))))))
     (fma
      y
      (+
       3.13060547623
       (/ (- (/ (+ t 457.9610022158428) z) 36.52704169880642) z))
      x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -3.4e+18) {
		tmp = x + ((y * 3.13060547623) - (y * ((36.52704169880642 - (((t + 457.9610022158428) + (((-6976.8927133548 + (t * -15.234687407)) + (a + 1112.0901850848957)) / z)) / z)) / z)));
	} else if (z <= 1.25e+24) {
		tmp = x + ((y * (b + (z * (a + (z * t))))) / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * (z * ((15.234687407 / z) + 1.0)))))))));
	} else {
		tmp = fma(y, (3.13060547623 + ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -3.4e+18)
		tmp = Float64(x + Float64(Float64(y * 3.13060547623) - Float64(y * Float64(Float64(36.52704169880642 - Float64(Float64(Float64(t + 457.9610022158428) + Float64(Float64(Float64(-6976.8927133548 + Float64(t * -15.234687407)) + Float64(a + 1112.0901850848957)) / z)) / z)) / z))));
	elseif (z <= 1.25e+24)
		tmp = Float64(x + Float64(Float64(y * Float64(b + Float64(z * Float64(a + Float64(z * t))))) / Float64(0.607771387771 + Float64(z * Float64(11.9400905721 + Float64(z * Float64(31.4690115749 + Float64(z * Float64(z * Float64(Float64(15.234687407 / z) + 1.0))))))))));
	else
		tmp = fma(y, Float64(3.13060547623 + Float64(Float64(Float64(Float64(t + 457.9610022158428) / z) - 36.52704169880642) / z)), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -3.4e+18], N[(x + N[(N[(y * 3.13060547623), $MachinePrecision] - N[(y * N[(N[(36.52704169880642 - N[(N[(N[(t + 457.9610022158428), $MachinePrecision] + N[(N[(N[(-6976.8927133548 + N[(t * -15.234687407), $MachinePrecision]), $MachinePrecision] + N[(a + 1112.0901850848957), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.25e+24], N[(x + N[(N[(y * N[(b + N[(z * N[(a + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(0.607771387771 + N[(z * N[(11.9400905721 + N[(z * N[(31.4690115749 + N[(z * N[(z * N[(N[(15.234687407 / z), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(3.13060547623 + N[(N[(N[(N[(t + 457.9610022158428), $MachinePrecision] / z), $MachinePrecision] - 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.4e18

   1. Initial program 12.4%

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

   3. Simplified 18.5%

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

   5. Taylor expanded in z around -inf 84.0%

      \[\leadsto \color{blue}{x + \left(-1 \cdot \frac{\left(-11.1667541262 \cdot y + -1 \cdot \frac{\left(-1 \cdot \frac{-1 \cdot \left(a \cdot y\right) - \left(-37.37971293169846 \cdot y + \left(-15.234687407 \cdot \left(t \cdot y - \left(-15.234687407 \cdot \left(-11.1667541262 \cdot y - -47.69379582500642 \cdot y\right) + 98.5170599679272 \cdot y\right)\right) + 31.4690115749 \cdot \left(-11.1667541262 \cdot y - -47.69379582500642 \cdot y\right)\right)\right)}{z} + t \cdot y\right) - \left(-15.234687407 \cdot \left(-11.1667541262 \cdot y - -47.69379582500642 \cdot y\right) + 98.5170599679272 \cdot y\right)}{z}\right) - -47.69379582500642 \cdot y}{z} + 3.13060547623 \cdot y\right)} \]

   6. Taylor expanded in y around 0 96.9%

      \[\leadsto x + \left(-1 \cdot \color{blue}{\frac{y \cdot \left(36.52704169880642 + -1 \cdot \frac{457.9610022158428 + \left(t + -1 \cdot \frac{-1 \cdot a - \left(1112.0901850848957 + -15.234687407 \cdot \left(457.9610022158428 + t\right)\right)}{z}\right)}{z}\right)}{z}} + 3.13060547623 \cdot y\right) \]

   8. Simplified 98.7%

      \[\leadsto x + \left(-1 \cdot \color{blue}{\left(y \cdot \frac{36.52704169880642 + \left(-\frac{\left(t + 457.9610022158428\right) + \left(-\frac{\left(\left(-a\right) - 1112.0901850848957\right) - \left(-6976.8927133548 + -15.234687407 \cdot t\right)}{z}\right)}{z}\right)}{z}\right)} + 3.13060547623 \cdot y\right) \]

   if -3.4e18 < z < 1.25000000000000011e24

   1. Initial program 99.1%

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

   3. Taylor expanded in z around inf 99.1%

      \[\leadsto x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\color{blue}{\left(z \cdot \left(1 + 15.234687407 \cdot \frac{1}{z}\right)\right)} \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   4. Step-by-step derivation

      1. associate-*r/ 99.1%

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

      2. metadata-eval 99.1%

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

   5. Simplified 99.1%

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

   6. Taylor expanded in z around 0 91.5%

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

   7. Taylor expanded in y around 0 99.1%

      \[\leadsto x + \frac{\color{blue}{y \cdot \left(b + z \cdot \left(a + t \cdot z\right)\right)}}{\left(\left(\left(z \cdot \left(1 + \frac{15.234687407}{z}\right)\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   8. Step-by-step derivation

      1. *-commutative 99.1%

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

   9. Simplified 99.1%

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

   if 1.25000000000000011e24 < z

   1. Initial program 8.8%

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

   3. Simplified 10.3%

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

   5. Taylor expanded in z around -inf 99.9%

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

      1. mul-1-neg 99.9%

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

      2. unsub-neg 99.9%

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

      3. mul-1-neg 99.9%

         \[\leadsto \mathsf{fma}\left(y, 3.13060547623 - \frac{36.52704169880642 + \color{blue}{\left(-\frac{457.9610022158428 + t}{z}\right)}}{z}, x\right) \]

      4. unsub-neg 99.9%

         \[\leadsto \mathsf{fma}\left(y, 3.13060547623 - \frac{\color{blue}{36.52704169880642 - \frac{457.9610022158428 + t}{z}}}{z}, x\right) \]

      5. +-commutative 99.9%

         \[\leadsto \mathsf{fma}\left(y, 3.13060547623 - \frac{36.52704169880642 - \frac{\color{blue}{t + 457.9610022158428}}{z}}{z}, x\right) \]

   7. Simplified 99.9%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+18}:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 - y \cdot \frac{36.52704169880642 - \frac{\left(t + 457.9610022158428\right) + \frac{\left(-6976.8927133548 + t \cdot -15.234687407\right) + \left(a + 1112.0901850848957\right)}{z}}{z}}{z}\right)\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+24}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot t\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z \cdot \left(\frac{15.234687407}{z} + 1\right)\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623 + \frac{\frac{t + 457.9610022158428}{z} - 36.52704169880642}{z}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 98.1% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771} \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right)}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 - y \cdot \frac{36.52704169880642 - \frac{\left(t + 457.9610022158428\right) + \frac{\left(-6976.8927133548 + t \cdot -15.234687407\right) + \left(a + 1112.0901850848957\right)}{z}}{z}}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<=
      (/
       (*
        y
        (+
         (* z (+ (* z (+ (* z (+ (* z 3.13060547623) 11.1667541262)) t)) a))
         b))
       (+
        (*
         z
         (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721))
        0.607771387771))
      INFINITY)
   (fma
    y
    (/
     (fma z (fma z (fma z (fma z 3.13060547623 11.1667541262) t) a) b)
     (fma
      z
      (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721)
      0.607771387771))
    x)
   (+
    x
    (-
     (* y 3.13060547623)
     (*
      y
      (/
       (-
        36.52704169880642
        (/
         (+
          (+ t 457.9610022158428)
          (/
           (+
            (+ -6976.8927133548 (* t -15.234687407))
            (+ a 1112.0901850848957))
           z))
         z))
       z))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)) <= ((double) INFINITY)) {
		tmp = fma(y, (fma(z, fma(z, fma(z, fma(z, 3.13060547623, 11.1667541262), t), a), b) / fma(z, fma(z, fma(z, (z + 15.234687407), 31.4690115749), 11.9400905721), 0.607771387771)), x);
	} else {
		tmp = x + ((y * 3.13060547623) - (y * ((36.52704169880642 - (((t + 457.9610022158428) + (((-6976.8927133548 + (t * -15.234687407)) + (a + 1112.0901850848957)) / z)) / z)) / z)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(Float64(y * Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)) <= Inf)
		tmp = fma(y, Float64(fma(z, fma(z, fma(z, fma(z, 3.13060547623, 11.1667541262), t), a), b) / fma(z, fma(z, fma(z, Float64(z + 15.234687407), 31.4690115749), 11.9400905721), 0.607771387771)), x);
	else
		tmp = Float64(x + Float64(Float64(y * 3.13060547623) - Float64(y * Float64(Float64(36.52704169880642 - Float64(Float64(Float64(t + 457.9610022158428) + Float64(Float64(Float64(-6976.8927133548 + Float64(t * -15.234687407)) + Float64(a + 1112.0901850848957)) / z)) / z)) / z))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(N[(y * N[(N[(z * N[(N[(z * N[(N[(z * N[(N[(z * 3.13060547623), $MachinePrecision] + 11.1667541262), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(N[(z * N[(N[(z * N[(N[(z * N[(z + 15.234687407), $MachinePrecision]), $MachinePrecision] + 31.4690115749), $MachinePrecision]), $MachinePrecision] + 11.9400905721), $MachinePrecision]), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision], Infinity], N[(y * N[(N[(z * N[(z * N[(z * N[(z * 3.13060547623 + 11.1667541262), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision] + b), $MachinePrecision] / N[(z * N[(z * N[(z * N[(z + 15.234687407), $MachinePrecision] + 31.4690115749), $MachinePrecision] + 11.9400905721), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(x + N[(N[(y * 3.13060547623), $MachinePrecision] - N[(y * N[(N[(36.52704169880642 - N[(N[(N[(t + 457.9610022158428), $MachinePrecision] + N[(N[(N[(-6976.8927133548 + N[(t * -15.234687407), $MachinePrecision]), $MachinePrecision] + N[(a + 1112.0901850848957), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 95.1%

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

   3. Simplified 98.5%

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

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

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in z around -inf 78.2%

      \[\leadsto \color{blue}{x + \left(-1 \cdot \frac{\left(-11.1667541262 \cdot y + -1 \cdot \frac{\left(-1 \cdot \frac{-1 \cdot \left(a \cdot y\right) - \left(-37.37971293169846 \cdot y + \left(-15.234687407 \cdot \left(t \cdot y - \left(-15.234687407 \cdot \left(-11.1667541262 \cdot y - -47.69379582500642 \cdot y\right) + 98.5170599679272 \cdot y\right)\right) + 31.4690115749 \cdot \left(-11.1667541262 \cdot y - -47.69379582500642 \cdot y\right)\right)\right)}{z} + t \cdot y\right) - \left(-15.234687407 \cdot \left(-11.1667541262 \cdot y - -47.69379582500642 \cdot y\right) + 98.5170599679272 \cdot y\right)}{z}\right) - -47.69379582500642 \cdot y}{z} + 3.13060547623 \cdot y\right)} \]

   6. Taylor expanded in y around 0 98.0%

      \[\leadsto x + \left(-1 \cdot \color{blue}{\frac{y \cdot \left(36.52704169880642 + -1 \cdot \frac{457.9610022158428 + \left(t + -1 \cdot \frac{-1 \cdot a - \left(1112.0901850848957 + -15.234687407 \cdot \left(457.9610022158428 + t\right)\right)}{z}\right)}{z}\right)}{z}} + 3.13060547623 \cdot y\right) \]

   8. Simplified 99.9%

      \[\leadsto x + \left(-1 \cdot \color{blue}{\left(y \cdot \frac{36.52704169880642 + \left(-\frac{\left(t + 457.9610022158428\right) + \left(-\frac{\left(\left(-a\right) - 1112.0901850848957\right) - \left(-6976.8927133548 + -15.234687407 \cdot t\right)}{z}\right)}{z}\right)}{z}\right)} + 3.13060547623 \cdot y\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771} \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right)}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 - y \cdot \frac{36.52704169880642 - \frac{\left(t + 457.9610022158428\right) + \frac{\left(-6976.8927133548 + t \cdot -15.234687407\right) + \left(a + 1112.0901850848957\right)}{z}}{z}}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 94.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right)\\ \mathbf{if}\;\frac{t\_1}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771} \leq 2 \cdot 10^{+268}:\\ \;\;\;\;x + \frac{t\_1}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z \cdot \left(\frac{15.234687407}{z} + 1\right)\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 - y \cdot \frac{36.52704169880642 - \frac{\left(t + 457.9610022158428\right) + \frac{\left(-6976.8927133548 + t \cdot -15.234687407\right) + \left(a + 1112.0901850848957\right)}{z}}{z}}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (*
          y
          (+
           (* z (+ (* z (+ (* z (+ (* z 3.13060547623) 11.1667541262)) t)) a))
           b))))
   (if (<=
        (/
         t_1
         (+
          (*
           z
           (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721))
          0.607771387771))
        2e+268)
     (+
      x
      (/
       t_1
       (+
        0.607771387771
        (*
         z
         (+
          11.9400905721
          (* z (+ 31.4690115749 (* z (* z (+ (/ 15.234687407 z) 1.0))))))))))
     (+
      x
      (-
       (* y 3.13060547623)
       (*
        y
        (/
         (-
          36.52704169880642
          (/
           (+
            (+ t 457.9610022158428)
            (/
             (+
              (+ -6976.8927133548 (* t -15.234687407))
              (+ a 1112.0901850848957))
             z))
           z))
         z)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b);
	double tmp;
	if ((t_1 / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)) <= 2e+268) {
		tmp = x + (t_1 / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * (z * ((15.234687407 / z) + 1.0)))))))));
	} else {
		tmp = x + ((y * 3.13060547623) - (y * ((36.52704169880642 - (((t + 457.9610022158428) + (((-6976.8927133548 + (t * -15.234687407)) + (a + 1112.0901850848957)) / z)) / z)) / z)));
	}
	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 = y * ((z * ((z * ((z * ((z * 3.13060547623d0) + 11.1667541262d0)) + t)) + a)) + b)
    if ((t_1 / ((z * ((z * ((z * (z + 15.234687407d0)) + 31.4690115749d0)) + 11.9400905721d0)) + 0.607771387771d0)) <= 2d+268) then
        tmp = x + (t_1 / (0.607771387771d0 + (z * (11.9400905721d0 + (z * (31.4690115749d0 + (z * (z * ((15.234687407d0 / z) + 1.0d0)))))))))
    else
        tmp = x + ((y * 3.13060547623d0) - (y * ((36.52704169880642d0 - (((t + 457.9610022158428d0) + ((((-6976.8927133548d0) + (t * (-15.234687407d0))) + (a + 1112.0901850848957d0)) / z)) / z)) / z)))
    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 = y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b);
	double tmp;
	if ((t_1 / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)) <= 2e+268) {
		tmp = x + (t_1 / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * (z * ((15.234687407 / z) + 1.0)))))))));
	} else {
		tmp = x + ((y * 3.13060547623) - (y * ((36.52704169880642 - (((t + 457.9610022158428) + (((-6976.8927133548 + (t * -15.234687407)) + (a + 1112.0901850848957)) / z)) / z)) / z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)
	tmp = 0
	if (t_1 / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)) <= 2e+268:
		tmp = x + (t_1 / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * (z * ((15.234687407 / z) + 1.0)))))))))
	else:
		tmp = x + ((y * 3.13060547623) - (y * ((36.52704169880642 - (((t + 457.9610022158428) + (((-6976.8927133548 + (t * -15.234687407)) + (a + 1112.0901850848957)) / z)) / z)) / z)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b))
	tmp = 0.0
	if (Float64(t_1 / Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)) <= 2e+268)
		tmp = Float64(x + Float64(t_1 / Float64(0.607771387771 + Float64(z * Float64(11.9400905721 + Float64(z * Float64(31.4690115749 + Float64(z * Float64(z * Float64(Float64(15.234687407 / z) + 1.0))))))))));
	else
		tmp = Float64(x + Float64(Float64(y * 3.13060547623) - Float64(y * Float64(Float64(36.52704169880642 - Float64(Float64(Float64(t + 457.9610022158428) + Float64(Float64(Float64(-6976.8927133548 + Float64(t * -15.234687407)) + Float64(a + 1112.0901850848957)) / z)) / z)) / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b);
	tmp = 0.0;
	if ((t_1 / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)) <= 2e+268)
		tmp = x + (t_1 / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * (z * ((15.234687407 / z) + 1.0)))))))));
	else
		tmp = x + ((y * 3.13060547623) - (y * ((36.52704169880642 - (((t + 457.9610022158428) + (((-6976.8927133548 + (t * -15.234687407)) + (a + 1112.0901850848957)) / z)) / z)) / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(N[(z * N[(N[(z * N[(N[(z * N[(N[(z * 3.13060547623), $MachinePrecision] + 11.1667541262), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$1 / N[(N[(z * N[(N[(z * N[(N[(z * N[(z + 15.234687407), $MachinePrecision]), $MachinePrecision] + 31.4690115749), $MachinePrecision]), $MachinePrecision] + 11.9400905721), $MachinePrecision]), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision], 2e+268], N[(x + N[(t$95$1 / N[(0.607771387771 + N[(z * N[(11.9400905721 + N[(z * N[(31.4690115749 + N[(z * N[(z * N[(N[(15.234687407 / z), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * 3.13060547623), $MachinePrecision] - N[(y * N[(N[(36.52704169880642 - N[(N[(N[(t + 457.9610022158428), $MachinePrecision] + N[(N[(N[(-6976.8927133548 + N[(t * -15.234687407), $MachinePrecision]), $MachinePrecision] + N[(a + 1112.0901850848957), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z #s(literal 313060547623/100000000000 binary64)) #s(literal 55833770631/5000000000 binary64)) z) t) z) a) z) b)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z #s(literal 15234687407/1000000000 binary64)) z) #s(literal 314690115749/10000000000 binary64)) z) #s(literal 119400905721/10000000000 binary64)) z) #s(literal 607771387771/1000000000000 binary64))) < 1.9999999999999999e268

   1. Initial program 98.4%

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

   3. Taylor expanded in z around inf 98.4%

      \[\leadsto x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\color{blue}{\left(z \cdot \left(1 + 15.234687407 \cdot \frac{1}{z}\right)\right)} \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   4. Step-by-step derivation

      1. associate-*r/ 98.4%

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

      2. metadata-eval 98.4%

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

   5. Simplified 98.4%

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

   if 1.9999999999999999e268 < (/.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 9.9%

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

   3. Simplified 13.8%

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

   5. Taylor expanded in z around -inf 74.7%

      \[\leadsto \color{blue}{x + \left(-1 \cdot \frac{\left(-11.1667541262 \cdot y + -1 \cdot \frac{\left(-1 \cdot \frac{-1 \cdot \left(a \cdot y\right) - \left(-37.37971293169846 \cdot y + \left(-15.234687407 \cdot \left(t \cdot y - \left(-15.234687407 \cdot \left(-11.1667541262 \cdot y - -47.69379582500642 \cdot y\right) + 98.5170599679272 \cdot y\right)\right) + 31.4690115749 \cdot \left(-11.1667541262 \cdot y - -47.69379582500642 \cdot y\right)\right)\right)}{z} + t \cdot y\right) - \left(-15.234687407 \cdot \left(-11.1667541262 \cdot y - -47.69379582500642 \cdot y\right) + 98.5170599679272 \cdot y\right)}{z}\right) - -47.69379582500642 \cdot y}{z} + 3.13060547623 \cdot y\right)} \]

   6. Taylor expanded in y around 0 94.2%

      \[\leadsto x + \left(-1 \cdot \color{blue}{\frac{y \cdot \left(36.52704169880642 + -1 \cdot \frac{457.9610022158428 + \left(t + -1 \cdot \frac{-1 \cdot a - \left(1112.0901850848957 + -15.234687407 \cdot \left(457.9610022158428 + t\right)\right)}{z}\right)}{z}\right)}{z}} + 3.13060547623 \cdot y\right) \]

   8. Simplified 96.7%

      \[\leadsto x + \left(-1 \cdot \color{blue}{\left(y \cdot \frac{36.52704169880642 + \left(-\frac{\left(t + 457.9610022158428\right) + \left(-\frac{\left(\left(-a\right) - 1112.0901850848957\right) - \left(-6976.8927133548 + -15.234687407 \cdot t\right)}{z}\right)}{z}\right)}{z}\right)} + 3.13060547623 \cdot y\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 97.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771} \leq 2 \cdot 10^{+268}:\\ \;\;\;\;x + \frac{y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z \cdot \left(\frac{15.234687407}{z} + 1\right)\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 - y \cdot \frac{36.52704169880642 - \frac{\left(t + 457.9610022158428\right) + \frac{\left(-6976.8927133548 + t \cdot -15.234687407\right) + \left(a + 1112.0901850848957\right)}{z}}{z}}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 97.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+23} \lor \neg \left(z \leq 1.02 \cdot 10^{+24}\right):\\ \;\;\;\;x + \left(y \cdot 3.13060547623 + y \cdot \frac{\frac{t + 457.9610022158428}{z} - 36.52704169880642}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot t\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z \cdot \left(\frac{15.234687407}{z} + 1\right)\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.2e+23) (not (<= z 1.02e+24)))
   (+
    x
    (+
     (* y 3.13060547623)
     (* y (/ (- (/ (+ t 457.9610022158428) z) 36.52704169880642) z))))
   (+
    x
    (/
     (* y (+ b (* z (+ a (* z t)))))
     (+
      0.607771387771
      (*
       z
       (+
        11.9400905721
        (* z (+ 31.4690115749 (* z (* z (+ (/ 15.234687407 z) 1.0))))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.2e+23) || !(z <= 1.02e+24)) {
		tmp = x + ((y * 3.13060547623) + (y * ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)));
	} else {
		tmp = x + ((y * (b + (z * (a + (z * t))))) / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * (z * ((15.234687407 / z) + 1.0)))))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-1.2d+23)) .or. (.not. (z <= 1.02d+24))) then
        tmp = x + ((y * 3.13060547623d0) + (y * ((((t + 457.9610022158428d0) / z) - 36.52704169880642d0) / z)))
    else
        tmp = x + ((y * (b + (z * (a + (z * t))))) / (0.607771387771d0 + (z * (11.9400905721d0 + (z * (31.4690115749d0 + (z * (z * ((15.234687407d0 / z) + 1.0d0)))))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.2e+23) || !(z <= 1.02e+24)) {
		tmp = x + ((y * 3.13060547623) + (y * ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)));
	} else {
		tmp = x + ((y * (b + (z * (a + (z * t))))) / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * (z * ((15.234687407 / z) + 1.0)))))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.2e+23) or not (z <= 1.02e+24):
		tmp = x + ((y * 3.13060547623) + (y * ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)))
	else:
		tmp = x + ((y * (b + (z * (a + (z * t))))) / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * (z * ((15.234687407 / z) + 1.0)))))))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.2e+23) || !(z <= 1.02e+24))
		tmp = Float64(x + Float64(Float64(y * 3.13060547623) + Float64(y * Float64(Float64(Float64(Float64(t + 457.9610022158428) / z) - 36.52704169880642) / z))));
	else
		tmp = Float64(x + Float64(Float64(y * Float64(b + Float64(z * Float64(a + Float64(z * t))))) / Float64(0.607771387771 + Float64(z * Float64(11.9400905721 + Float64(z * Float64(31.4690115749 + Float64(z * Float64(z * Float64(Float64(15.234687407 / z) + 1.0))))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.2e+23) || ~((z <= 1.02e+24)))
		tmp = x + ((y * 3.13060547623) + (y * ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)));
	else
		tmp = x + ((y * (b + (z * (a + (z * t))))) / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * (z * ((15.234687407 / z) + 1.0)))))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.2e+23], N[Not[LessEqual[z, 1.02e+24]], $MachinePrecision]], N[(x + N[(N[(y * 3.13060547623), $MachinePrecision] + N[(y * N[(N[(N[(N[(t + 457.9610022158428), $MachinePrecision] / z), $MachinePrecision] - 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * N[(b + N[(z * N[(a + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(0.607771387771 + N[(z * N[(11.9400905721 + N[(z * N[(31.4690115749 + N[(z * N[(z * N[(N[(15.234687407 / z), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.2e23 or 1.02000000000000004e24 < z

   1. Initial program 9.1%

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

   3. Simplified 11.5%

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

   5. Taylor expanded in z around -inf 85.4%

      \[\leadsto \color{blue}{x + \left(-1 \cdot \frac{\left(-11.1667541262 \cdot y + -1 \cdot \frac{t \cdot y - \left(-15.234687407 \cdot \left(-11.1667541262 \cdot y - -47.69379582500642 \cdot y\right) + 98.5170599679272 \cdot y\right)}{z}\right) - -47.69379582500642 \cdot y}{z} + 3.13060547623 \cdot y\right)} \]

   6. Taylor expanded in y around 0 95.9%

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

      1. associate-/l* 98.4%

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

      2. mul-1-neg 98.4%

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

      3. unsub-neg 98.4%

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

      4. +-commutative 98.4%

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

   8. Simplified 98.4%

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

   if -1.2e23 < z < 1.02000000000000004e24

   1. Initial program 97.8%

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

   3. Taylor expanded in z around inf 97.8%

      \[\leadsto x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\color{blue}{\left(z \cdot \left(1 + 15.234687407 \cdot \frac{1}{z}\right)\right)} \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   4. Step-by-step derivation

      1. associate-*r/ 97.8%

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

      2. metadata-eval 97.8%

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

   5. Simplified 97.8%

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

   6. Taylor expanded in z around 0 90.4%

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

   7. Taylor expanded in y around 0 97.8%

      \[\leadsto x + \frac{\color{blue}{y \cdot \left(b + z \cdot \left(a + t \cdot z\right)\right)}}{\left(\left(\left(z \cdot \left(1 + \frac{15.234687407}{z}\right)\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   8. Step-by-step derivation

      1. *-commutative 97.8%

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

   9. Simplified 97.8%

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

4. Final simplification 98.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+23} \lor \neg \left(z \leq 1.02 \cdot 10^{+24}\right):\\ \;\;\;\;x + \left(y \cdot 3.13060547623 + y \cdot \frac{\frac{t + 457.9610022158428}{z} - 36.52704169880642}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot t\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z \cdot \left(\frac{15.234687407}{z} + 1\right)\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 97.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+18}:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 - y \cdot \frac{36.52704169880642 - \frac{\left(t + 457.9610022158428\right) + \frac{\left(-6976.8927133548 + t \cdot -15.234687407\right) + \left(a + 1112.0901850848957\right)}{z}}{z}}{z}\right)\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+24}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot t\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z \cdot \left(\frac{15.234687407}{z} + 1\right)\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 + y \cdot \frac{\frac{t + 457.9610022158428}{z} - 36.52704169880642}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -3.3e+18)
   (+
    x
    (-
     (* y 3.13060547623)
     (*
      y
      (/
       (-
        36.52704169880642
        (/
         (+
          (+ t 457.9610022158428)
          (/
           (+
            (+ -6976.8927133548 (* t -15.234687407))
            (+ a 1112.0901850848957))
           z))
         z))
       z))))
   (if (<= z 1.1e+24)
     (+
      x
      (/
       (* y (+ b (* z (+ a (* z t)))))
       (+
        0.607771387771
        (*
         z
         (+
          11.9400905721
          (* z (+ 31.4690115749 (* z (* z (+ (/ 15.234687407 z) 1.0))))))))))
     (+
      x
      (+
       (* y 3.13060547623)
       (* y (/ (- (/ (+ t 457.9610022158428) z) 36.52704169880642) z)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -3.3e+18) {
		tmp = x + ((y * 3.13060547623) - (y * ((36.52704169880642 - (((t + 457.9610022158428) + (((-6976.8927133548 + (t * -15.234687407)) + (a + 1112.0901850848957)) / z)) / z)) / z)));
	} else if (z <= 1.1e+24) {
		tmp = x + ((y * (b + (z * (a + (z * t))))) / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * (z * ((15.234687407 / z) + 1.0)))))))));
	} else {
		tmp = x + ((y * 3.13060547623) + (y * ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-3.3d+18)) then
        tmp = x + ((y * 3.13060547623d0) - (y * ((36.52704169880642d0 - (((t + 457.9610022158428d0) + ((((-6976.8927133548d0) + (t * (-15.234687407d0))) + (a + 1112.0901850848957d0)) / z)) / z)) / z)))
    else if (z <= 1.1d+24) then
        tmp = x + ((y * (b + (z * (a + (z * t))))) / (0.607771387771d0 + (z * (11.9400905721d0 + (z * (31.4690115749d0 + (z * (z * ((15.234687407d0 / z) + 1.0d0)))))))))
    else
        tmp = x + ((y * 3.13060547623d0) + (y * ((((t + 457.9610022158428d0) / z) - 36.52704169880642d0) / z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -3.3e+18) {
		tmp = x + ((y * 3.13060547623) - (y * ((36.52704169880642 - (((t + 457.9610022158428) + (((-6976.8927133548 + (t * -15.234687407)) + (a + 1112.0901850848957)) / z)) / z)) / z)));
	} else if (z <= 1.1e+24) {
		tmp = x + ((y * (b + (z * (a + (z * t))))) / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * (z * ((15.234687407 / z) + 1.0)))))))));
	} else {
		tmp = x + ((y * 3.13060547623) + (y * ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -3.3e+18:
		tmp = x + ((y * 3.13060547623) - (y * ((36.52704169880642 - (((t + 457.9610022158428) + (((-6976.8927133548 + (t * -15.234687407)) + (a + 1112.0901850848957)) / z)) / z)) / z)))
	elif z <= 1.1e+24:
		tmp = x + ((y * (b + (z * (a + (z * t))))) / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * (z * ((15.234687407 / z) + 1.0)))))))))
	else:
		tmp = x + ((y * 3.13060547623) + (y * ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -3.3e+18)
		tmp = Float64(x + Float64(Float64(y * 3.13060547623) - Float64(y * Float64(Float64(36.52704169880642 - Float64(Float64(Float64(t + 457.9610022158428) + Float64(Float64(Float64(-6976.8927133548 + Float64(t * -15.234687407)) + Float64(a + 1112.0901850848957)) / z)) / z)) / z))));
	elseif (z <= 1.1e+24)
		tmp = Float64(x + Float64(Float64(y * Float64(b + Float64(z * Float64(a + Float64(z * t))))) / Float64(0.607771387771 + Float64(z * Float64(11.9400905721 + Float64(z * Float64(31.4690115749 + Float64(z * Float64(z * Float64(Float64(15.234687407 / z) + 1.0))))))))));
	else
		tmp = Float64(x + Float64(Float64(y * 3.13060547623) + Float64(y * Float64(Float64(Float64(Float64(t + 457.9610022158428) / z) - 36.52704169880642) / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -3.3e+18)
		tmp = x + ((y * 3.13060547623) - (y * ((36.52704169880642 - (((t + 457.9610022158428) + (((-6976.8927133548 + (t * -15.234687407)) + (a + 1112.0901850848957)) / z)) / z)) / z)));
	elseif (z <= 1.1e+24)
		tmp = x + ((y * (b + (z * (a + (z * t))))) / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * (z * ((15.234687407 / z) + 1.0)))))))));
	else
		tmp = x + ((y * 3.13060547623) + (y * ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -3.3e+18], N[(x + N[(N[(y * 3.13060547623), $MachinePrecision] - N[(y * N[(N[(36.52704169880642 - N[(N[(N[(t + 457.9610022158428), $MachinePrecision] + N[(N[(N[(-6976.8927133548 + N[(t * -15.234687407), $MachinePrecision]), $MachinePrecision] + N[(a + 1112.0901850848957), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.1e+24], N[(x + N[(N[(y * N[(b + N[(z * N[(a + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(0.607771387771 + N[(z * N[(11.9400905721 + N[(z * N[(31.4690115749 + N[(z * N[(z * N[(N[(15.234687407 / z), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * 3.13060547623), $MachinePrecision] + N[(y * N[(N[(N[(N[(t + 457.9610022158428), $MachinePrecision] / z), $MachinePrecision] - 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.3e18

   1. Initial program 12.4%

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

   3. Simplified 18.5%

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

   5. Taylor expanded in z around -inf 84.0%

      \[\leadsto \color{blue}{x + \left(-1 \cdot \frac{\left(-11.1667541262 \cdot y + -1 \cdot \frac{\left(-1 \cdot \frac{-1 \cdot \left(a \cdot y\right) - \left(-37.37971293169846 \cdot y + \left(-15.234687407 \cdot \left(t \cdot y - \left(-15.234687407 \cdot \left(-11.1667541262 \cdot y - -47.69379582500642 \cdot y\right) + 98.5170599679272 \cdot y\right)\right) + 31.4690115749 \cdot \left(-11.1667541262 \cdot y - -47.69379582500642 \cdot y\right)\right)\right)}{z} + t \cdot y\right) - \left(-15.234687407 \cdot \left(-11.1667541262 \cdot y - -47.69379582500642 \cdot y\right) + 98.5170599679272 \cdot y\right)}{z}\right) - -47.69379582500642 \cdot y}{z} + 3.13060547623 \cdot y\right)} \]

   6. Taylor expanded in y around 0 96.9%

      \[\leadsto x + \left(-1 \cdot \color{blue}{\frac{y \cdot \left(36.52704169880642 + -1 \cdot \frac{457.9610022158428 + \left(t + -1 \cdot \frac{-1 \cdot a - \left(1112.0901850848957 + -15.234687407 \cdot \left(457.9610022158428 + t\right)\right)}{z}\right)}{z}\right)}{z}} + 3.13060547623 \cdot y\right) \]

   8. Simplified 98.7%

      \[\leadsto x + \left(-1 \cdot \color{blue}{\left(y \cdot \frac{36.52704169880642 + \left(-\frac{\left(t + 457.9610022158428\right) + \left(-\frac{\left(\left(-a\right) - 1112.0901850848957\right) - \left(-6976.8927133548 + -15.234687407 \cdot t\right)}{z}\right)}{z}\right)}{z}\right)} + 3.13060547623 \cdot y\right) \]

   if -3.3e18 < z < 1.10000000000000001e24

   1. Initial program 99.1%

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

   3. Taylor expanded in z around inf 99.1%

      \[\leadsto x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\color{blue}{\left(z \cdot \left(1 + 15.234687407 \cdot \frac{1}{z}\right)\right)} \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   4. Step-by-step derivation

      1. associate-*r/ 99.1%

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

      2. metadata-eval 99.1%

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

   5. Simplified 99.1%

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

   6. Taylor expanded in z around 0 91.5%

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

   7. Taylor expanded in y around 0 99.1%

      \[\leadsto x + \frac{\color{blue}{y \cdot \left(b + z \cdot \left(a + t \cdot z\right)\right)}}{\left(\left(\left(z \cdot \left(1 + \frac{15.234687407}{z}\right)\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   8. Step-by-step derivation

      1. *-commutative 99.1%

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

   9. Simplified 99.1%

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

   if 1.10000000000000001e24 < z

   1. Initial program 8.8%

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

   3. Simplified 10.3%

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

   5. Taylor expanded in z around -inf 82.9%

      \[\leadsto \color{blue}{x + \left(-1 \cdot \frac{\left(-11.1667541262 \cdot y + -1 \cdot \frac{t \cdot y - \left(-15.234687407 \cdot \left(-11.1667541262 \cdot y - -47.69379582500642 \cdot y\right) + 98.5170599679272 \cdot y\right)}{z}\right) - -47.69379582500642 \cdot y}{z} + 3.13060547623 \cdot y\right)} \]

   6. Taylor expanded in y around 0 96.6%

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

      1. associate-/l* 99.9%

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

      2. mul-1-neg 99.9%

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

      3. unsub-neg 99.9%

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

      4. +-commutative 99.9%

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

   8. Simplified 99.9%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+18}:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 - y \cdot \frac{36.52704169880642 - \frac{\left(t + 457.9610022158428\right) + \frac{\left(-6976.8927133548 + t \cdot -15.234687407\right) + \left(a + 1112.0901850848957\right)}{z}}{z}}{z}\right)\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+24}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot t\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z \cdot \left(\frac{15.234687407}{z} + 1\right)\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 + y \cdot \frac{\frac{t + 457.9610022158428}{z} - 36.52704169880642}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 93.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.12 \cdot 10^{+23} \lor \neg \left(z \leq 1.05 \cdot 10^{+24}\right):\\ \;\;\;\;x + \left(y \cdot 3.13060547623 + y \cdot \frac{\frac{t + 457.9610022158428}{z} - 36.52704169880642}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot a\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.12e+23) (not (<= z 1.05e+24)))
   (+
    x
    (+
     (* y 3.13060547623)
     (* y (/ (- (/ (+ t 457.9610022158428) z) 36.52704169880642) z))))
   (+
    x
    (/
     (* y (+ b (* z a)))
     (+
      (* z (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721))
      0.607771387771)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.12e+23) || !(z <= 1.05e+24)) {
		tmp = x + ((y * 3.13060547623) + (y * ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)));
	} else {
		tmp = x + ((y * (b + (z * a))) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-1.12d+23)) .or. (.not. (z <= 1.05d+24))) then
        tmp = x + ((y * 3.13060547623d0) + (y * ((((t + 457.9610022158428d0) / z) - 36.52704169880642d0) / z)))
    else
        tmp = x + ((y * (b + (z * a))) / ((z * ((z * ((z * (z + 15.234687407d0)) + 31.4690115749d0)) + 11.9400905721d0)) + 0.607771387771d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.12e+23) || !(z <= 1.05e+24)) {
		tmp = x + ((y * 3.13060547623) + (y * ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)));
	} else {
		tmp = x + ((y * (b + (z * a))) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.12e+23) or not (z <= 1.05e+24):
		tmp = x + ((y * 3.13060547623) + (y * ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)))
	else:
		tmp = x + ((y * (b + (z * a))) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.12e+23) || !(z <= 1.05e+24))
		tmp = Float64(x + Float64(Float64(y * 3.13060547623) + Float64(y * Float64(Float64(Float64(Float64(t + 457.9610022158428) / z) - 36.52704169880642) / z))));
	else
		tmp = Float64(x + Float64(Float64(y * Float64(b + Float64(z * a))) / Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.12e+23) || ~((z <= 1.05e+24)))
		tmp = x + ((y * 3.13060547623) + (y * ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)));
	else
		tmp = x + ((y * (b + (z * a))) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.12e+23], N[Not[LessEqual[z, 1.05e+24]], $MachinePrecision]], N[(x + N[(N[(y * 3.13060547623), $MachinePrecision] + N[(y * N[(N[(N[(N[(t + 457.9610022158428), $MachinePrecision] / z), $MachinePrecision] - 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * N[(b + N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(z * N[(N[(z * N[(N[(z * N[(z + 15.234687407), $MachinePrecision]), $MachinePrecision] + 31.4690115749), $MachinePrecision]), $MachinePrecision] + 11.9400905721), $MachinePrecision]), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.12e23 or 1.0500000000000001e24 < z

   1. Initial program 9.1%

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

   3. Simplified 11.5%

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

   5. Taylor expanded in z around -inf 85.4%

      \[\leadsto \color{blue}{x + \left(-1 \cdot \frac{\left(-11.1667541262 \cdot y + -1 \cdot \frac{t \cdot y - \left(-15.234687407 \cdot \left(-11.1667541262 \cdot y - -47.69379582500642 \cdot y\right) + 98.5170599679272 \cdot y\right)}{z}\right) - -47.69379582500642 \cdot y}{z} + 3.13060547623 \cdot y\right)} \]

   6. Taylor expanded in y around 0 95.9%

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

      1. associate-/l* 98.4%

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

      2. mul-1-neg 98.4%

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

      3. unsub-neg 98.4%

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

      4. +-commutative 98.4%

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

   8. Simplified 98.4%

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

   if -1.12e23 < z < 1.0500000000000001e24

   1. Initial program 97.8%

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

   3. Taylor expanded in z around 0 91.0%

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

   4. Taylor expanded in y around 0 91.7%

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

      1. +-commutative 91.7%

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

      2. *-commutative 91.7%

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

   6. Simplified 91.7%

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

4. Final simplification 94.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.12 \cdot 10^{+23} \lor \neg \left(z \leq 1.05 \cdot 10^{+24}\right):\\ \;\;\;\;x + \left(y \cdot 3.13060547623 + y \cdot \frac{\frac{t + 457.9610022158428}{z} - 36.52704169880642}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot a\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 93.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+19} \lor \neg \left(z \leq 0.55\right):\\ \;\;\;\;x + \left(y \cdot 3.13060547623 + y \cdot \frac{\frac{t + 457.9610022158428}{z} - 36.52704169880642}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot a\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot 31.4690115749\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2.3e+19) (not (<= z 0.55)))
   (+
    x
    (+
     (* y 3.13060547623)
     (* y (/ (- (/ (+ t 457.9610022158428) z) 36.52704169880642) z))))
   (+
    x
    (/
     (* y (+ b (* z a)))
     (+ 0.607771387771 (* z (+ 11.9400905721 (* z 31.4690115749))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.3e+19) || !(z <= 0.55)) {
		tmp = x + ((y * 3.13060547623) + (y * ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)));
	} else {
		tmp = x + ((y * (b + (z * a))) / (0.607771387771 + (z * (11.9400905721 + (z * 31.4690115749)))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-2.3d+19)) .or. (.not. (z <= 0.55d0))) then
        tmp = x + ((y * 3.13060547623d0) + (y * ((((t + 457.9610022158428d0) / z) - 36.52704169880642d0) / z)))
    else
        tmp = x + ((y * (b + (z * a))) / (0.607771387771d0 + (z * (11.9400905721d0 + (z * 31.4690115749d0)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.3e+19) || !(z <= 0.55)) {
		tmp = x + ((y * 3.13060547623) + (y * ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)));
	} else {
		tmp = x + ((y * (b + (z * a))) / (0.607771387771 + (z * (11.9400905721 + (z * 31.4690115749)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -2.3e+19) or not (z <= 0.55):
		tmp = x + ((y * 3.13060547623) + (y * ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)))
	else:
		tmp = x + ((y * (b + (z * a))) / (0.607771387771 + (z * (11.9400905721 + (z * 31.4690115749)))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2.3e+19) || !(z <= 0.55))
		tmp = Float64(x + Float64(Float64(y * 3.13060547623) + Float64(y * Float64(Float64(Float64(Float64(t + 457.9610022158428) / z) - 36.52704169880642) / z))));
	else
		tmp = Float64(x + Float64(Float64(y * Float64(b + Float64(z * a))) / Float64(0.607771387771 + Float64(z * Float64(11.9400905721 + Float64(z * 31.4690115749))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -2.3e+19) || ~((z <= 0.55)))
		tmp = x + ((y * 3.13060547623) + (y * ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)));
	else
		tmp = x + ((y * (b + (z * a))) / (0.607771387771 + (z * (11.9400905721 + (z * 31.4690115749)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2.3e+19], N[Not[LessEqual[z, 0.55]], $MachinePrecision]], N[(x + N[(N[(y * 3.13060547623), $MachinePrecision] + N[(y * N[(N[(N[(N[(t + 457.9610022158428), $MachinePrecision] / z), $MachinePrecision] - 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * N[(b + N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(0.607771387771 + N[(z * N[(11.9400905721 + N[(z * 31.4690115749), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.3e19 or 0.55000000000000004 < z

   1. Initial program 12.2%

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

   3. Simplified 15.9%

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

   5. Taylor expanded in z around -inf 82.8%

      \[\leadsto \color{blue}{x + \left(-1 \cdot \frac{\left(-11.1667541262 \cdot y + -1 \cdot \frac{t \cdot y - \left(-15.234687407 \cdot \left(-11.1667541262 \cdot y - -47.69379582500642 \cdot y\right) + 98.5170599679272 \cdot y\right)}{z}\right) - -47.69379582500642 \cdot y}{z} + 3.13060547623 \cdot y\right)} \]

   6. Taylor expanded in y around 0 92.7%

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

      1. associate-/l* 95.2%

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

      2. mul-1-neg 95.2%

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

      3. unsub-neg 95.2%

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

      4. +-commutative 95.2%

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

   8. Simplified 95.2%

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

   if -2.3e19 < z < 0.55000000000000004

   1. Initial program 99.0%

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

   3. Taylor expanded in z around 0 92.7%

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

   4. Taylor expanded in y around 0 93.4%

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

      1. +-commutative 93.4%

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

      2. *-commutative 93.4%

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

   6. Simplified 93.4%

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

   7. Taylor expanded in z around 0 92.2%

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

      1. *-commutative 92.2%

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

   9. Simplified 92.2%

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

4. Final simplification 93.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+19} \lor \neg \left(z \leq 0.55\right):\\ \;\;\;\;x + \left(y \cdot 3.13060547623 + y \cdot \frac{\frac{t + 457.9610022158428}{z} - 36.52704169880642}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot a\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot 31.4690115749\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 86.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+18} \lor \neg \left(z \leq 10^{+24}\right):\\ \;\;\;\;x + \left(y \cdot 3.13060547623 + y \cdot \frac{\frac{t + 457.9610022158428}{z} - 36.52704169880642}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -3.3e+18) (not (<= z 1e+24)))
   (+
    x
    (+
     (* y 3.13060547623)
     (* y (/ (- (/ (+ t 457.9610022158428) z) 36.52704169880642) z))))
   (+ x (* y (* b 1.6453555072203998)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3.3e+18) || !(z <= 1e+24)) {
		tmp = x + ((y * 3.13060547623) + (y * ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)));
	} else {
		tmp = x + (y * (b * 1.6453555072203998));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-3.3d+18)) .or. (.not. (z <= 1d+24))) then
        tmp = x + ((y * 3.13060547623d0) + (y * ((((t + 457.9610022158428d0) / z) - 36.52704169880642d0) / z)))
    else
        tmp = x + (y * (b * 1.6453555072203998d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3.3e+18) || !(z <= 1e+24)) {
		tmp = x + ((y * 3.13060547623) + (y * ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)));
	} else {
		tmp = x + (y * (b * 1.6453555072203998));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -3.3e+18) or not (z <= 1e+24):
		tmp = x + ((y * 3.13060547623) + (y * ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)))
	else:
		tmp = x + (y * (b * 1.6453555072203998))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -3.3e+18) || !(z <= 1e+24))
		tmp = Float64(x + Float64(Float64(y * 3.13060547623) + Float64(y * Float64(Float64(Float64(Float64(t + 457.9610022158428) / z) - 36.52704169880642) / z))));
	else
		tmp = Float64(x + Float64(y * Float64(b * 1.6453555072203998)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -3.3e+18) || ~((z <= 1e+24)))
		tmp = x + ((y * 3.13060547623) + (y * ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)));
	else
		tmp = x + (y * (b * 1.6453555072203998));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -3.3e+18], N[Not[LessEqual[z, 1e+24]], $MachinePrecision]], N[(x + N[(N[(y * 3.13060547623), $MachinePrecision] + N[(y * N[(N[(N[(N[(t + 457.9610022158428), $MachinePrecision] / z), $MachinePrecision] - 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(b * 1.6453555072203998), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.3e18 or 9.9999999999999998e23 < z

   1. Initial program 10.6%

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

   3. Simplified 14.5%

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

   5. Taylor expanded in z around -inf 83.5%

      \[\leadsto \color{blue}{x + \left(-1 \cdot \frac{\left(-11.1667541262 \cdot y + -1 \cdot \frac{t \cdot y - \left(-15.234687407 \cdot \left(-11.1667541262 \cdot y - -47.69379582500642 \cdot y\right) + 98.5170599679272 \cdot y\right)}{z}\right) - -47.69379582500642 \cdot y}{z} + 3.13060547623 \cdot y\right)} \]

   6. Taylor expanded in y around 0 93.6%

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

      1. associate-/l* 96.1%

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

      2. mul-1-neg 96.1%

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

      3. unsub-neg 96.1%

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

      4. +-commutative 96.1%

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

   8. Simplified 96.1%

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

   if -3.3e18 < z < 9.9999999999999998e23

   1. Initial program 99.1%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around 0 80.0%

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

      1. associate-*r* 80.0%

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

      2. *-commutative 80.0%

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

   7. Simplified 80.0%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+18} \lor \neg \left(z \leq 10^{+24}\right):\\ \;\;\;\;x + \left(y \cdot 3.13060547623 + y \cdot \frac{\frac{t + 457.9610022158428}{z} - 36.52704169880642}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 85.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+18} \lor \neg \left(z \leq 10^{+24}\right):\\ \;\;\;\;x + \left(y \cdot 3.13060547623 + \frac{y \cdot \left(\frac{t}{z} - 36.52704169880642\right)}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -3.4e+18) (not (<= z 1e+24)))
   (+ x (+ (* y 3.13060547623) (/ (* y (- (/ t z) 36.52704169880642)) z)))
   (+ x (* y (* b 1.6453555072203998)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3.4e+18) || !(z <= 1e+24)) {
		tmp = x + ((y * 3.13060547623) + ((y * ((t / z) - 36.52704169880642)) / z));
	} else {
		tmp = x + (y * (b * 1.6453555072203998));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-3.4d+18)) .or. (.not. (z <= 1d+24))) then
        tmp = x + ((y * 3.13060547623d0) + ((y * ((t / z) - 36.52704169880642d0)) / z))
    else
        tmp = x + (y * (b * 1.6453555072203998d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3.4e+18) || !(z <= 1e+24)) {
		tmp = x + ((y * 3.13060547623) + ((y * ((t / z) - 36.52704169880642)) / z));
	} else {
		tmp = x + (y * (b * 1.6453555072203998));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -3.4e+18) or not (z <= 1e+24):
		tmp = x + ((y * 3.13060547623) + ((y * ((t / z) - 36.52704169880642)) / z))
	else:
		tmp = x + (y * (b * 1.6453555072203998))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -3.4e+18) || !(z <= 1e+24))
		tmp = Float64(x + Float64(Float64(y * 3.13060547623) + Float64(Float64(y * Float64(Float64(t / z) - 36.52704169880642)) / z)));
	else
		tmp = Float64(x + Float64(y * Float64(b * 1.6453555072203998)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -3.4e+18) || ~((z <= 1e+24)))
		tmp = x + ((y * 3.13060547623) + ((y * ((t / z) - 36.52704169880642)) / z));
	else
		tmp = x + (y * (b * 1.6453555072203998));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -3.4e+18], N[Not[LessEqual[z, 1e+24]], $MachinePrecision]], N[(x + N[(N[(y * 3.13060547623), $MachinePrecision] + N[(N[(y * N[(N[(t / z), $MachinePrecision] - 36.52704169880642), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(b * 1.6453555072203998), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.4e18 or 9.9999999999999998e23 < z

   1. Initial program 10.6%

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

   3. Simplified 14.5%

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

   5. Taylor expanded in z around -inf 83.5%

      \[\leadsto \color{blue}{x + \left(-1 \cdot \frac{\left(-11.1667541262 \cdot y + -1 \cdot \frac{t \cdot y - \left(-15.234687407 \cdot \left(-11.1667541262 \cdot y - -47.69379582500642 \cdot y\right) + 98.5170599679272 \cdot y\right)}{z}\right) - -47.69379582500642 \cdot y}{z} + 3.13060547623 \cdot y\right)} \]

   6. Taylor expanded in t around inf 83.5%

      \[\leadsto x + \left(-1 \cdot \frac{\left(-11.1667541262 \cdot y + \color{blue}{-1 \cdot \frac{t \cdot y}{z}}\right) - -47.69379582500642 \cdot y}{z} + 3.13060547623 \cdot y\right) \]
   7. Step-by-step derivation

      1. associate-*r/ 83.5%

         \[\leadsto x + \left(-1 \cdot \frac{\left(-11.1667541262 \cdot y + \color{blue}{\frac{-1 \cdot \left(t \cdot y\right)}{z}}\right) - -47.69379582500642 \cdot y}{z} + 3.13060547623 \cdot y\right) \]

      2. *-commutative 83.5%

         \[\leadsto x + \left(-1 \cdot \frac{\left(-11.1667541262 \cdot y + \frac{-1 \cdot \color{blue}{\left(y \cdot t\right)}}{z}\right) - -47.69379582500642 \cdot y}{z} + 3.13060547623 \cdot y\right) \]

      3. neg-mul-1 83.5%

         \[\leadsto x + \left(-1 \cdot \frac{\left(-11.1667541262 \cdot y + \frac{\color{blue}{-y \cdot t}}{z}\right) - -47.69379582500642 \cdot y}{z} + 3.13060547623 \cdot y\right) \]

   8. Simplified 83.5%

      \[\leadsto x + \left(-1 \cdot \frac{\left(-11.1667541262 \cdot y + \color{blue}{\frac{-y \cdot t}{z}}\right) - -47.69379582500642 \cdot y}{z} + 3.13060547623 \cdot y\right) \]

   9. Taylor expanded in y around -inf 93.6%

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

   if -3.4e18 < z < 9.9999999999999998e23

   1. Initial program 99.1%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around 0 80.0%

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

      1. associate-*r* 80.0%

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

      2. *-commutative 80.0%

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

   7. Simplified 80.0%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+18} \lor \neg \left(z \leq 10^{+24}\right):\\ \;\;\;\;x + \left(y \cdot 3.13060547623 + \frac{y \cdot \left(\frac{t}{z} - 36.52704169880642\right)}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 63.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot 3.13060547623\\ \mathbf{if}\;z \leq -7.4 \cdot 10^{-140}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-219}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-44}:\\ \;\;\;\;\frac{y \cdot b}{0.607771387771}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* y 3.13060547623))))
   (if (<= z -7.4e-140)
     t_1
     (if (<= z 1.35e-219)
       x
       (if (<= z 1.9e-44) (/ (* y b) 0.607771387771) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * 3.13060547623);
	double tmp;
	if (z <= -7.4e-140) {
		tmp = t_1;
	} else if (z <= 1.35e-219) {
		tmp = x;
	} else if (z <= 1.9e-44) {
		tmp = (y * b) / 0.607771387771;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * 3.13060547623d0)
    if (z <= (-7.4d-140)) then
        tmp = t_1
    else if (z <= 1.35d-219) then
        tmp = x
    else if (z <= 1.9d-44) then
        tmp = (y * b) / 0.607771387771d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * 3.13060547623);
	double tmp;
	if (z <= -7.4e-140) {
		tmp = t_1;
	} else if (z <= 1.35e-219) {
		tmp = x;
	} else if (z <= 1.9e-44) {
		tmp = (y * b) / 0.607771387771;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y * 3.13060547623)
	tmp = 0
	if z <= -7.4e-140:
		tmp = t_1
	elif z <= 1.35e-219:
		tmp = x
	elif z <= 1.9e-44:
		tmp = (y * b) / 0.607771387771
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y * 3.13060547623))
	tmp = 0.0
	if (z <= -7.4e-140)
		tmp = t_1;
	elseif (z <= 1.35e-219)
		tmp = x;
	elseif (z <= 1.9e-44)
		tmp = Float64(Float64(y * b) / 0.607771387771);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (y * 3.13060547623);
	tmp = 0.0;
	if (z <= -7.4e-140)
		tmp = t_1;
	elseif (z <= 1.35e-219)
		tmp = x;
	elseif (z <= 1.9e-44)
		tmp = (y * b) / 0.607771387771;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.4e-140], t$95$1, If[LessEqual[z, 1.35e-219], x, If[LessEqual[z, 1.9e-44], N[(N[(y * b), $MachinePrecision] / 0.607771387771), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.39999999999999955e-140 or 1.9e-44 < z

   1. Initial program 36.9%

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

   3. Simplified 40.2%

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

   5. Taylor expanded in z around inf 74.9%

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

   if -7.39999999999999955e-140 < z < 1.35e-219

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 58.5%

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

   if 1.35e-219 < z < 1.9e-44

   1. Initial program 99.8%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in b around inf 56.0%

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

   6. Taylor expanded in z around 0 56.0%

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

      1. *-commutative 56.0%

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

   8. Simplified 56.0%

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

   9. Taylor expanded in z around 0 56.0%

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

4. Final simplification 69.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.4 \cdot 10^{-140}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-219}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-44}:\\ \;\;\;\;\frac{y \cdot b}{0.607771387771}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 63.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot 3.13060547623\\ \mathbf{if}\;z \leq -6.5 \cdot 10^{-143}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-219}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{-45}:\\ \;\;\;\;1.6453555072203998 \cdot \left(y \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* y 3.13060547623))))
   (if (<= z -6.5e-143)
     t_1
     (if (<= z 2.4e-219)
       x
       (if (<= z 2.35e-45) (* 1.6453555072203998 (* y b)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * 3.13060547623);
	double tmp;
	if (z <= -6.5e-143) {
		tmp = t_1;
	} else if (z <= 2.4e-219) {
		tmp = x;
	} else if (z <= 2.35e-45) {
		tmp = 1.6453555072203998 * (y * 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 + (y * 3.13060547623d0)
    if (z <= (-6.5d-143)) then
        tmp = t_1
    else if (z <= 2.4d-219) then
        tmp = x
    else if (z <= 2.35d-45) then
        tmp = 1.6453555072203998d0 * (y * 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 + (y * 3.13060547623);
	double tmp;
	if (z <= -6.5e-143) {
		tmp = t_1;
	} else if (z <= 2.4e-219) {
		tmp = x;
	} else if (z <= 2.35e-45) {
		tmp = 1.6453555072203998 * (y * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y * 3.13060547623)
	tmp = 0
	if z <= -6.5e-143:
		tmp = t_1
	elif z <= 2.4e-219:
		tmp = x
	elif z <= 2.35e-45:
		tmp = 1.6453555072203998 * (y * b)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y * 3.13060547623))
	tmp = 0.0
	if (z <= -6.5e-143)
		tmp = t_1;
	elseif (z <= 2.4e-219)
		tmp = x;
	elseif (z <= 2.35e-45)
		tmp = Float64(1.6453555072203998 * Float64(y * b));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (y * 3.13060547623);
	tmp = 0.0;
	if (z <= -6.5e-143)
		tmp = t_1;
	elseif (z <= 2.4e-219)
		tmp = x;
	elseif (z <= 2.35e-45)
		tmp = 1.6453555072203998 * (y * 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[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.5e-143], t$95$1, If[LessEqual[z, 2.4e-219], x, If[LessEqual[z, 2.35e-45], N[(1.6453555072203998 * N[(y * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.4999999999999999e-143 or 2.3499999999999999e-45 < z

   1. Initial program 36.9%

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

   3. Simplified 40.2%

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

   5. Taylor expanded in z around inf 74.9%

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

   if -6.4999999999999999e-143 < z < 2.40000000000000014e-219

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 58.5%

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

   if 2.40000000000000014e-219 < z < 2.3499999999999999e-45

   1. Initial program 99.8%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in b around inf 56.0%

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

   6. Taylor expanded in z around 0 56.0%

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

      1. *-commutative 56.0%

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

   8. Simplified 56.0%

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

   9. Taylor expanded in z around 0 55.9%

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

       1. *-commutative 55.9%

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

   11. Simplified 55.9%

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

4. Final simplification 69.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{-143}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-219}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{-45}:\\ \;\;\;\;1.6453555072203998 \cdot \left(y \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 50.2% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+143}:\\ \;\;\;\;1.6453555072203998 \cdot \left(y \cdot b\right)\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{+17} \lor \neg \left(y \leq 2.2 \cdot 10^{+33}\right):\\ \;\;\;\;y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.3e+143)
   (* 1.6453555072203998 (* y b))
   (if (or (<= y -3.9e+17) (not (<= y 2.2e+33))) (* y 3.13060547623) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.3e+143) {
		tmp = 1.6453555072203998 * (y * b);
	} else if ((y <= -3.9e+17) || !(y <= 2.2e+33)) {
		tmp = y * 3.13060547623;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-1.3d+143)) then
        tmp = 1.6453555072203998d0 * (y * b)
    else if ((y <= (-3.9d+17)) .or. (.not. (y <= 2.2d+33))) then
        tmp = y * 3.13060547623d0
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.3e+143) {
		tmp = 1.6453555072203998 * (y * b);
	} else if ((y <= -3.9e+17) || !(y <= 2.2e+33)) {
		tmp = y * 3.13060547623;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.3e+143:
		tmp = 1.6453555072203998 * (y * b)
	elif (y <= -3.9e+17) or not (y <= 2.2e+33):
		tmp = y * 3.13060547623
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.3e+143)
		tmp = Float64(1.6453555072203998 * Float64(y * b));
	elseif ((y <= -3.9e+17) || !(y <= 2.2e+33))
		tmp = Float64(y * 3.13060547623);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.3e+143)
		tmp = 1.6453555072203998 * (y * b);
	elseif ((y <= -3.9e+17) || ~((y <= 2.2e+33)))
		tmp = y * 3.13060547623;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.3e+143], N[(1.6453555072203998 * N[(y * b), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -3.9e+17], N[Not[LessEqual[y, 2.2e+33]], $MachinePrecision]], N[(y * 3.13060547623), $MachinePrecision], x]]

Derivation

1. Split input into 3 regimes

2. if y < -1.2999999999999999e143

   1. Initial program 66.8%

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

   3. Simplified 69.6%

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

   5. Taylor expanded in b around inf 49.4%

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

   6. Taylor expanded in z around 0 43.8%

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

      1. *-commutative 43.8%

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

   8. Simplified 43.8%

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

   9. Taylor expanded in z around 0 50.0%

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

       1. *-commutative 50.0%

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

   11. Simplified 50.0%

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

   if -1.2999999999999999e143 < y < -3.9e17 or 2.19999999999999994e33 < y

   1. Initial program 47.0%

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

   3. Simplified 51.0%

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

   5. Taylor expanded in z around inf 61.3%

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

   6. Taylor expanded in x around 0 46.0%

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

      1. *-commutative 46.0%

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

   8. Simplified 46.0%

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

   if -3.9e17 < y < 2.19999999999999994e33

   1. Initial program 63.8%

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

   3. Simplified 64.5%

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

   5. Taylor expanded in y around 0 65.8%

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

4. Final simplification 56.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+143}:\\ \;\;\;\;1.6453555072203998 \cdot \left(y \cdot b\right)\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{+17} \lor \neg \left(y \leq 2.2 \cdot 10^{+33}\right):\\ \;\;\;\;y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 83.4% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+19} \lor \neg \left(z \leq 4.1 \cdot 10^{+43}\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2.3e+19) (not (<= z 4.1e+43)))
   (+ x (* y 3.13060547623))
   (+ x (* y (* b 1.6453555072203998)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.3e+19) || !(z <= 4.1e+43)) {
		tmp = x + (y * 3.13060547623);
	} else {
		tmp = x + (y * (b * 1.6453555072203998));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-2.3d+19)) .or. (.not. (z <= 4.1d+43))) then
        tmp = x + (y * 3.13060547623d0)
    else
        tmp = x + (y * (b * 1.6453555072203998d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.3e+19) || !(z <= 4.1e+43)) {
		tmp = x + (y * 3.13060547623);
	} else {
		tmp = x + (y * (b * 1.6453555072203998));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -2.3e+19) or not (z <= 4.1e+43):
		tmp = x + (y * 3.13060547623)
	else:
		tmp = x + (y * (b * 1.6453555072203998))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2.3e+19) || !(z <= 4.1e+43))
		tmp = Float64(x + Float64(y * 3.13060547623));
	else
		tmp = Float64(x + Float64(y * Float64(b * 1.6453555072203998)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -2.3e+19) || ~((z <= 4.1e+43)))
		tmp = x + (y * 3.13060547623);
	else
		tmp = x + (y * (b * 1.6453555072203998));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2.3e+19], N[Not[LessEqual[z, 4.1e+43]], $MachinePrecision]], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(b * 1.6453555072203998), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.3e19 or 4.1e43 < z

   1. Initial program 7.5%

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

   3. Simplified 10.7%

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

   5. Taylor expanded in z around inf 93.2%

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

   if -2.3e19 < z < 4.1e43

   1. Initial program 98.5%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around 0 78.7%

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

      1. associate-*r* 78.7%

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

      2. *-commutative 78.7%

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

   7. Simplified 78.7%

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

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+19} \lor \neg \left(z \leq 4.1 \cdot 10^{+43}\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 83.5% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{+19} \lor \neg \left(z \leq 2.1 \cdot 10^{+43}\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x + 1.6453555072203998 \cdot \left(y \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -5.4e+19) (not (<= z 2.1e+43)))
   (+ x (* y 3.13060547623))
   (+ x (* 1.6453555072203998 (* y b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -5.4e+19) || !(z <= 2.1e+43)) {
		tmp = x + (y * 3.13060547623);
	} else {
		tmp = x + (1.6453555072203998 * (y * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-5.4d+19)) .or. (.not. (z <= 2.1d+43))) then
        tmp = x + (y * 3.13060547623d0)
    else
        tmp = x + (1.6453555072203998d0 * (y * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -5.4e+19) || !(z <= 2.1e+43)) {
		tmp = x + (y * 3.13060547623);
	} else {
		tmp = x + (1.6453555072203998 * (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -5.4e+19) or not (z <= 2.1e+43):
		tmp = x + (y * 3.13060547623)
	else:
		tmp = x + (1.6453555072203998 * (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -5.4e+19) || !(z <= 2.1e+43))
		tmp = Float64(x + Float64(y * 3.13060547623));
	else
		tmp = Float64(x + Float64(1.6453555072203998 * Float64(y * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -5.4e+19) || ~((z <= 2.1e+43)))
		tmp = x + (y * 3.13060547623);
	else
		tmp = x + (1.6453555072203998 * (y * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -5.4e+19], N[Not[LessEqual[z, 2.1e+43]], $MachinePrecision]], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision], N[(x + N[(1.6453555072203998 * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.4e19 or 2.10000000000000002e43 < z

   1. Initial program 7.5%

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

   3. Simplified 10.7%

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

   5. Taylor expanded in z around inf 93.2%

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

   if -5.4e19 < z < 2.10000000000000002e43

   1. Initial program 98.5%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around 0 78.7%

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

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{+19} \lor \neg \left(z \leq 2.1 \cdot 10^{+43}\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x + 1.6453555072203998 \cdot \left(y \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 51.1% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{-111}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 7.1 \cdot 10^{-103}:\\ \;\;\;\;y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -5.8e-111) x (if (<= x 7.1e-103) (* y 3.13060547623) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -5.8e-111) {
		tmp = x;
	} else if (x <= 7.1e-103) {
		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 <= (-5.8d-111)) then
        tmp = x
    else if (x <= 7.1d-103) 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 <= -5.8e-111) {
		tmp = x;
	} else if (x <= 7.1e-103) {
		tmp = y * 3.13060547623;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -5.8e-111:
		tmp = x
	elif x <= 7.1e-103:
		tmp = y * 3.13060547623
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -5.8e-111)
		tmp = x;
	elseif (x <= 7.1e-103)
		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 <= -5.8e-111)
		tmp = x;
	elseif (x <= 7.1e-103)
		tmp = y * 3.13060547623;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -5.8e-111], x, If[LessEqual[x, 7.1e-103], N[(y * 3.13060547623), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -5.80000000000000003e-111 or 7.10000000000000045e-103 < x

   1. Initial program 61.4%

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

   3. Simplified 63.5%

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

   5. Taylor expanded in y around 0 56.7%

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

   if -5.80000000000000003e-111 < x < 7.10000000000000045e-103

   1. Initial program 52.3%

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

   3. Simplified 54.4%

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

   5. Taylor expanded in z around inf 58.6%

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

   6. Taylor expanded in x around 0 48.3%

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

      1. *-commutative 48.3%

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

   8. Simplified 48.3%

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

Alternative 16: 45.2% accurate, 37.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 58.3%

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

3. Simplified 60.4%

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

5. Taylor expanded in y around 0 43.4%

   \[\leadsto \color{blue}{x} \]
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 2024165 
(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))))