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

Percentage Accurate: 58.0% → 98.8%

Time: 16.8s

Alternatives: 14

Speedup: 2.5×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 58.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+29} \lor \neg \left(z \leq 2.8 \cdot 10^{+18}\right):\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623 + \frac{\frac{\left(t + 457.9610022158428\right) + \frac{a + \left(1112.0901850848957 + \left(-6976.8927133548 + t \cdot -15.234687407\right)\right)}{z}}{z} - 36.52704169880642}{z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -9.2e+29) (not (<= z 2.8e+18)))
   (fma
    y
    (+
     3.13060547623
     (/
      (-
       (/
        (+
         (+ t 457.9610022158428)
         (/
          (+ a (+ 1112.0901850848957 (+ -6976.8927133548 (* t -15.234687407))))
          z))
        z)
       36.52704169880642)
      z))
    x)
   (+
    x
    (/
     y
     (/
      (fma
       z
       (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721)
       0.607771387771)
      (fma z (fma z (fma z (fma z 3.13060547623 11.1667541262) t) a) b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -9.2e+29) || !(z <= 2.8e+18)) {
		tmp = fma(y, (3.13060547623 + (((((t + 457.9610022158428) + ((a + (1112.0901850848957 + (-6976.8927133548 + (t * -15.234687407)))) / z)) / z) - 36.52704169880642) / z)), x);
	} else {
		tmp = x + (y / (fma(z, fma(z, fma(z, (z + 15.234687407), 31.4690115749), 11.9400905721), 0.607771387771) / fma(z, fma(z, fma(z, fma(z, 3.13060547623, 11.1667541262), t), a), b)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -9.2e+29) || !(z <= 2.8e+18))
		tmp = fma(y, Float64(3.13060547623 + Float64(Float64(Float64(Float64(Float64(t + 457.9610022158428) + Float64(Float64(a + Float64(1112.0901850848957 + Float64(-6976.8927133548 + Float64(t * -15.234687407)))) / z)) / z) - 36.52704169880642) / z)), x);
	else
		tmp = Float64(x + Float64(y / Float64(fma(z, fma(z, fma(z, Float64(z + 15.234687407), 31.4690115749), 11.9400905721), 0.607771387771) / fma(z, fma(z, fma(z, fma(z, 3.13060547623, 11.1667541262), t), a), b))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -9.2e+29], N[Not[LessEqual[z, 2.8e+18]], $MachinePrecision]], N[(y * N[(3.13060547623 + N[(N[(N[(N[(N[(t + 457.9610022158428), $MachinePrecision] + N[(N[(a + N[(1112.0901850848957 + N[(-6976.8927133548 + N[(t * -15.234687407), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] - 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(x + N[(y / N[(N[(z * N[(z * N[(z * N[(z + 15.234687407), $MachinePrecision] + 31.4690115749), $MachinePrecision] + 11.9400905721), $MachinePrecision] + 0.607771387771), $MachinePrecision] / N[(z * N[(z * N[(z * N[(z * 3.13060547623 + 11.1667541262), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.2000000000000004e29 or 2.8e18 < z

   1. Initial program 5.8%

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

   3. Simplified 8.7%

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

   5. Taylor expanded in z around -inf 100.0%

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

   7. Simplified 100.0%

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

   if -9.2000000000000004e29 < z < 2.8e18

   1. Initial program 98.9%

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

   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. Step-by-step derivation

      1. fma-undefine 99.6%

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

      2. clear-num 99.6%

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

      3. un-div-inv 99.7%

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

   6. Applied egg-rr 99.7%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+29} \lor \neg \left(z \leq 2.8 \cdot 10^{+18}\right):\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623 + \frac{\frac{\left(t + 457.9610022158428\right) + \frac{a + \left(1112.0901850848957 + \left(-6976.8927133548 + t \cdot -15.234687407\right)\right)}{z}}{z} - 36.52704169880642}{z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 98.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+29} \lor \neg \left(z \leq 1.22 \cdot 10^{+17}\right):\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623 + \frac{\frac{\left(t + 457.9610022158428\right) + \frac{a + \left(1112.0901850848957 + \left(-6976.8927133548 + t \cdot -15.234687407\right)\right)}{z}}{z} - 36.52704169880642}{z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \frac{\mathsf{fma}\left(z, z, -232.09570038900438\right)}{z + -15.234687407}\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -5.2e+29) (not (<= z 1.22e+17)))
   (fma
    y
    (+
     3.13060547623
     (/
      (-
       (/
        (+
         (+ t 457.9610022158428)
         (/
          (+ a (+ 1112.0901850848957 (+ -6976.8927133548 (* t -15.234687407))))
          z))
        z)
       36.52704169880642)
      z))
    x)
   (+
    x
    (/
     (*
      y
      (+
       b
       (* z (+ a (* z (+ t (* z (+ 11.1667541262 (* z 3.13060547623)))))))))
     (+
      0.607771387771
      (*
       z
       (+
        11.9400905721
        (*
         z
         (+
          31.4690115749
          (* z (/ (fma z z -232.09570038900438) (+ z -15.234687407))))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -5.2e+29) || !(z <= 1.22e+17)) {
		tmp = fma(y, (3.13060547623 + (((((t + 457.9610022158428) + ((a + (1112.0901850848957 + (-6976.8927133548 + (t * -15.234687407)))) / z)) / z) - 36.52704169880642) / z)), x);
	} else {
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * (11.1667541262 + (z * 3.13060547623))))))))) / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * (fma(z, z, -232.09570038900438) / (z + -15.234687407)))))))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -5.2e+29) || !(z <= 1.22e+17))
		tmp = fma(y, Float64(3.13060547623 + Float64(Float64(Float64(Float64(Float64(t + 457.9610022158428) + Float64(Float64(a + Float64(1112.0901850848957 + Float64(-6976.8927133548 + Float64(t * -15.234687407)))) / z)) / z) - 36.52704169880642) / z)), x);
	else
		tmp = Float64(x + Float64(Float64(y * Float64(b + Float64(z * Float64(a + Float64(z * Float64(t + Float64(z * Float64(11.1667541262 + Float64(z * 3.13060547623))))))))) / Float64(0.607771387771 + Float64(z * Float64(11.9400905721 + Float64(z * Float64(31.4690115749 + Float64(z * Float64(fma(z, z, -232.09570038900438) / Float64(z + -15.234687407))))))))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -5.2e+29], N[Not[LessEqual[z, 1.22e+17]], $MachinePrecision]], N[(y * N[(3.13060547623 + N[(N[(N[(N[(N[(t + 457.9610022158428), $MachinePrecision] + N[(N[(a + N[(1112.0901850848957 + N[(-6976.8927133548 + N[(t * -15.234687407), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] - 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(x + N[(N[(y * N[(b + N[(z * N[(a + N[(z * N[(t + N[(z * N[(11.1667541262 + N[(z * 3.13060547623), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(0.607771387771 + N[(z * N[(11.9400905721 + N[(z * N[(31.4690115749 + N[(z * N[(N[(z * z + -232.09570038900438), $MachinePrecision] / N[(z + -15.234687407), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.2e29 or 1.22e17 < z

   1. Initial program 5.8%

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

   3. Simplified 8.7%

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

   5. Taylor expanded in z around -inf 100.0%

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

   7. Simplified 100.0%

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

   if -5.2e29 < z < 1.22e17

   1. Initial program 98.9%

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

      1. flip-+ 98.9%

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

      2. div-inv 98.9%

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

      3. fmm-def 98.9%

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

      4. metadata-eval 98.9%

         \[\leadsto x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(\mathsf{fma}\left(z, z, -\color{blue}{232.09570038900438}\right) \cdot \frac{1}{z - 15.234687407}\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

      5. metadata-eval 98.9%

         \[\leadsto x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(\mathsf{fma}\left(z, z, \color{blue}{-232.09570038900438}\right) \cdot \frac{1}{z - 15.234687407}\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

      6. sub-neg 98.9%

         \[\leadsto x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(\mathsf{fma}\left(z, z, -232.09570038900438\right) \cdot \frac{1}{\color{blue}{z + \left(-15.234687407\right)}}\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

      7. metadata-eval 98.9%

         \[\leadsto x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(\mathsf{fma}\left(z, z, -232.09570038900438\right) \cdot \frac{1}{z + \color{blue}{-15.234687407}}\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

   4. Applied egg-rr 98.9%

      \[\leadsto x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\color{blue}{\left(\mathsf{fma}\left(z, z, -232.09570038900438\right) \cdot \frac{1}{z + -15.234687407}\right)} \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
   5. Step-by-step derivation

      1. associate-*r/ 98.9%

         \[\leadsto x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\color{blue}{\frac{\mathsf{fma}\left(z, z, -232.09570038900438\right) \cdot 1}{z + -15.234687407}} \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

      2. *-rgt-identity 98.9%

         \[\leadsto x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\frac{\color{blue}{\mathsf{fma}\left(z, z, -232.09570038900438\right)}}{z + -15.234687407} \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]

   6. Simplified 98.9%

      \[\leadsto x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\color{blue}{\frac{\mathsf{fma}\left(z, z, -232.09570038900438\right)}{z + -15.234687407}} \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+29} \lor \neg \left(z \leq 1.22 \cdot 10^{+17}\right):\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623 + \frac{\frac{\left(t + 457.9610022158428\right) + \frac{a + \left(1112.0901850848957 + \left(-6976.8927133548 + t \cdot -15.234687407\right)\right)}{z}}{z} - 36.52704169880642}{z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \frac{\mathsf{fma}\left(z, z, -232.09570038900438\right)}{z + -15.234687407}\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+29} \lor \neg \left(z \leq 8 \cdot 10^{+17}\right):\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623 + \frac{\frac{\left(t + 457.9610022158428\right) + \frac{a + \left(1112.0901850848957 + \left(-6976.8927133548 + t \cdot -15.234687407\right)\right)}{z}}{z} - 36.52704169880642}{z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -8e+29) (not (<= z 8e+17)))
   (fma
    y
    (+
     3.13060547623
     (/
      (-
       (/
        (+
         (+ t 457.9610022158428)
         (/
          (+ a (+ 1112.0901850848957 (+ -6976.8927133548 (* t -15.234687407))))
          z))
        z)
       36.52704169880642)
      z))
    x)
   (+
    x
    (/
     (*
      y
      (+
       b
       (* z (+ a (* z (+ t (* z (+ 11.1667541262 (* z 3.13060547623)))))))))
     (+
      0.607771387771
      (*
       z
       (+ 11.9400905721 (* z (+ 31.4690115749 (* z (+ z 15.234687407)))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -8e+29) || !(z <= 8e+17)) {
		tmp = fma(y, (3.13060547623 + (((((t + 457.9610022158428) + ((a + (1112.0901850848957 + (-6976.8927133548 + (t * -15.234687407)))) / z)) / z) - 36.52704169880642) / z)), x);
	} else {
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * (11.1667541262 + (z * 3.13060547623))))))))) / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * (z + 15.234687407))))))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -8e+29) || !(z <= 8e+17))
		tmp = fma(y, Float64(3.13060547623 + Float64(Float64(Float64(Float64(Float64(t + 457.9610022158428) + Float64(Float64(a + Float64(1112.0901850848957 + Float64(-6976.8927133548 + Float64(t * -15.234687407)))) / z)) / z) - 36.52704169880642) / z)), x);
	else
		tmp = Float64(x + Float64(Float64(y * Float64(b + Float64(z * Float64(a + Float64(z * Float64(t + Float64(z * Float64(11.1667541262 + Float64(z * 3.13060547623))))))))) / Float64(0.607771387771 + Float64(z * Float64(11.9400905721 + Float64(z * Float64(31.4690115749 + Float64(z * Float64(z + 15.234687407)))))))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -8e+29], N[Not[LessEqual[z, 8e+17]], $MachinePrecision]], N[(y * N[(3.13060547623 + N[(N[(N[(N[(N[(t + 457.9610022158428), $MachinePrecision] + N[(N[(a + N[(1112.0901850848957 + N[(-6976.8927133548 + N[(t * -15.234687407), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] - 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(x + N[(N[(y * N[(b + N[(z * N[(a + N[(z * N[(t + N[(z * N[(11.1667541262 + N[(z * 3.13060547623), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(0.607771387771 + N[(z * N[(11.9400905721 + N[(z * N[(31.4690115749 + N[(z * N[(z + 15.234687407), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.99999999999999931e29 or 8e17 < z

   1. Initial program 5.8%

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

   3. Simplified 8.7%

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

   5. Taylor expanded in z around -inf 100.0%

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

   7. Simplified 100.0%

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

   if -7.99999999999999931e29 < z < 8e17

   1. Initial program 98.9%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+29} \lor \neg \left(z \leq 8 \cdot 10^{+17}\right):\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623 + \frac{\frac{\left(t + 457.9610022158428\right) + \frac{a + \left(1112.0901850848957 + \left(-6976.8927133548 + t \cdot -15.234687407\right)\right)}{z}}{z} - 36.52704169880642}{z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 97.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+31} \lor \neg \left(z \leq 1.45 \cdot 10^{+56}\right):\\ \;\;\;\;x + \left(y \cdot \frac{\frac{t + 457.9610022158428}{z} - 36.52704169880642}{z} + y \cdot 3.13060547623\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.95e+31) (not (<= z 1.45e+56)))
   (+
    x
    (+
     (* y (/ (- (/ (+ t 457.9610022158428) z) 36.52704169880642) z))
     (* y 3.13060547623)))
   (+
    x
    (/
     (*
      y
      (+
       b
       (* z (+ a (* z (+ t (* z (+ 11.1667541262 (* z 3.13060547623)))))))))
     (+
      0.607771387771
      (*
       z
       (+ 11.9400905721 (* z (+ 31.4690115749 (* z (+ z 15.234687407)))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.95e+31) || !(z <= 1.45e+56)) {
		tmp = x + ((y * ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)) + (y * 3.13060547623));
	} else {
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * (11.1667541262 + (z * 3.13060547623))))))))) / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * (z + 15.234687407))))))));
	}
	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 <= (-1.95d+31)) .or. (.not. (z <= 1.45d+56))) then
        tmp = x + ((y * ((((t + 457.9610022158428d0) / z) - 36.52704169880642d0) / z)) + (y * 3.13060547623d0))
    else
        tmp = x + ((y * (b + (z * (a + (z * (t + (z * (11.1667541262d0 + (z * 3.13060547623d0))))))))) / (0.607771387771d0 + (z * (11.9400905721d0 + (z * (31.4690115749d0 + (z * (z + 15.234687407d0))))))))
    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 <= -1.95e+31) || !(z <= 1.45e+56)) {
		tmp = x + ((y * ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)) + (y * 3.13060547623));
	} else {
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * (11.1667541262 + (z * 3.13060547623))))))))) / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * (z + 15.234687407))))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.95e+31) or not (z <= 1.45e+56):
		tmp = x + ((y * ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)) + (y * 3.13060547623))
	else:
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * (11.1667541262 + (z * 3.13060547623))))))))) / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * (z + 15.234687407))))))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.95e+31) || !(z <= 1.45e+56))
		tmp = Float64(x + Float64(Float64(y * Float64(Float64(Float64(Float64(t + 457.9610022158428) / z) - 36.52704169880642) / z)) + Float64(y * 3.13060547623)));
	else
		tmp = Float64(x + Float64(Float64(y * Float64(b + Float64(z * Float64(a + Float64(z * Float64(t + Float64(z * Float64(11.1667541262 + Float64(z * 3.13060547623))))))))) / Float64(0.607771387771 + Float64(z * Float64(11.9400905721 + Float64(z * Float64(31.4690115749 + Float64(z * Float64(z + 15.234687407)))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.95e+31) || ~((z <= 1.45e+56)))
		tmp = x + ((y * ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)) + (y * 3.13060547623));
	else
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * (11.1667541262 + (z * 3.13060547623))))))))) / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * (z + 15.234687407))))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.95e+31], N[Not[LessEqual[z, 1.45e+56]], $MachinePrecision]], N[(x + N[(N[(y * N[(N[(N[(N[(t + 457.9610022158428), $MachinePrecision] / z), $MachinePrecision] - 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * N[(b + N[(z * N[(a + N[(z * N[(t + N[(z * N[(11.1667541262 + N[(z * 3.13060547623), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(0.607771387771 + N[(z * N[(11.9400905721 + N[(z * N[(31.4690115749 + N[(z * N[(z + 15.234687407), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.95e31 or 1.45000000000000004e56 < z

   1. Initial program 3.6%

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

   3. Taylor expanded in z around -inf 91.0%

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

   4. Taylor expanded in y around 0 96.3%

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

      1. associate-/l* 97.7%

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

      2. mul-1-neg 97.7%

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

      3. unsub-neg 97.7%

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

      4. +-commutative 97.7%

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

   6. Simplified 97.7%

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

   if -1.95e31 < z < 1.45000000000000004e56

   1. Initial program 98.9%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+31} \lor \neg \left(z \leq 1.45 \cdot 10^{+56}\right):\\ \;\;\;\;x + \left(y \cdot \frac{\frac{t + 457.9610022158428}{z} - 36.52704169880642}{z} + y \cdot 3.13060547623\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 96.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+31} \lor \neg \left(z \leq 1.45 \cdot 10^{+56}\right):\\ \;\;\;\;x + \left(y \cdot \frac{\frac{t + 457.9610022158428}{z} - 36.52704169880642}{z} + y \cdot 3.13060547623\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot 11.1667541262\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2e+31) (not (<= z 1.45e+56)))
   (+
    x
    (+
     (* y (/ (- (/ (+ t 457.9610022158428) z) 36.52704169880642) z))
     (* y 3.13060547623)))
   (+
    x
    (/
     (* y (+ b (* z (+ a (* z (+ t (* z 11.1667541262)))))))
     (+
      0.607771387771
      (*
       z
       (+ 11.9400905721 (* z (+ 31.4690115749 (* z (+ z 15.234687407)))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2e+31) || !(z <= 1.45e+56)) {
		tmp = x + ((y * ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)) + (y * 3.13060547623));
	} else {
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))) / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * (z + 15.234687407))))))));
	}
	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 <= (-2d+31)) .or. (.not. (z <= 1.45d+56))) then
        tmp = x + ((y * ((((t + 457.9610022158428d0) / z) - 36.52704169880642d0) / z)) + (y * 3.13060547623d0))
    else
        tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262d0))))))) / (0.607771387771d0 + (z * (11.9400905721d0 + (z * (31.4690115749d0 + (z * (z + 15.234687407d0))))))))
    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 <= -2e+31) || !(z <= 1.45e+56)) {
		tmp = x + ((y * ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)) + (y * 3.13060547623));
	} else {
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))) / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * (z + 15.234687407))))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -2e+31) or not (z <= 1.45e+56):
		tmp = x + ((y * ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)) + (y * 3.13060547623))
	else:
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))) / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * (z + 15.234687407))))))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2e+31) || !(z <= 1.45e+56))
		tmp = Float64(x + Float64(Float64(y * Float64(Float64(Float64(Float64(t + 457.9610022158428) / z) - 36.52704169880642) / z)) + Float64(y * 3.13060547623)));
	else
		tmp = Float64(x + Float64(Float64(y * Float64(b + Float64(z * Float64(a + Float64(z * Float64(t + Float64(z * 11.1667541262))))))) / Float64(0.607771387771 + Float64(z * Float64(11.9400905721 + Float64(z * Float64(31.4690115749 + Float64(z * Float64(z + 15.234687407)))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -2e+31) || ~((z <= 1.45e+56)))
		tmp = x + ((y * ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)) + (y * 3.13060547623));
	else
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))) / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * (z + 15.234687407))))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2e+31], N[Not[LessEqual[z, 1.45e+56]], $MachinePrecision]], N[(x + N[(N[(y * N[(N[(N[(N[(t + 457.9610022158428), $MachinePrecision] / z), $MachinePrecision] - 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * N[(b + N[(z * N[(a + N[(z * N[(t + N[(z * 11.1667541262), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(0.607771387771 + N[(z * N[(11.9400905721 + N[(z * N[(31.4690115749 + N[(z * N[(z + 15.234687407), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.9999999999999999e31 or 1.45000000000000004e56 < z

   1. Initial program 3.6%

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

   3. Taylor expanded in z around -inf 91.0%

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

   4. Taylor expanded in y around 0 96.3%

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

      1. associate-/l* 97.7%

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

      2. mul-1-neg 97.7%

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

      3. unsub-neg 97.7%

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

      4. +-commutative 97.7%

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

   6. Simplified 97.7%

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

   if -1.9999999999999999e31 < z < 1.45000000000000004e56

   1. Initial program 98.9%

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

   3. Taylor expanded in z around 0 98.3%

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

      1. *-commutative 98.3%

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

   5. Simplified 98.3%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+31} \lor \neg \left(z \leq 1.45 \cdot 10^{+56}\right):\\ \;\;\;\;x + \left(y \cdot \frac{\frac{t + 457.9610022158428}{z} - 36.52704169880642}{z} + y \cdot 3.13060547623\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot 11.1667541262\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 96.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+30} \lor \neg \left(z \leq 1.45 \cdot 10^{+56}\right):\\ \;\;\;\;x + \left(y \cdot \frac{\frac{t + 457.9610022158428}{z} - 36.52704169880642}{z} + y \cdot 3.13060547623\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot t\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.6e+30) (not (<= z 1.45e+56)))
   (+
    x
    (+
     (* y (/ (- (/ (+ t 457.9610022158428) z) 36.52704169880642) z))
     (* y 3.13060547623)))
   (+
    x
    (/
     (* y (+ b (* z (+ a (* z t)))))
     (+
      0.607771387771
      (*
       z
       (+ 11.9400905721 (* z (+ 31.4690115749 (* z (+ z 15.234687407)))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.6e+30) || !(z <= 1.45e+56)) {
		tmp = x + ((y * ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)) + (y * 3.13060547623));
	} else {
		tmp = x + ((y * (b + (z * (a + (z * t))))) / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * (z + 15.234687407))))))));
	}
	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 <= (-1.6d+30)) .or. (.not. (z <= 1.45d+56))) then
        tmp = x + ((y * ((((t + 457.9610022158428d0) / z) - 36.52704169880642d0) / z)) + (y * 3.13060547623d0))
    else
        tmp = x + ((y * (b + (z * (a + (z * t))))) / (0.607771387771d0 + (z * (11.9400905721d0 + (z * (31.4690115749d0 + (z * (z + 15.234687407d0))))))))
    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 <= -1.6e+30) || !(z <= 1.45e+56)) {
		tmp = x + ((y * ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)) + (y * 3.13060547623));
	} else {
		tmp = x + ((y * (b + (z * (a + (z * t))))) / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * (z + 15.234687407))))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.6e+30) or not (z <= 1.45e+56):
		tmp = x + ((y * ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)) + (y * 3.13060547623))
	else:
		tmp = x + ((y * (b + (z * (a + (z * t))))) / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * (z + 15.234687407))))))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.6e+30) || !(z <= 1.45e+56))
		tmp = Float64(x + Float64(Float64(y * Float64(Float64(Float64(Float64(t + 457.9610022158428) / z) - 36.52704169880642) / z)) + Float64(y * 3.13060547623)));
	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 + 15.234687407)))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.6e+30) || ~((z <= 1.45e+56)))
		tmp = x + ((y * ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)) + (y * 3.13060547623));
	else
		tmp = x + ((y * (b + (z * (a + (z * t))))) / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * (z + 15.234687407))))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.6e+30], N[Not[LessEqual[z, 1.45e+56]], $MachinePrecision]], N[(x + N[(N[(y * N[(N[(N[(N[(t + 457.9610022158428), $MachinePrecision] / z), $MachinePrecision] - 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(y * 3.13060547623), $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 + 15.234687407), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.59999999999999986e30 or 1.45000000000000004e56 < z

   1. Initial program 3.6%

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

   3. Taylor expanded in z around -inf 91.0%

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

   4. Taylor expanded in y around 0 96.3%

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

      1. associate-/l* 97.7%

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

      2. mul-1-neg 97.7%

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

      3. unsub-neg 97.7%

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

      4. +-commutative 97.7%

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

   6. Simplified 97.7%

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

   if -1.59999999999999986e30 < z < 1.45000000000000004e56

   1. Initial program 98.9%

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

   3. Taylor expanded in z around 0 84.4%

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

   4. Taylor expanded in y around 0 97.0%

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

4. Final simplification 97.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+30} \lor \neg \left(z \leq 1.45 \cdot 10^{+56}\right):\\ \;\;\;\;x + \left(y \cdot \frac{\frac{t + 457.9610022158428}{z} - 36.52704169880642}{z} + y \cdot 3.13060547623\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot t\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 92.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+15} \lor \neg \left(z \leq 8.4 \cdot 10^{-13}\right):\\ \;\;\;\;x + \left(y \cdot \frac{\frac{t + 457.9610022158428}{z} - 36.52704169880642}{z} + y \cdot 3.13060547623\right)\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \left(z \cdot \left(b \cdot 32.324150453290734 - a \cdot 1.6453555072203998\right) - b \cdot 1.6453555072203998\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.95e+15) (not (<= z 8.4e-13)))
   (+
    x
    (+
     (* y (/ (- (/ (+ t 457.9610022158428) z) 36.52704169880642) z))
     (* y 3.13060547623)))
   (-
    x
    (*
     y
     (-
      (* z (- (* b 32.324150453290734) (* a 1.6453555072203998)))
      (* b 1.6453555072203998))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.95e+15) || !(z <= 8.4e-13)) {
		tmp = x + ((y * ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)) + (y * 3.13060547623));
	} else {
		tmp = x - (y * ((z * ((b * 32.324150453290734) - (a * 1.6453555072203998))) - (b * 1.6453555072203998)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-1.95d+15)) .or. (.not. (z <= 8.4d-13))) then
        tmp = x + ((y * ((((t + 457.9610022158428d0) / z) - 36.52704169880642d0) / z)) + (y * 3.13060547623d0))
    else
        tmp = x - (y * ((z * ((b * 32.324150453290734d0) - (a * 1.6453555072203998d0))) - (b * 1.6453555072203998d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.95e+15) || !(z <= 8.4e-13)) {
		tmp = x + ((y * ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)) + (y * 3.13060547623));
	} else {
		tmp = x - (y * ((z * ((b * 32.324150453290734) - (a * 1.6453555072203998))) - (b * 1.6453555072203998)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.95e+15) or not (z <= 8.4e-13):
		tmp = x + ((y * ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)) + (y * 3.13060547623))
	else:
		tmp = x - (y * ((z * ((b * 32.324150453290734) - (a * 1.6453555072203998))) - (b * 1.6453555072203998)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.95e+15) || !(z <= 8.4e-13))
		tmp = Float64(x + Float64(Float64(y * Float64(Float64(Float64(Float64(t + 457.9610022158428) / z) - 36.52704169880642) / z)) + Float64(y * 3.13060547623)));
	else
		tmp = Float64(x - Float64(y * Float64(Float64(z * Float64(Float64(b * 32.324150453290734) - Float64(a * 1.6453555072203998))) - Float64(b * 1.6453555072203998))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.95e+15) || ~((z <= 8.4e-13)))
		tmp = x + ((y * ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)) + (y * 3.13060547623));
	else
		tmp = x - (y * ((z * ((b * 32.324150453290734) - (a * 1.6453555072203998))) - (b * 1.6453555072203998)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.95e+15], N[Not[LessEqual[z, 8.4e-13]], $MachinePrecision]], N[(x + N[(N[(y * N[(N[(N[(N[(t + 457.9610022158428), $MachinePrecision] / z), $MachinePrecision] - 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * N[(N[(z * N[(N[(b * 32.324150453290734), $MachinePrecision] - N[(a * 1.6453555072203998), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * 1.6453555072203998), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.95e15 or 8.39999999999999955e-13 < z

   1. Initial program 11.2%

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

   3. Taylor expanded in z around -inf 89.7%

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

   4. Taylor expanded in y around 0 94.5%

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

      1. associate-/l* 95.8%

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

      2. mul-1-neg 95.8%

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

      3. unsub-neg 95.8%

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

      4. +-commutative 95.8%

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

   6. Simplified 95.8%

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

   if -1.95e15 < z < 8.39999999999999955e-13

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0 82.5%

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

   4. Taylor expanded in y around 0 93.2%

      \[\leadsto x + \color{blue}{y \cdot \left(1.6453555072203998 \cdot b + z \cdot \left(1.6453555072203998 \cdot a - 32.324150453290734 \cdot b\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 94.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+15} \lor \neg \left(z \leq 8.4 \cdot 10^{-13}\right):\\ \;\;\;\;x + \left(y \cdot \frac{\frac{t + 457.9610022158428}{z} - 36.52704169880642}{z} + y \cdot 3.13060547623\right)\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \left(z \cdot \left(b \cdot 32.324150453290734 - a \cdot 1.6453555072203998\right) - b \cdot 1.6453555072203998\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 89.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{+16}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{elif}\;z \leq 61:\\ \;\;\;\;x - y \cdot \left(z \cdot \left(b \cdot 32.324150453290734 - a \cdot 1.6453555072203998\right) - b \cdot 1.6453555072203998\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + \left(y \cdot 3.13060547623 + 11.1667541262 \cdot \frac{y}{z}\right)\right) - \frac{y}{z} \cdot 47.69379582500642\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -8.6e+16)
   (+ x (* y 3.13060547623))
   (if (<= z 61.0)
     (-
      x
      (*
       y
       (-
        (* z (- (* b 32.324150453290734) (* a 1.6453555072203998)))
        (* b 1.6453555072203998))))
     (-
      (+ x (+ (* y 3.13060547623) (* 11.1667541262 (/ y z))))
      (* (/ y z) 47.69379582500642)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -8.6e+16) {
		tmp = x + (y * 3.13060547623);
	} else if (z <= 61.0) {
		tmp = x - (y * ((z * ((b * 32.324150453290734) - (a * 1.6453555072203998))) - (b * 1.6453555072203998)));
	} else {
		tmp = (x + ((y * 3.13060547623) + (11.1667541262 * (y / z)))) - ((y / z) * 47.69379582500642);
	}
	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 <= (-8.6d+16)) then
        tmp = x + (y * 3.13060547623d0)
    else if (z <= 61.0d0) then
        tmp = x - (y * ((z * ((b * 32.324150453290734d0) - (a * 1.6453555072203998d0))) - (b * 1.6453555072203998d0)))
    else
        tmp = (x + ((y * 3.13060547623d0) + (11.1667541262d0 * (y / z)))) - ((y / z) * 47.69379582500642d0)
    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 <= -8.6e+16) {
		tmp = x + (y * 3.13060547623);
	} else if (z <= 61.0) {
		tmp = x - (y * ((z * ((b * 32.324150453290734) - (a * 1.6453555072203998))) - (b * 1.6453555072203998)));
	} else {
		tmp = (x + ((y * 3.13060547623) + (11.1667541262 * (y / z)))) - ((y / z) * 47.69379582500642);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -8.6e+16:
		tmp = x + (y * 3.13060547623)
	elif z <= 61.0:
		tmp = x - (y * ((z * ((b * 32.324150453290734) - (a * 1.6453555072203998))) - (b * 1.6453555072203998)))
	else:
		tmp = (x + ((y * 3.13060547623) + (11.1667541262 * (y / z)))) - ((y / z) * 47.69379582500642)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -8.6e+16)
		tmp = Float64(x + Float64(y * 3.13060547623));
	elseif (z <= 61.0)
		tmp = Float64(x - Float64(y * Float64(Float64(z * Float64(Float64(b * 32.324150453290734) - Float64(a * 1.6453555072203998))) - Float64(b * 1.6453555072203998))));
	else
		tmp = Float64(Float64(x + Float64(Float64(y * 3.13060547623) + Float64(11.1667541262 * Float64(y / z)))) - Float64(Float64(y / z) * 47.69379582500642));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -8.6e+16)
		tmp = x + (y * 3.13060547623);
	elseif (z <= 61.0)
		tmp = x - (y * ((z * ((b * 32.324150453290734) - (a * 1.6453555072203998))) - (b * 1.6453555072203998)));
	else
		tmp = (x + ((y * 3.13060547623) + (11.1667541262 * (y / z)))) - ((y / z) * 47.69379582500642);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -8.6e+16], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 61.0], N[(x - N[(y * N[(N[(z * N[(N[(b * 32.324150453290734), $MachinePrecision] - N[(a * 1.6453555072203998), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * 1.6453555072203998), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(N[(y * 3.13060547623), $MachinePrecision] + N[(11.1667541262 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y / z), $MachinePrecision] * 47.69379582500642), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.6e16

   1. Initial program 10.0%

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

   3. Simplified 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 92.2%

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

      1. +-commutative 92.2%

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

      2. *-commutative 92.2%

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

   7. Simplified 92.2%

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

   if -8.6e16 < z < 61

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0 81.8%

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

   4. Taylor expanded in y around 0 92.4%

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

   if 61 < z

   1. Initial program 11.1%

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

   3. Simplified 13.6%

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

   5. Taylor expanded in z around inf 89.8%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{+16}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{elif}\;z \leq 61:\\ \;\;\;\;x - y \cdot \left(z \cdot \left(b \cdot 32.324150453290734 - a \cdot 1.6453555072203998\right) - b \cdot 1.6453555072203998\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + \left(y \cdot 3.13060547623 + 11.1667541262 \cdot \frac{y}{z}\right)\right) - \frac{y}{z} \cdot 47.69379582500642\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 89.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+18}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{elif}\;z \leq 280:\\ \;\;\;\;x - y \cdot \left(z \cdot \left(b \cdot 32.324150453290734 - a \cdot 1.6453555072203998\right) - b \cdot 1.6453555072203998\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 - \frac{y \cdot 36.52704169880642}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -4.1e+18)
   (+ x (* y 3.13060547623))
   (if (<= z 280.0)
     (-
      x
      (*
       y
       (-
        (* z (- (* b 32.324150453290734) (* a 1.6453555072203998)))
        (* b 1.6453555072203998))))
     (+ x (- (* y 3.13060547623) (/ (* y 36.52704169880642) z))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -4.1e+18) {
		tmp = x + (y * 3.13060547623);
	} else if (z <= 280.0) {
		tmp = x - (y * ((z * ((b * 32.324150453290734) - (a * 1.6453555072203998))) - (b * 1.6453555072203998)));
	} else {
		tmp = x + ((y * 3.13060547623) - ((y * 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 <= (-4.1d+18)) then
        tmp = x + (y * 3.13060547623d0)
    else if (z <= 280.0d0) then
        tmp = x - (y * ((z * ((b * 32.324150453290734d0) - (a * 1.6453555072203998d0))) - (b * 1.6453555072203998d0)))
    else
        tmp = x + ((y * 3.13060547623d0) - ((y * 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 <= -4.1e+18) {
		tmp = x + (y * 3.13060547623);
	} else if (z <= 280.0) {
		tmp = x - (y * ((z * ((b * 32.324150453290734) - (a * 1.6453555072203998))) - (b * 1.6453555072203998)));
	} else {
		tmp = x + ((y * 3.13060547623) - ((y * 36.52704169880642) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -4.1e+18:
		tmp = x + (y * 3.13060547623)
	elif z <= 280.0:
		tmp = x - (y * ((z * ((b * 32.324150453290734) - (a * 1.6453555072203998))) - (b * 1.6453555072203998)))
	else:
		tmp = x + ((y * 3.13060547623) - ((y * 36.52704169880642) / z))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -4.1e+18)
		tmp = Float64(x + Float64(y * 3.13060547623));
	elseif (z <= 280.0)
		tmp = Float64(x - Float64(y * Float64(Float64(z * Float64(Float64(b * 32.324150453290734) - Float64(a * 1.6453555072203998))) - Float64(b * 1.6453555072203998))));
	else
		tmp = Float64(x + Float64(Float64(y * 3.13060547623) - Float64(Float64(y * 36.52704169880642) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -4.1e+18)
		tmp = x + (y * 3.13060547623);
	elseif (z <= 280.0)
		tmp = x - (y * ((z * ((b * 32.324150453290734) - (a * 1.6453555072203998))) - (b * 1.6453555072203998)));
	else
		tmp = x + ((y * 3.13060547623) - ((y * 36.52704169880642) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -4.1e+18], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 280.0], N[(x - N[(y * N[(N[(z * N[(N[(b * 32.324150453290734), $MachinePrecision] - N[(a * 1.6453555072203998), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * 1.6453555072203998), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * 3.13060547623), $MachinePrecision] - N[(N[(y * 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.1e18

   1. Initial program 10.0%

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

   3. Simplified 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 92.2%

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

      1. +-commutative 92.2%

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

      2. *-commutative 92.2%

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

   7. Simplified 92.2%

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

   if -4.1e18 < z < 280

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0 81.8%

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

   4. Taylor expanded in y around 0 92.4%

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

   if 280 < z

   1. Initial program 11.1%

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

   3. Simplified 13.6%

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

   5. Taylor expanded in z around -inf 89.8%

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

      1. +-commutative 89.8%

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

      2. +-commutative 89.8%

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

      3. mul-1-neg 89.8%

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

      4. unsub-neg 89.8%

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

      5. *-commutative 89.8%

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

      6. distribute-rgt-out-- 89.8%

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

      7. metadata-eval 89.8%

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

   7. Simplified 89.8%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+18}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{elif}\;z \leq 280:\\ \;\;\;\;x - y \cdot \left(z \cdot \left(b \cdot 32.324150453290734 - a \cdot 1.6453555072203998\right) - b \cdot 1.6453555072203998\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 - \frac{y \cdot 36.52704169880642}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 89.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+18} \lor \neg \left(z \leq 8.4 \cdot 10^{-13}\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(1.6453555072203998 \cdot \left(b + z \cdot a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.9e+18) (not (<= z 8.4e-13)))
   (+ x (* y 3.13060547623))
   (+ x (* y (* 1.6453555072203998 (+ b (* z a)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.9e+18) || !(z <= 8.4e-13)) {
		tmp = x + (y * 3.13060547623);
	} else {
		tmp = x + (y * (1.6453555072203998 * (b + (z * a))));
	}
	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 <= (-1.9d+18)) .or. (.not. (z <= 8.4d-13))) then
        tmp = x + (y * 3.13060547623d0)
    else
        tmp = x + (y * (1.6453555072203998d0 * (b + (z * a))))
    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 <= -1.9e+18) || !(z <= 8.4e-13)) {
		tmp = x + (y * 3.13060547623);
	} else {
		tmp = x + (y * (1.6453555072203998 * (b + (z * a))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.9e+18) or not (z <= 8.4e-13):
		tmp = x + (y * 3.13060547623)
	else:
		tmp = x + (y * (1.6453555072203998 * (b + (z * a))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.9e+18) || !(z <= 8.4e-13))
		tmp = Float64(x + Float64(y * 3.13060547623));
	else
		tmp = Float64(x + Float64(y * Float64(1.6453555072203998 * Float64(b + Float64(z * a)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.9e+18) || ~((z <= 8.4e-13)))
		tmp = x + (y * 3.13060547623);
	else
		tmp = x + (y * (1.6453555072203998 * (b + (z * a))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.9e+18], N[Not[LessEqual[z, 8.4e-13]], $MachinePrecision]], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(1.6453555072203998 * N[(b + N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.9e18 or 8.39999999999999955e-13 < z

   1. Initial program 11.2%

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

   3. Simplified 14.6%

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

   5. Taylor expanded in z around inf 90.0%

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

      1. +-commutative 90.0%

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

      2. *-commutative 90.0%

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

   7. Simplified 90.0%

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

   if -1.9e18 < z < 8.39999999999999955e-13

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0 82.5%

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

   4. Taylor expanded in a around inf 91.8%

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

   5. Taylor expanded in b around 0 91.8%

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

      1. associate-*r* 91.8%

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

      2. *-commutative 91.8%

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

      3. associate-*r* 92.3%

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

      4. associate-*r* 92.3%

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

      5. associate-*r* 92.3%

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

      6. distribute-rgt-in 93.1%

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

      7. distribute-lft-out 93.1%

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

      8. *-commutative 93.1%

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

   7. Simplified 93.1%

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

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+18} \lor \neg \left(z \leq 8.4 \cdot 10^{-13}\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(1.6453555072203998 \cdot \left(b + z \cdot a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 89.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+19}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{elif}\;z \leq 550:\\ \;\;\;\;x + y \cdot \left(1.6453555072203998 \cdot \left(b + z \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 - \frac{y \cdot 36.52704169880642}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.9e+19)
   (+ x (* y 3.13060547623))
   (if (<= z 550.0)
     (+ x (* y (* 1.6453555072203998 (+ b (* z a)))))
     (+ x (- (* y 3.13060547623) (/ (* y 36.52704169880642) z))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.9e+19) {
		tmp = x + (y * 3.13060547623);
	} else if (z <= 550.0) {
		tmp = x + (y * (1.6453555072203998 * (b + (z * a))));
	} else {
		tmp = x + ((y * 3.13060547623) - ((y * 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 <= (-1.9d+19)) then
        tmp = x + (y * 3.13060547623d0)
    else if (z <= 550.0d0) then
        tmp = x + (y * (1.6453555072203998d0 * (b + (z * a))))
    else
        tmp = x + ((y * 3.13060547623d0) - ((y * 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 <= -1.9e+19) {
		tmp = x + (y * 3.13060547623);
	} else if (z <= 550.0) {
		tmp = x + (y * (1.6453555072203998 * (b + (z * a))));
	} else {
		tmp = x + ((y * 3.13060547623) - ((y * 36.52704169880642) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.9e+19:
		tmp = x + (y * 3.13060547623)
	elif z <= 550.0:
		tmp = x + (y * (1.6453555072203998 * (b + (z * a))))
	else:
		tmp = x + ((y * 3.13060547623) - ((y * 36.52704169880642) / z))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.9e+19)
		tmp = Float64(x + Float64(y * 3.13060547623));
	elseif (z <= 550.0)
		tmp = Float64(x + Float64(y * Float64(1.6453555072203998 * Float64(b + Float64(z * a)))));
	else
		tmp = Float64(x + Float64(Float64(y * 3.13060547623) - Float64(Float64(y * 36.52704169880642) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1.9e+19)
		tmp = x + (y * 3.13060547623);
	elseif (z <= 550.0)
		tmp = x + (y * (1.6453555072203998 * (b + (z * a))));
	else
		tmp = x + ((y * 3.13060547623) - ((y * 36.52704169880642) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.9e+19], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 550.0], N[(x + N[(y * N[(1.6453555072203998 * N[(b + N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * 3.13060547623), $MachinePrecision] - N[(N[(y * 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.9e19

   1. Initial program 10.0%

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

   3. Simplified 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 92.2%

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

      1. +-commutative 92.2%

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

      2. *-commutative 92.2%

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

   7. Simplified 92.2%

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

   if -1.9e19 < z < 550

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0 81.8%

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

   4. Taylor expanded in a around inf 91.0%

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

   5. Taylor expanded in b around 0 91.0%

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

      1. associate-*r* 91.0%

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

      2. *-commutative 91.0%

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

      3. associate-*r* 91.5%

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

      4. associate-*r* 91.5%

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

      5. associate-*r* 91.5%

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

      6. distribute-rgt-in 92.3%

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

      7. distribute-lft-out 92.3%

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

      8. *-commutative 92.3%

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

   7. Simplified 92.3%

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

   if 550 < z

   1. Initial program 11.1%

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

   3. Simplified 13.6%

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

   5. Taylor expanded in z around -inf 89.8%

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

      1. +-commutative 89.8%

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

      2. +-commutative 89.8%

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

      3. mul-1-neg 89.8%

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

      4. unsub-neg 89.8%

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

      5. *-commutative 89.8%

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

      6. distribute-rgt-out-- 89.8%

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

      7. metadata-eval 89.8%

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

   7. Simplified 89.8%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+19}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{elif}\;z \leq 550:\\ \;\;\;\;x + y \cdot \left(1.6453555072203998 \cdot \left(b + z \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 - \frac{y \cdot 36.52704169880642}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 83.0% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+15} \lor \neg \left(z \leq 8.4 \cdot 10^{-13}\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x + 1.6453555072203998 \cdot \left(y \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -5.5e+15) (not (<= z 8.4e-13)))
   (+ 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 <= -5.5e+15) || !(z <= 8.4e-13)) {
		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 <= (-5.5d+15)) .or. (.not. (z <= 8.4d-13))) 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 <= -5.5e+15) || !(z <= 8.4e-13)) {
		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 <= -5.5e+15) or not (z <= 8.4e-13):
		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 <= -5.5e+15) || !(z <= 8.4e-13))
		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 <= -5.5e+15) || ~((z <= 8.4e-13)))
		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, -5.5e+15], N[Not[LessEqual[z, 8.4e-13]], $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 < -5.5e15 or 8.39999999999999955e-13 < z

   1. Initial program 11.2%

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

   3. Simplified 14.6%

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

   5. Taylor expanded in z around inf 90.0%

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

      1. +-commutative 90.0%

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

      2. *-commutative 90.0%

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

   7. Simplified 90.0%

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

   if -5.5e15 < z < 8.39999999999999955e-13

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0 81.3%

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

4. Final simplification 86.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+15} \lor \neg \left(z \leq 8.4 \cdot 10^{-13}\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x + 1.6453555072203998 \cdot \left(y \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 64.0% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.85 \cdot 10^{-216} \lor \neg \left(z \leq 1.85 \cdot 10^{-15}\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2.85e-216) (not (<= z 1.85e-15))) (+ x (* y 3.13060547623)) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.85e-216) || !(z <= 1.85e-15)) {
		tmp = x + (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 ((z <= (-2.85d-216)) .or. (.not. (z <= 1.85d-15))) then
        tmp = x + (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 ((z <= -2.85e-216) || !(z <= 1.85e-15)) {
		tmp = x + (y * 3.13060547623);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -2.85e-216) or not (z <= 1.85e-15):
		tmp = x + (y * 3.13060547623)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2.85e-216) || !(z <= 1.85e-15))
		tmp = Float64(x + 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 ((z <= -2.85e-216) || ~((z <= 1.85e-15)))
		tmp = x + (y * 3.13060547623);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2.85e-216], N[Not[LessEqual[z, 1.85e-15]], $MachinePrecision]], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -2.85000000000000002e-216 or 1.85000000000000008e-15 < z

   1. Initial program 33.9%

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

   3. Simplified 36.4%

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

   5. Taylor expanded in z around inf 78.9%

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

      1. +-commutative 78.9%

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

      2. *-commutative 78.9%

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

   7. Simplified 78.9%

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

   if -2.85000000000000002e-216 < z < 1.85000000000000008e-15

   1. Initial program 99.7%

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

   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 y around 0 51.1%

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

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.85 \cdot 10^{-216} \lor \neg \left(z \leq 1.85 \cdot 10^{-15}\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 45.3% accurate, 37.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 51.6%

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

3. Simplified 53.4%

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

5. Taylor expanded in y around 0 52.8%

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

Developer Target 1: 98.4% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024139 
(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))))