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

Percentage Accurate: 58.8% → 97.8%

Time: 27.3s

Alternatives: 18

Speedup: 7.4×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 58.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+46} \lor \neg \left(z \leq 5.2 \cdot 10^{+42}\right):\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623 + \frac{\frac{t + 457.9610022158428}{z} - 36.52704169880642}{z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), z, t\right), z, a\right), z, b\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687407, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.1e+46) (not (<= z 5.2e+42)))
   (fma
    y
    (+ 3.13060547623 (/ (- (/ (+ t 457.9610022158428) z) 36.52704169880642) z))
    x)
   (+
    x
    (/
     (* y (fma (fma (fma (fma z 3.13060547623 11.1667541262) z t) z a) z b))
     (fma
      (fma (fma (+ z 15.234687407) z 31.4690115749) z 11.9400905721)
      z
      0.607771387771)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.1e+46) || !(z <= 5.2e+42)) {
		tmp = fma(y, (3.13060547623 + ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)), x);
	} else {
		tmp = x + ((y * fma(fma(fma(fma(z, 3.13060547623, 11.1667541262), z, t), z, a), z, b)) / fma(fma(fma((z + 15.234687407), z, 31.4690115749), z, 11.9400905721), z, 0.607771387771));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.1e+46) || !(z <= 5.2e+42))
		tmp = fma(y, Float64(3.13060547623 + Float64(Float64(Float64(Float64(t + 457.9610022158428) / z) - 36.52704169880642) / z)), x);
	else
		tmp = Float64(x + Float64(Float64(y * fma(fma(fma(fma(z, 3.13060547623, 11.1667541262), z, t), z, a), z, b)) / fma(fma(fma(Float64(z + 15.234687407), z, 31.4690115749), z, 11.9400905721), z, 0.607771387771)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.1e+46], N[Not[LessEqual[z, 5.2e+42]], $MachinePrecision]], N[(y * N[(3.13060547623 + N[(N[(N[(N[(t + 457.9610022158428), $MachinePrecision] / z), $MachinePrecision] - 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(x + N[(N[(y * N[(N[(N[(N[(z * 3.13060547623 + 11.1667541262), $MachinePrecision] * z + t), $MachinePrecision] * z + a), $MachinePrecision] * z + b), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(N[(z + 15.234687407), $MachinePrecision] * z + 31.4690115749), $MachinePrecision] * z + 11.9400905721), $MachinePrecision] * z + 0.607771387771), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.1e46 or 5.1999999999999998e42 < z

   1. Initial program 2.6%

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

   3. Simplified 5.5%

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

   5. Taylor expanded in z around -inf 97.9%

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

      1. mul-1-neg 97.9%

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

      2. unsub-neg 97.9%

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

      3. mul-1-neg 97.9%

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

      4. unsub-neg 97.9%

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

      5. +-commutative 97.9%

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

   7. Simplified 97.9%

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

   if -1.1e46 < z < 5.1999999999999998e42

   1. Initial program 98.1%

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

      1. remove-double-neg 98.1%

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

      2. distribute-lft-neg-out 98.1%

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

      3. distribute-lft-neg-in 98.1%

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

      4. remove-double-neg 98.1%

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

      5. fma-define 98.1%

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

      6. fma-define 98.1%

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

      7. fma-define 98.1%

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

      8. fma-define 98.1%

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

   3. Simplified 98.1%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+46} \lor \neg \left(z \leq 5.2 \cdot 10^{+42}\right):\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623 + \frac{\frac{t + 457.9610022158428}{z} - 36.52704169880642}{z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), z, t\right), z, a\right), z, b\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687407, z, 31.4690115749\right), z, 11.9400905721\right), z, 0.607771387771\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 93.6% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771} \leq 10^{+248}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right), \frac{y}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623 + \frac{\frac{t + 457.9610022158428}{z} - 36.52704169880642}{z}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<=
      (/
       (*
        y
        (+
         (* z (+ (* z (+ (* z (+ (* z 3.13060547623) 11.1667541262)) t)) a))
         b))
       (+
        (*
         z
         (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721))
        0.607771387771))
      1e+248)
   (fma
    (fma z (fma z (fma z (fma z 3.13060547623 11.1667541262) t) a) b)
    (/
     y
     (fma
      z
      (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721)
      0.607771387771))
    x)
   (fma
    y
    (+ 3.13060547623 (/ (- (/ (+ t 457.9610022158428) z) 36.52704169880642) z))
    x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)) <= 1e+248) {
		tmp = fma(fma(z, fma(z, fma(z, fma(z, 3.13060547623, 11.1667541262), t), a), b), (y / fma(z, fma(z, fma(z, (z + 15.234687407), 31.4690115749), 11.9400905721), 0.607771387771)), x);
	} else {
		tmp = fma(y, (3.13060547623 + ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(Float64(y * Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)) <= 1e+248)
		tmp = fma(fma(z, fma(z, fma(z, fma(z, 3.13060547623, 11.1667541262), t), a), b), Float64(y / fma(z, fma(z, fma(z, Float64(z + 15.234687407), 31.4690115749), 11.9400905721), 0.607771387771)), x);
	else
		tmp = fma(y, Float64(3.13060547623 + Float64(Float64(Float64(Float64(t + 457.9610022158428) / z) - 36.52704169880642) / z)), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(N[(y * N[(N[(z * N[(N[(z * N[(N[(z * N[(N[(z * 3.13060547623), $MachinePrecision] + 11.1667541262), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(N[(z * N[(N[(z * N[(N[(z * N[(z + 15.234687407), $MachinePrecision]), $MachinePrecision] + 31.4690115749), $MachinePrecision]), $MachinePrecision] + 11.9400905721), $MachinePrecision]), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision], 1e+248], N[(N[(z * N[(z * N[(z * N[(z * 3.13060547623 + 11.1667541262), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision] + b), $MachinePrecision] * N[(y / N[(z * N[(z * N[(z * N[(z + 15.234687407), $MachinePrecision] + 31.4690115749), $MachinePrecision] + 11.9400905721), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(y * N[(3.13060547623 + N[(N[(N[(N[(t + 457.9610022158428), $MachinePrecision] / z), $MachinePrecision] - 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z #s(literal 313060547623/100000000000 binary64)) #s(literal 55833770631/5000000000 binary64)) z) t) z) a) z) b)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z #s(literal 15234687407/1000000000 binary64)) z) #s(literal 314690115749/10000000000 binary64)) z) #s(literal 119400905721/10000000000 binary64)) z) #s(literal 607771387771/1000000000000 binary64))) < 1.00000000000000005e248

   1. Initial program 96.5%

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

   3. Simplified 98.9%

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

   if 1.00000000000000005e248 < (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z #s(literal 313060547623/100000000000 binary64)) #s(literal 55833770631/5000000000 binary64)) z) t) z) a) z) b)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z #s(literal 15234687407/1000000000 binary64)) z) #s(literal 314690115749/10000000000 binary64)) z) #s(literal 119400905721/10000000000 binary64)) z) #s(literal 607771387771/1000000000000 binary64)))

   1. Initial program 8.3%

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

   3. Simplified 9.0%

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

   5. Taylor expanded in z around -inf 94.1%

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

      1. mul-1-neg 94.1%

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

      2. unsub-neg 94.1%

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

      3. mul-1-neg 94.1%

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

      4. unsub-neg 94.1%

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

      5. +-commutative 94.1%

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

   7. Simplified 94.1%

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

4. Final simplification 96.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771} \leq 10^{+248}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right), \frac{y}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623 + \frac{\frac{t + 457.9610022158428}{z} - 36.52704169880642}{z}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 94.1% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771} \leq 10^{+248}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right)}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623 + \frac{\frac{t + 457.9610022158428}{z} - 36.52704169880642}{z}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<=
      (/
       (*
        y
        (+
         (* z (+ (* z (+ (* z (+ (* z 3.13060547623) 11.1667541262)) t)) a))
         b))
       (+
        (*
         z
         (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721))
        0.607771387771))
      1e+248)
   (fma
    y
    (/
     (fma z (fma z (fma z (fma z 3.13060547623 11.1667541262) t) a) b)
     (fma
      z
      (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721)
      0.607771387771))
    x)
   (fma
    y
    (+ 3.13060547623 (/ (- (/ (+ t 457.9610022158428) z) 36.52704169880642) z))
    x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)) <= 1e+248) {
		tmp = fma(y, (fma(z, fma(z, fma(z, fma(z, 3.13060547623, 11.1667541262), t), a), b) / fma(z, fma(z, fma(z, (z + 15.234687407), 31.4690115749), 11.9400905721), 0.607771387771)), x);
	} else {
		tmp = fma(y, (3.13060547623 + ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(Float64(y * Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)) <= 1e+248)
		tmp = fma(y, Float64(fma(z, fma(z, fma(z, fma(z, 3.13060547623, 11.1667541262), t), a), b) / fma(z, fma(z, fma(z, Float64(z + 15.234687407), 31.4690115749), 11.9400905721), 0.607771387771)), x);
	else
		tmp = fma(y, Float64(3.13060547623 + Float64(Float64(Float64(Float64(t + 457.9610022158428) / z) - 36.52704169880642) / z)), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(N[(y * N[(N[(z * N[(N[(z * N[(N[(z * N[(N[(z * 3.13060547623), $MachinePrecision] + 11.1667541262), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(N[(z * N[(N[(z * N[(N[(z * N[(z + 15.234687407), $MachinePrecision]), $MachinePrecision] + 31.4690115749), $MachinePrecision]), $MachinePrecision] + 11.9400905721), $MachinePrecision]), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision], 1e+248], N[(y * N[(N[(z * N[(z * N[(z * N[(z * 3.13060547623 + 11.1667541262), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision] + b), $MachinePrecision] / N[(z * N[(z * N[(z * N[(z + 15.234687407), $MachinePrecision] + 31.4690115749), $MachinePrecision] + 11.9400905721), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(y * N[(3.13060547623 + N[(N[(N[(N[(t + 457.9610022158428), $MachinePrecision] / z), $MachinePrecision] - 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z #s(literal 313060547623/100000000000 binary64)) #s(literal 55833770631/5000000000 binary64)) z) t) z) a) z) b)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z #s(literal 15234687407/1000000000 binary64)) z) #s(literal 314690115749/10000000000 binary64)) z) #s(literal 119400905721/10000000000 binary64)) z) #s(literal 607771387771/1000000000000 binary64))) < 1.00000000000000005e248

   1. Initial program 96.5%

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

   3. Simplified 98.8%

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

   if 1.00000000000000005e248 < (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z #s(literal 313060547623/100000000000 binary64)) #s(literal 55833770631/5000000000 binary64)) z) t) z) a) z) b)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z #s(literal 15234687407/1000000000 binary64)) z) #s(literal 314690115749/10000000000 binary64)) z) #s(literal 119400905721/10000000000 binary64)) z) #s(literal 607771387771/1000000000000 binary64)))

   1. Initial program 8.3%

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

   3. Simplified 9.0%

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

   5. Taylor expanded in z around -inf 94.1%

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

      1. mul-1-neg 94.1%

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

      2. unsub-neg 94.1%

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

      3. mul-1-neg 94.1%

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

      4. unsub-neg 94.1%

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

      5. +-commutative 94.1%

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

   7. Simplified 94.1%

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

4. Final simplification 96.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771} \leq 10^{+248}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right)}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623 + \frac{\frac{t + 457.9610022158428}{z} - 36.52704169880642}{z}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 94.8% accurate, 0.3× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 92.7%

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

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

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in z around inf 95.7%

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

4. Final simplification 94.1%

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

Alternative 5: 97.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+46} \lor \neg \left(z \leq 1.35 \cdot 10^{+38}\right):\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623 + \frac{\frac{t + 457.9610022158428}{z} - 36.52704169880642}{z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771} + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1e+46) (not (<= z 1.35e+38)))
   (fma
    y
    (+ 3.13060547623 (/ (- (/ (+ t 457.9610022158428) z) 36.52704169880642) z))
    x)
   (+
    (/
     (*
      y
      (+
       (* z (+ (* z (+ (* z (+ (* z 3.13060547623) 11.1667541262)) t)) a))
       b))
     (+
      (* z (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721))
      0.607771387771))
    x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1e+46) || !(z <= 1.35e+38)) {
		tmp = fma(y, (3.13060547623 + ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)), x);
	} else {
		tmp = ((y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)) + x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1e+46) || !(z <= 1.35e+38))
		tmp = fma(y, Float64(3.13060547623 + Float64(Float64(Float64(Float64(t + 457.9610022158428) / z) - 36.52704169880642) / z)), x);
	else
		tmp = Float64(Float64(Float64(y * Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)) + x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1e+46], N[Not[LessEqual[z, 1.35e+38]], $MachinePrecision]], N[(y * N[(3.13060547623 + N[(N[(N[(N[(t + 457.9610022158428), $MachinePrecision] / z), $MachinePrecision] - 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(N[(N[(y * N[(N[(z * N[(N[(z * N[(N[(z * N[(N[(z * 3.13060547623), $MachinePrecision] + 11.1667541262), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(N[(z * N[(N[(z * N[(N[(z * N[(z + 15.234687407), $MachinePrecision]), $MachinePrecision] + 31.4690115749), $MachinePrecision]), $MachinePrecision] + 11.9400905721), $MachinePrecision]), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.9999999999999999e45 or 1.34999999999999998e38 < z

   1. Initial program 3.3%

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

   3. Simplified 6.3%

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

   5. Taylor expanded in z around -inf 97.2%

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

      1. mul-1-neg 97.2%

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

      2. unsub-neg 97.2%

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

      3. mul-1-neg 97.2%

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

      4. unsub-neg 97.2%

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

      5. +-commutative 97.2%

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

   7. Simplified 97.2%

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

   if -9.9999999999999999e45 < z < 1.34999999999999998e38

   1. Initial program 98.1%

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

4. Final simplification 97.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+46} \lor \neg \left(z \leq 1.35 \cdot 10^{+38}\right):\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623 + \frac{\frac{t + 457.9610022158428}{z} - 36.52704169880642}{z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771} + x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 94.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\\ \mathbf{if}\;t\_1 \leq \infty:\\ \;\;\;\;t\_1 + x\\ \mathbf{else}:\\ \;\;\;\;\left(x + \left(y \cdot 3.13060547623 + 11.1667541262 \cdot \frac{y}{z}\right)\right) - \frac{y}{z} \cdot 47.69379582500642\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (/
          (*
           y
           (+
            (* z (+ (* z (+ (* z (+ (* z 3.13060547623) 11.1667541262)) t)) a))
            b))
          (+
           (*
            z
            (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721))
           0.607771387771))))
   (if (<= t_1 INFINITY)
     (+ t_1 x)
     (-
      (+ 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 t_1 = (y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771);
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1 + x;
	} else {
		tmp = (x + ((y * 3.13060547623) + (11.1667541262 * (y / z)))) - ((y / z) * 47.69379582500642);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771);
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1 + x;
	} else {
		tmp = (x + ((y * 3.13060547623) + (11.1667541262 * (y / z)))) - ((y / z) * 47.69379582500642);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1 + x
	else:
		tmp = (x + ((y * 3.13060547623) + (11.1667541262 * (y / z)))) - ((y / z) * 47.69379582500642)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y * Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = Float64(t_1 + x);
	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)
	t_1 = (y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771);
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1 + x;
	else
		tmp = (x + ((y * 3.13060547623) + (11.1667541262 * (y / z)))) - ((y / z) * 47.69379582500642);
	end
	tmp_2 = tmp;
end

Wolfram

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

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

   1. Initial program 92.7%

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

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

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in z around inf 95.7%

      \[\leadsto \color{blue}{\left(x + \left(3.13060547623 \cdot y + 11.1667541262 \cdot \frac{y}{z}\right)\right) - 47.69379582500642 \cdot \frac{y}{z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 94.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771} \leq \infty:\\ \;\;\;\;\frac{y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771} + x\\ \mathbf{else}:\\ \;\;\;\;\left(x + \left(y \cdot 3.13060547623 + 11.1667541262 \cdot \frac{y}{z}\right)\right) - \frac{y}{z} \cdot 47.69379582500642\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 93.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+149}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{elif}\;z \leq -3 \cdot 10^{+47}:\\ \;\;\;\;y \cdot \left(\left(\frac{x}{y} - \frac{36.52704169880642 - \frac{t + 457.9610022158428}{z}}{z}\right) - -3.13060547623\right)\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{+47}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 0.0018:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot t\right)\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \left(y \cdot 3.13060547623 + 11.1667541262 \cdot \frac{y}{z}\right)\right) - \frac{y}{z} \cdot 47.69379582500642\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -2e+149)
   (+ x (* y 3.13060547623))
   (if (<= z -3e+47)
     (*
      y
      (-
       (- (/ x y) (/ (- 36.52704169880642 (/ (+ t 457.9610022158428) z)) z))
       -3.13060547623))
     (if (<= z -2.9e+47)
       x
       (if (<= z 0.0018)
         (+
          x
          (/
           (* y (+ b (* z (+ a (* z t)))))
           (+
            (*
             z
             (+
              (* z (+ (* z (+ z 15.234687407)) 31.4690115749))
              11.9400905721))
            0.607771387771)))
         (-
          (+ 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 <= -2e+149) {
		tmp = x + (y * 3.13060547623);
	} else if (z <= -3e+47) {
		tmp = y * (((x / y) - ((36.52704169880642 - ((t + 457.9610022158428) / z)) / z)) - -3.13060547623);
	} else if (z <= -2.9e+47) {
		tmp = x;
	} else if (z <= 0.0018) {
		tmp = x + ((y * (b + (z * (a + (z * t))))) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771));
	} 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 <= (-2d+149)) then
        tmp = x + (y * 3.13060547623d0)
    else if (z <= (-3d+47)) then
        tmp = y * (((x / y) - ((36.52704169880642d0 - ((t + 457.9610022158428d0) / z)) / z)) - (-3.13060547623d0))
    else if (z <= (-2.9d+47)) then
        tmp = x
    else if (z <= 0.0018d0) then
        tmp = x + ((y * (b + (z * (a + (z * t))))) / ((z * ((z * ((z * (z + 15.234687407d0)) + 31.4690115749d0)) + 11.9400905721d0)) + 0.607771387771d0))
    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 <= -2e+149) {
		tmp = x + (y * 3.13060547623);
	} else if (z <= -3e+47) {
		tmp = y * (((x / y) - ((36.52704169880642 - ((t + 457.9610022158428) / z)) / z)) - -3.13060547623);
	} else if (z <= -2.9e+47) {
		tmp = x;
	} else if (z <= 0.0018) {
		tmp = x + ((y * (b + (z * (a + (z * t))))) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771));
	} 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 <= -2e+149:
		tmp = x + (y * 3.13060547623)
	elif z <= -3e+47:
		tmp = y * (((x / y) - ((36.52704169880642 - ((t + 457.9610022158428) / z)) / z)) - -3.13060547623)
	elif z <= -2.9e+47:
		tmp = x
	elif z <= 0.0018:
		tmp = x + ((y * (b + (z * (a + (z * t))))) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771))
	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 <= -2e+149)
		tmp = Float64(x + Float64(y * 3.13060547623));
	elseif (z <= -3e+47)
		tmp = Float64(y * Float64(Float64(Float64(x / y) - Float64(Float64(36.52704169880642 - Float64(Float64(t + 457.9610022158428) / z)) / z)) - -3.13060547623));
	elseif (z <= -2.9e+47)
		tmp = x;
	elseif (z <= 0.0018)
		tmp = Float64(x + Float64(Float64(y * Float64(b + Float64(z * Float64(a + Float64(z * t))))) / Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)));
	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 <= -2e+149)
		tmp = x + (y * 3.13060547623);
	elseif (z <= -3e+47)
		tmp = y * (((x / y) - ((36.52704169880642 - ((t + 457.9610022158428) / z)) / z)) - -3.13060547623);
	elseif (z <= -2.9e+47)
		tmp = x;
	elseif (z <= 0.0018)
		tmp = x + ((y * (b + (z * (a + (z * t))))) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771));
	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, -2e+149], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3e+47], N[(y * N[(N[(N[(x / y), $MachinePrecision] - N[(N[(36.52704169880642 - N[(N[(t + 457.9610022158428), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] - -3.13060547623), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.9e+47], x, If[LessEqual[z, 0.0018], N[(x + N[(N[(y * N[(b + N[(z * N[(a + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(z * N[(N[(z * N[(N[(z * N[(z + 15.234687407), $MachinePrecision]), $MachinePrecision] + 31.4690115749), $MachinePrecision]), $MachinePrecision] + 11.9400905721), $MachinePrecision]), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(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 5 regimes

2. if z < -2.0000000000000001e149

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in z around inf 100.0%

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

      1. +-commutative 100.0%

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

      2. *-commutative 100.0%

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

   7. Simplified 100.0%

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

   if -2.0000000000000001e149 < z < -3.0000000000000001e47

   1. Initial program 7.3%

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

   3. Simplified 14.0%

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

   5. Taylor expanded in y around -inf 14.0%

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

   6. Taylor expanded in z around -inf 93.4%

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

      1. mul-1-neg 93.4%

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

      2. unsub-neg 93.4%

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

      3. mul-1-neg 93.4%

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

      4. unsub-neg 93.4%

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

      5. +-commutative 93.4%

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

   8. Simplified 93.4%

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

   9. Taylor expanded in z around inf 93.4%

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

       1. sub-neg 93.4%

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

   11. Simplified 93.4%

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

   if -3.0000000000000001e47 < z < -2.8999999999999998e47

   1. Initial program 0.4%

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

   3. Simplified 0.4%

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

   5. Taylor expanded in y around 0 100.0%

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

   if -2.8999999999999998e47 < z < 0.0018

   1. Initial program 98.8%

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

   3. Taylor expanded in z around 0 87.1%

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

   4. Taylor expanded in y around 0 95.7%

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

      1. *-commutative 95.7%

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

   6. Simplified 95.7%

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

   if 0.0018 < z

   1. Initial program 10.7%

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

   3. Simplified 13.5%

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

   5. Taylor expanded in z around inf 88.3%

      \[\leadsto \color{blue}{\left(x + \left(3.13060547623 \cdot y + 11.1667541262 \cdot \frac{y}{z}\right)\right) - 47.69379582500642 \cdot \frac{y}{z}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 94.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+149}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{elif}\;z \leq -3 \cdot 10^{+47}:\\ \;\;\;\;y \cdot \left(\left(\frac{x}{y} - \frac{36.52704169880642 - \frac{t + 457.9610022158428}{z}}{z}\right) - -3.13060547623\right)\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{+47}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 0.0018:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot t\right)\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \left(y \cdot 3.13060547623 + 11.1667541262 \cdot \frac{y}{z}\right)\right) - \frac{y}{z} \cdot 47.69379582500642\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 95.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(\frac{x}{y} + \left(3.13060547623 + \frac{\frac{457.9610022158428 + \left(t + \frac{a + \left(-5864.8025282699045 + t \cdot -15.234687407\right)}{z}\right)}{z} - 36.52704169880642}{z}\right)\right)\\ \mathbf{if}\;z \leq -1.9 \cdot 10^{+149}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{elif}\;z \leq -1 \cdot 10^{+46}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 16500000000:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot t\right)\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+84}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(x + \left(y \cdot 3.13060547623 + 11.1667541262 \cdot \frac{y}{z}\right)\right) - \frac{y}{z} \cdot 47.69379582500642\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (*
          y
          (+
           (/ x y)
           (+
            3.13060547623
            (/
             (-
              (/
               (+
                457.9610022158428
                (+ t (/ (+ a (+ -5864.8025282699045 (* t -15.234687407))) z)))
               z)
              36.52704169880642)
             z))))))
   (if (<= z -1.9e+149)
     (+ x (* y 3.13060547623))
     (if (<= z -1e+46)
       t_1
       (if (<= z 16500000000.0)
         (+
          x
          (/
           (* y (+ b (* z (+ a (* z t)))))
           (+
            (*
             z
             (+
              (* z (+ (* z (+ z 15.234687407)) 31.4690115749))
              11.9400905721))
            0.607771387771)))
         (if (<= z 2.1e+84)
           t_1
           (-
            (+ 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 t_1 = y * ((x / y) + (3.13060547623 + ((((457.9610022158428 + (t + ((a + (-5864.8025282699045 + (t * -15.234687407))) / z))) / z) - 36.52704169880642) / z)));
	double tmp;
	if (z <= -1.9e+149) {
		tmp = x + (y * 3.13060547623);
	} else if (z <= -1e+46) {
		tmp = t_1;
	} else if (z <= 16500000000.0) {
		tmp = x + ((y * (b + (z * (a + (z * t))))) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771));
	} else if (z <= 2.1e+84) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = y * ((x / y) + (3.13060547623d0 + ((((457.9610022158428d0 + (t + ((a + ((-5864.8025282699045d0) + (t * (-15.234687407d0)))) / z))) / z) - 36.52704169880642d0) / z)))
    if (z <= (-1.9d+149)) then
        tmp = x + (y * 3.13060547623d0)
    else if (z <= (-1d+46)) then
        tmp = t_1
    else if (z <= 16500000000.0d0) then
        tmp = x + ((y * (b + (z * (a + (z * t))))) / ((z * ((z * ((z * (z + 15.234687407d0)) + 31.4690115749d0)) + 11.9400905721d0)) + 0.607771387771d0))
    else if (z <= 2.1d+84) then
        tmp = t_1
    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 t_1 = y * ((x / y) + (3.13060547623 + ((((457.9610022158428 + (t + ((a + (-5864.8025282699045 + (t * -15.234687407))) / z))) / z) - 36.52704169880642) / z)));
	double tmp;
	if (z <= -1.9e+149) {
		tmp = x + (y * 3.13060547623);
	} else if (z <= -1e+46) {
		tmp = t_1;
	} else if (z <= 16500000000.0) {
		tmp = x + ((y * (b + (z * (a + (z * t))))) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771));
	} else if (z <= 2.1e+84) {
		tmp = t_1;
	} 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):
	t_1 = y * ((x / y) + (3.13060547623 + ((((457.9610022158428 + (t + ((a + (-5864.8025282699045 + (t * -15.234687407))) / z))) / z) - 36.52704169880642) / z)))
	tmp = 0
	if z <= -1.9e+149:
		tmp = x + (y * 3.13060547623)
	elif z <= -1e+46:
		tmp = t_1
	elif z <= 16500000000.0:
		tmp = x + ((y * (b + (z * (a + (z * t))))) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771))
	elif z <= 2.1e+84:
		tmp = t_1
	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)
	t_1 = Float64(y * Float64(Float64(x / y) + Float64(3.13060547623 + Float64(Float64(Float64(Float64(457.9610022158428 + Float64(t + Float64(Float64(a + Float64(-5864.8025282699045 + Float64(t * -15.234687407))) / z))) / z) - 36.52704169880642) / z))))
	tmp = 0.0
	if (z <= -1.9e+149)
		tmp = Float64(x + Float64(y * 3.13060547623));
	elseif (z <= -1e+46)
		tmp = t_1;
	elseif (z <= 16500000000.0)
		tmp = Float64(x + Float64(Float64(y * Float64(b + Float64(z * Float64(a + Float64(z * t))))) / Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)));
	elseif (z <= 2.1e+84)
		tmp = t_1;
	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)
	t_1 = y * ((x / y) + (3.13060547623 + ((((457.9610022158428 + (t + ((a + (-5864.8025282699045 + (t * -15.234687407))) / z))) / z) - 36.52704169880642) / z)));
	tmp = 0.0;
	if (z <= -1.9e+149)
		tmp = x + (y * 3.13060547623);
	elseif (z <= -1e+46)
		tmp = t_1;
	elseif (z <= 16500000000.0)
		tmp = x + ((y * (b + (z * (a + (z * t))))) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771));
	elseif (z <= 2.1e+84)
		tmp = t_1;
	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_] := Block[{t$95$1 = N[(y * N[(N[(x / y), $MachinePrecision] + N[(3.13060547623 + N[(N[(N[(N[(457.9610022158428 + N[(t + N[(N[(a + N[(-5864.8025282699045 + N[(t * -15.234687407), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] - 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.9e+149], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1e+46], t$95$1, If[LessEqual[z, 16500000000.0], N[(x + N[(N[(y * N[(b + N[(z * N[(a + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(z * N[(N[(z * N[(N[(z * N[(z + 15.234687407), $MachinePrecision]), $MachinePrecision] + 31.4690115749), $MachinePrecision]), $MachinePrecision] + 11.9400905721), $MachinePrecision]), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.1e+84], t$95$1, 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 4 regimes

2. if z < -1.9e149

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in z around inf 100.0%

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

      1. +-commutative 100.0%

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

      2. *-commutative 100.0%

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

   7. Simplified 100.0%

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

   if -1.9e149 < z < -9.9999999999999999e45 or 1.65e10 < z < 2.10000000000000019e84

   1. Initial program 16.2%

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

   3. Simplified 25.9%

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

   5. Taylor expanded in y around -inf 25.9%

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

   6. Taylor expanded in z around -inf 91.8%

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

   8. Simplified 91.8%

      \[\leadsto -1 \cdot \left(y \cdot \left(-1 \cdot \frac{x}{y} + -1 \cdot \color{blue}{\left(3.13060547623 - \frac{36.52704169880642 - \frac{457.9610022158428 + \left(t - \frac{\left(-a\right) - \left(-5864.8025282699045 + -15.234687407 \cdot t\right)}{z}\right)}{z}}{z}\right)}\right)\right) \]

   if -9.9999999999999999e45 < z < 1.65e10

   1. Initial program 98.8%

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

   3. Taylor expanded in z around 0 87.3%

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

   4. Taylor expanded in y around 0 95.8%

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

      1. *-commutative 95.8%

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

   6. Simplified 95.8%

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

   if 2.10000000000000019e84 < z

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in z around inf 96.3%

      \[\leadsto \color{blue}{\left(x + \left(3.13060547623 \cdot y + 11.1667541262 \cdot \frac{y}{z}\right)\right) - 47.69379582500642 \cdot \frac{y}{z}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 95.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+149}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{elif}\;z \leq -1 \cdot 10^{+46}:\\ \;\;\;\;y \cdot \left(\frac{x}{y} + \left(3.13060547623 + \frac{\frac{457.9610022158428 + \left(t + \frac{a + \left(-5864.8025282699045 + t \cdot -15.234687407\right)}{z}\right)}{z} - 36.52704169880642}{z}\right)\right)\\ \mathbf{elif}\;z \leq 16500000000:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot t\right)\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+84}:\\ \;\;\;\;y \cdot \left(\frac{x}{y} + \left(3.13060547623 + \frac{\frac{457.9610022158428 + \left(t + \frac{a + \left(-5864.8025282699045 + t \cdot -15.234687407\right)}{z}\right)}{z} - 36.52704169880642}{z}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + \left(y \cdot 3.13060547623 + 11.1667541262 \cdot \frac{y}{z}\right)\right) - \frac{y}{z} \cdot 47.69379582500642\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 92.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot 3.13060547623\\ \mathbf{if}\;z \leq -1.9 \cdot 10^{+149}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{+17}:\\ \;\;\;\;y \cdot \left(\left(\frac{x}{y} - \frac{36.52704169880642 - \frac{t + 457.9610022158428}{z}}{z}\right) - -3.13060547623\right)\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{-23}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot t\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot 31.4690115749\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* y 3.13060547623))))
   (if (<= z -1.9e+149)
     t_1
     (if (<= z -8.5e+17)
       (*
        y
        (-
         (- (/ x y) (/ (- 36.52704169880642 (/ (+ t 457.9610022158428) z)) z))
         -3.13060547623))
       (if (<= z 1.22e-23)
         (+
          x
          (/
           (* y (+ b (* z (+ a (* z t)))))
           (+ 0.607771387771 (* z (+ 11.9400905721 (* z 31.4690115749))))))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * 3.13060547623);
	double tmp;
	if (z <= -1.9e+149) {
		tmp = t_1;
	} else if (z <= -8.5e+17) {
		tmp = y * (((x / y) - ((36.52704169880642 - ((t + 457.9610022158428) / z)) / z)) - -3.13060547623);
	} else if (z <= 1.22e-23) {
		tmp = x + ((y * (b + (z * (a + (z * t))))) / (0.607771387771 + (z * (11.9400905721 + (z * 31.4690115749)))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * 3.13060547623d0)
    if (z <= (-1.9d+149)) then
        tmp = t_1
    else if (z <= (-8.5d+17)) then
        tmp = y * (((x / y) - ((36.52704169880642d0 - ((t + 457.9610022158428d0) / z)) / z)) - (-3.13060547623d0))
    else if (z <= 1.22d-23) then
        tmp = x + ((y * (b + (z * (a + (z * t))))) / (0.607771387771d0 + (z * (11.9400905721d0 + (z * 31.4690115749d0)))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * 3.13060547623);
	double tmp;
	if (z <= -1.9e+149) {
		tmp = t_1;
	} else if (z <= -8.5e+17) {
		tmp = y * (((x / y) - ((36.52704169880642 - ((t + 457.9610022158428) / z)) / z)) - -3.13060547623);
	} else if (z <= 1.22e-23) {
		tmp = x + ((y * (b + (z * (a + (z * t))))) / (0.607771387771 + (z * (11.9400905721 + (z * 31.4690115749)))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y * 3.13060547623)
	tmp = 0
	if z <= -1.9e+149:
		tmp = t_1
	elif z <= -8.5e+17:
		tmp = y * (((x / y) - ((36.52704169880642 - ((t + 457.9610022158428) / z)) / z)) - -3.13060547623)
	elif z <= 1.22e-23:
		tmp = x + ((y * (b + (z * (a + (z * t))))) / (0.607771387771 + (z * (11.9400905721 + (z * 31.4690115749)))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y * 3.13060547623))
	tmp = 0.0
	if (z <= -1.9e+149)
		tmp = t_1;
	elseif (z <= -8.5e+17)
		tmp = Float64(y * Float64(Float64(Float64(x / y) - Float64(Float64(36.52704169880642 - Float64(Float64(t + 457.9610022158428) / z)) / z)) - -3.13060547623));
	elseif (z <= 1.22e-23)
		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 * 31.4690115749))))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (y * 3.13060547623);
	tmp = 0.0;
	if (z <= -1.9e+149)
		tmp = t_1;
	elseif (z <= -8.5e+17)
		tmp = y * (((x / y) - ((36.52704169880642 - ((t + 457.9610022158428) / z)) / z)) - -3.13060547623);
	elseif (z <= 1.22e-23)
		tmp = x + ((y * (b + (z * (a + (z * t))))) / (0.607771387771 + (z * (11.9400905721 + (z * 31.4690115749)))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.9e+149], t$95$1, If[LessEqual[z, -8.5e+17], N[(y * N[(N[(N[(x / y), $MachinePrecision] - N[(N[(36.52704169880642 - N[(N[(t + 457.9610022158428), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] - -3.13060547623), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.22e-23], 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 * 31.4690115749), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.9e149 or 1.22000000000000007e-23 < z

   1. Initial program 9.4%

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

   3. Simplified 11.1%

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

   5. Taylor expanded in z around inf 91.8%

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

      1. +-commutative 91.8%

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

      2. *-commutative 91.8%

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

   7. Simplified 91.8%

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

   if -1.9e149 < z < -8.5e17

   1. Initial program 23.8%

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

   3. Simplified 29.0%

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

   5. Taylor expanded in y around -inf 29.0%

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

   6. Taylor expanded in z around -inf 90.0%

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

      1. mul-1-neg 90.0%

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

      2. unsub-neg 90.0%

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

      3. mul-1-neg 90.0%

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

      4. unsub-neg 90.0%

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

      5. +-commutative 90.0%

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

   8. Simplified 90.0%

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

   9. Taylor expanded in z around inf 90.1%

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

       1. sub-neg 90.1%

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

   11. Simplified 90.0%

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

   if -8.5e17 < z < 1.22000000000000007e-23

   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 88.4%

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

   4. Taylor expanded in y around 0 98.8%

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

      1. *-commutative 98.8%

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

   6. Simplified 98.8%

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

   7. Taylor expanded in z around 0 98.0%

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

      1. *-commutative 98.0%

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

   9. Simplified 98.0%

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

4. Final simplification 94.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+149}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{+17}:\\ \;\;\;\;y \cdot \left(\left(\frac{x}{y} - \frac{36.52704169880642 - \frac{t + 457.9610022158428}{z}}{z}\right) - -3.13060547623\right)\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{-23}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot t\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot 31.4690115749\right)}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 88.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot 3.13060547623\\ t_2 := x + \left(y \cdot 1.6453555072203998\right) \cdot \left(b + z \cdot a\right)\\ \mathbf{if}\;z \leq -2.25 \cdot 10^{+18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-40}:\\ \;\;\;\;x + \left(b \cdot 1.6453555072203998\right) \cdot \left(y + y \cdot \frac{z \cdot a}{b}\right)\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-120}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-78}:\\ \;\;\;\;x + \frac{y \cdot \left(z \cdot \left(a + z \cdot t\right)\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{-23}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* y 3.13060547623)))
        (t_2 (+ x (* (* y 1.6453555072203998) (+ b (* z a))))))
   (if (<= z -2.25e+18)
     t_1
     (if (<= z -7e-40)
       (+ x (* (* b 1.6453555072203998) (+ y (* y (/ (* z a) b)))))
       (if (<= z 9e-120)
         t_2
         (if (<= z 9e-78)
           (+
            x
            (/
             (* y (* z (+ a (* z t))))
             (+ 0.607771387771 (* z 11.9400905721))))
           (if (<= z 1.22e-23) t_2 t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * 3.13060547623);
	double t_2 = x + ((y * 1.6453555072203998) * (b + (z * a)));
	double tmp;
	if (z <= -2.25e+18) {
		tmp = t_1;
	} else if (z <= -7e-40) {
		tmp = x + ((b * 1.6453555072203998) * (y + (y * ((z * a) / b))));
	} else if (z <= 9e-120) {
		tmp = t_2;
	} else if (z <= 9e-78) {
		tmp = x + ((y * (z * (a + (z * t)))) / (0.607771387771 + (z * 11.9400905721)));
	} else if (z <= 1.22e-23) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = x + (y * 3.13060547623d0)
    t_2 = x + ((y * 1.6453555072203998d0) * (b + (z * a)))
    if (z <= (-2.25d+18)) then
        tmp = t_1
    else if (z <= (-7d-40)) then
        tmp = x + ((b * 1.6453555072203998d0) * (y + (y * ((z * a) / b))))
    else if (z <= 9d-120) then
        tmp = t_2
    else if (z <= 9d-78) then
        tmp = x + ((y * (z * (a + (z * t)))) / (0.607771387771d0 + (z * 11.9400905721d0)))
    else if (z <= 1.22d-23) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * 3.13060547623);
	double t_2 = x + ((y * 1.6453555072203998) * (b + (z * a)));
	double tmp;
	if (z <= -2.25e+18) {
		tmp = t_1;
	} else if (z <= -7e-40) {
		tmp = x + ((b * 1.6453555072203998) * (y + (y * ((z * a) / b))));
	} else if (z <= 9e-120) {
		tmp = t_2;
	} else if (z <= 9e-78) {
		tmp = x + ((y * (z * (a + (z * t)))) / (0.607771387771 + (z * 11.9400905721)));
	} else if (z <= 1.22e-23) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y * 3.13060547623)
	t_2 = x + ((y * 1.6453555072203998) * (b + (z * a)))
	tmp = 0
	if z <= -2.25e+18:
		tmp = t_1
	elif z <= -7e-40:
		tmp = x + ((b * 1.6453555072203998) * (y + (y * ((z * a) / b))))
	elif z <= 9e-120:
		tmp = t_2
	elif z <= 9e-78:
		tmp = x + ((y * (z * (a + (z * t)))) / (0.607771387771 + (z * 11.9400905721)))
	elif z <= 1.22e-23:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y * 3.13060547623))
	t_2 = Float64(x + Float64(Float64(y * 1.6453555072203998) * Float64(b + Float64(z * a))))
	tmp = 0.0
	if (z <= -2.25e+18)
		tmp = t_1;
	elseif (z <= -7e-40)
		tmp = Float64(x + Float64(Float64(b * 1.6453555072203998) * Float64(y + Float64(y * Float64(Float64(z * a) / b)))));
	elseif (z <= 9e-120)
		tmp = t_2;
	elseif (z <= 9e-78)
		tmp = Float64(x + Float64(Float64(y * Float64(z * Float64(a + Float64(z * t)))) / Float64(0.607771387771 + Float64(z * 11.9400905721))));
	elseif (z <= 1.22e-23)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (y * 3.13060547623);
	t_2 = x + ((y * 1.6453555072203998) * (b + (z * a)));
	tmp = 0.0;
	if (z <= -2.25e+18)
		tmp = t_1;
	elseif (z <= -7e-40)
		tmp = x + ((b * 1.6453555072203998) * (y + (y * ((z * a) / b))));
	elseif (z <= 9e-120)
		tmp = t_2;
	elseif (z <= 9e-78)
		tmp = x + ((y * (z * (a + (z * t)))) / (0.607771387771 + (z * 11.9400905721)));
	elseif (z <= 1.22e-23)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y * 1.6453555072203998), $MachinePrecision] * N[(b + N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.25e+18], t$95$1, If[LessEqual[z, -7e-40], N[(x + N[(N[(b * 1.6453555072203998), $MachinePrecision] * N[(y + N[(y * N[(N[(z * a), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9e-120], t$95$2, If[LessEqual[z, 9e-78], N[(x + N[(N[(y * N[(z * N[(a + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(0.607771387771 + N[(z * 11.9400905721), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.22e-23], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.25e18 or 1.22000000000000007e-23 < z

   1. Initial program 13.2%

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

   3. Simplified 15.8%

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

   5. Taylor expanded in z around inf 88.0%

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

      1. +-commutative 88.0%

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

      2. *-commutative 88.0%

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

   7. Simplified 88.0%

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

   if -2.25e18 < z < -7.0000000000000003e-40

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 68.3%

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

   4. Taylor expanded in a around inf 68.3%

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

      1. associate-*r* 68.3%

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

      2. *-commutative 68.3%

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

   6. Simplified 68.3%

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

   7. Taylor expanded in b around inf 78.2%

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

      1. distribute-lft-out 78.2%

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

      2. associate-*r* 78.2%

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

      3. *-commutative 78.2%

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

      4. *-commutative 78.2%

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

      5. associate-*r* 78.2%

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

      6. associate-/l* 77.8%

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

      7. *-commutative 77.8%

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

   9. Simplified 77.8%

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

   if -7.0000000000000003e-40 < z < 9e-120 or 9e-78 < z < 1.22000000000000007e-23

   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 87.0%

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

   4. Taylor expanded in a around inf 89.2%

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

      1. associate-*r* 89.2%

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

      2. *-commutative 89.2%

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

   6. Simplified 89.2%

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

   7. Taylor expanded in b around 0 92.2%

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

      1. associate-*r* 92.2%

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

      2. *-commutative 92.2%

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

      3. associate-*r* 93.3%

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

      4. associate-*r* 93.2%

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

      5. associate-*r* 93.2%

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

      6. distribute-rgt-in 97.6%

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

      7. +-commutative 97.6%

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

      8. distribute-lft-out 97.6%

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

      9. associate-*r* 97.7%

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

      10. *-commutative 97.7%

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

   9. Simplified 97.7%

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

   if 9e-120 < z < 9e-78

   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 99.7%

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

   4. Taylor expanded in y around 0 99.7%

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

      1. *-commutative 99.7%

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

   6. Simplified 99.7%

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

   7. Taylor expanded in b around 0 87.9%

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

   8. Taylor expanded in z around 0 87.9%

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

      1. *-commutative 99.7%

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

   10. Simplified 87.9%

       \[\leadsto x + \frac{y \cdot \left(z \cdot \left(a + t \cdot z\right)\right)}{\color{blue}{z \cdot 11.9400905721} + 0.607771387771} \]
3. Recombined 4 regimes into one program.

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{+18}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-40}:\\ \;\;\;\;x + \left(b \cdot 1.6453555072203998\right) \cdot \left(y + y \cdot \frac{z \cdot a}{b}\right)\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-120}:\\ \;\;\;\;x + \left(y \cdot 1.6453555072203998\right) \cdot \left(b + z \cdot a\right)\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-78}:\\ \;\;\;\;x + \frac{y \cdot \left(z \cdot \left(a + z \cdot t\right)\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{-23}:\\ \;\;\;\;x + \left(y \cdot 1.6453555072203998\right) \cdot \left(b + z \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 91.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot 3.13060547623\\ \mathbf{if}\;z \leq -2 \cdot 10^{+153}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{+16}:\\ \;\;\;\;y \cdot \left(\left(\frac{x}{y} - \frac{36.52704169880642 - \frac{t + 457.9610022158428}{z}}{z}\right) - -3.13060547623\right)\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{-23}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot t\right)\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* y 3.13060547623))))
   (if (<= z -2e+153)
     t_1
     (if (<= z -3.2e+16)
       (*
        y
        (-
         (- (/ x y) (/ (- 36.52704169880642 (/ (+ t 457.9610022158428) z)) z))
         -3.13060547623))
       (if (<= z 1.22e-23)
         (+
          x
          (/
           (* y (+ b (* z (+ a (* z t)))))
           (+ 0.607771387771 (* z 11.9400905721))))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * 3.13060547623);
	double tmp;
	if (z <= -2e+153) {
		tmp = t_1;
	} else if (z <= -3.2e+16) {
		tmp = y * (((x / y) - ((36.52704169880642 - ((t + 457.9610022158428) / z)) / z)) - -3.13060547623);
	} else if (z <= 1.22e-23) {
		tmp = x + ((y * (b + (z * (a + (z * t))))) / (0.607771387771 + (z * 11.9400905721)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * 3.13060547623d0)
    if (z <= (-2d+153)) then
        tmp = t_1
    else if (z <= (-3.2d+16)) then
        tmp = y * (((x / y) - ((36.52704169880642d0 - ((t + 457.9610022158428d0) / z)) / z)) - (-3.13060547623d0))
    else if (z <= 1.22d-23) then
        tmp = x + ((y * (b + (z * (a + (z * t))))) / (0.607771387771d0 + (z * 11.9400905721d0)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * 3.13060547623);
	double tmp;
	if (z <= -2e+153) {
		tmp = t_1;
	} else if (z <= -3.2e+16) {
		tmp = y * (((x / y) - ((36.52704169880642 - ((t + 457.9610022158428) / z)) / z)) - -3.13060547623);
	} else if (z <= 1.22e-23) {
		tmp = x + ((y * (b + (z * (a + (z * t))))) / (0.607771387771 + (z * 11.9400905721)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y * 3.13060547623)
	tmp = 0
	if z <= -2e+153:
		tmp = t_1
	elif z <= -3.2e+16:
		tmp = y * (((x / y) - ((36.52704169880642 - ((t + 457.9610022158428) / z)) / z)) - -3.13060547623)
	elif z <= 1.22e-23:
		tmp = x + ((y * (b + (z * (a + (z * t))))) / (0.607771387771 + (z * 11.9400905721)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y * 3.13060547623))
	tmp = 0.0
	if (z <= -2e+153)
		tmp = t_1;
	elseif (z <= -3.2e+16)
		tmp = Float64(y * Float64(Float64(Float64(x / y) - Float64(Float64(36.52704169880642 - Float64(Float64(t + 457.9610022158428) / z)) / z)) - -3.13060547623));
	elseif (z <= 1.22e-23)
		tmp = Float64(x + Float64(Float64(y * Float64(b + Float64(z * Float64(a + Float64(z * t))))) / Float64(0.607771387771 + Float64(z * 11.9400905721))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (y * 3.13060547623);
	tmp = 0.0;
	if (z <= -2e+153)
		tmp = t_1;
	elseif (z <= -3.2e+16)
		tmp = y * (((x / y) - ((36.52704169880642 - ((t + 457.9610022158428) / z)) / z)) - -3.13060547623);
	elseif (z <= 1.22e-23)
		tmp = x + ((y * (b + (z * (a + (z * t))))) / (0.607771387771 + (z * 11.9400905721)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2e+153], t$95$1, If[LessEqual[z, -3.2e+16], N[(y * N[(N[(N[(x / y), $MachinePrecision] - N[(N[(36.52704169880642 - N[(N[(t + 457.9610022158428), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] - -3.13060547623), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.22e-23], N[(x + N[(N[(y * N[(b + N[(z * N[(a + N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(0.607771387771 + N[(z * 11.9400905721), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2e153 or 1.22000000000000007e-23 < z

   1. Initial program 9.4%

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

   3. Simplified 11.1%

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

   5. Taylor expanded in z around inf 91.8%

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

      1. +-commutative 91.8%

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

      2. *-commutative 91.8%

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

   7. Simplified 91.8%

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

   if -2e153 < z < -3.2e16

   1. Initial program 23.8%

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

   3. Simplified 29.0%

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

   5. Taylor expanded in y around -inf 29.0%

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

   6. Taylor expanded in z around -inf 90.0%

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

      1. mul-1-neg 90.0%

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

      2. unsub-neg 90.0%

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

      3. mul-1-neg 90.0%

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

      4. unsub-neg 90.0%

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

      5. +-commutative 90.0%

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

   8. Simplified 90.0%

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

   9. Taylor expanded in z around inf 90.1%

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

       1. sub-neg 90.1%

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

   11. Simplified 90.0%

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

   if -3.2e16 < z < 1.22000000000000007e-23

   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 88.4%

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

   4. Taylor expanded in y around 0 98.8%

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

      1. *-commutative 98.8%

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

   6. Simplified 98.8%

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

   7. Taylor expanded in z around 0 96.1%

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

      1. *-commutative 96.1%

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

   9. Simplified 96.1%

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

4. Final simplification 93.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+153}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{+16}:\\ \;\;\;\;y \cdot \left(\left(\frac{x}{y} - \frac{36.52704169880642 - \frac{t + 457.9610022158428}{z}}{z}\right) - -3.13060547623\right)\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{-23}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot t\right)\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 89.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{+149}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{+16}:\\ \;\;\;\;y \cdot \left(\left(\frac{x}{y} - \frac{36.52704169880642 - \frac{t + 457.9610022158428}{z}}{z}\right) - -3.13060547623\right)\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{-27}:\\ \;\;\;\;x + \left(y \cdot 1.6453555072203998\right) \cdot \left(b + z \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + \left(y \cdot 3.13060547623 + 11.1667541262 \cdot \frac{y}{z}\right)\right) - \frac{y}{z} \cdot 47.69379582500642\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -2.05e+149)
   (+ x (* y 3.13060547623))
   (if (<= z -6.2e+16)
     (*
      y
      (-
       (- (/ x y) (/ (- 36.52704169880642 (/ (+ t 457.9610022158428) z)) z))
       -3.13060547623))
     (if (<= z 1.06e-27)
       (+ x (* (* y 1.6453555072203998) (+ b (* z a))))
       (-
        (+ 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 <= -2.05e+149) {
		tmp = x + (y * 3.13060547623);
	} else if (z <= -6.2e+16) {
		tmp = y * (((x / y) - ((36.52704169880642 - ((t + 457.9610022158428) / z)) / z)) - -3.13060547623);
	} else if (z <= 1.06e-27) {
		tmp = x + ((y * 1.6453555072203998) * (b + (z * a)));
	} 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 <= (-2.05d+149)) then
        tmp = x + (y * 3.13060547623d0)
    else if (z <= (-6.2d+16)) then
        tmp = y * (((x / y) - ((36.52704169880642d0 - ((t + 457.9610022158428d0) / z)) / z)) - (-3.13060547623d0))
    else if (z <= 1.06d-27) then
        tmp = x + ((y * 1.6453555072203998d0) * (b + (z * a)))
    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 <= -2.05e+149) {
		tmp = x + (y * 3.13060547623);
	} else if (z <= -6.2e+16) {
		tmp = y * (((x / y) - ((36.52704169880642 - ((t + 457.9610022158428) / z)) / z)) - -3.13060547623);
	} else if (z <= 1.06e-27) {
		tmp = x + ((y * 1.6453555072203998) * (b + (z * a)));
	} 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 <= -2.05e+149:
		tmp = x + (y * 3.13060547623)
	elif z <= -6.2e+16:
		tmp = y * (((x / y) - ((36.52704169880642 - ((t + 457.9610022158428) / z)) / z)) - -3.13060547623)
	elif z <= 1.06e-27:
		tmp = x + ((y * 1.6453555072203998) * (b + (z * a)))
	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 <= -2.05e+149)
		tmp = Float64(x + Float64(y * 3.13060547623));
	elseif (z <= -6.2e+16)
		tmp = Float64(y * Float64(Float64(Float64(x / y) - Float64(Float64(36.52704169880642 - Float64(Float64(t + 457.9610022158428) / z)) / z)) - -3.13060547623));
	elseif (z <= 1.06e-27)
		tmp = Float64(x + Float64(Float64(y * 1.6453555072203998) * Float64(b + Float64(z * a))));
	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 <= -2.05e+149)
		tmp = x + (y * 3.13060547623);
	elseif (z <= -6.2e+16)
		tmp = y * (((x / y) - ((36.52704169880642 - ((t + 457.9610022158428) / z)) / z)) - -3.13060547623);
	elseif (z <= 1.06e-27)
		tmp = x + ((y * 1.6453555072203998) * (b + (z * a)));
	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, -2.05e+149], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -6.2e+16], N[(y * N[(N[(N[(x / y), $MachinePrecision] - N[(N[(36.52704169880642 - N[(N[(t + 457.9610022158428), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] - -3.13060547623), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.06e-27], N[(x + N[(N[(y * 1.6453555072203998), $MachinePrecision] * N[(b + N[(z * a), $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 4 regimes

2. if z < -2.0499999999999998e149

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in z around inf 100.0%

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

      1. +-commutative 100.0%

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

      2. *-commutative 100.0%

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

   7. Simplified 100.0%

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

   if -2.0499999999999998e149 < z < -6.2e16

   1. Initial program 23.8%

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

   3. Simplified 29.0%

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

   5. Taylor expanded in y around -inf 29.0%

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

   6. Taylor expanded in z around -inf 90.0%

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

      1. mul-1-neg 90.0%

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

      2. unsub-neg 90.0%

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

      3. mul-1-neg 90.0%

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

      4. unsub-neg 90.0%

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

      5. +-commutative 90.0%

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

   8. Simplified 90.0%

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

   9. Taylor expanded in z around inf 90.1%

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

       1. sub-neg 90.1%

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

   11. Simplified 90.0%

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

   if -6.2e16 < z < 1.05999999999999998e-27

   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 83.5%

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

   4. Taylor expanded in a around inf 85.3%

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

      1. associate-*r* 85.3%

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

      2. *-commutative 85.3%

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

   6. Simplified 85.3%

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

   7. Taylor expanded in b around 0 87.9%

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

      1. associate-*r* 87.9%

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

      2. *-commutative 87.9%

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

      3. associate-*r* 88.8%

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

      4. associate-*r* 88.8%

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

      5. associate-*r* 88.7%

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

      6. distribute-rgt-in 92.4%

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

      7. +-commutative 92.4%

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

      8. distribute-lft-out 92.4%

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

      9. associate-*r* 92.5%

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

      10. *-commutative 92.5%

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

   9. Simplified 92.5%

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

   if 1.05999999999999998e-27 < z

   1. Initial program 16.9%

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

   3. Simplified 19.5%

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

   5. Taylor expanded in z around inf 86.4%

      \[\leadsto \color{blue}{\left(x + \left(3.13060547623 \cdot y + 11.1667541262 \cdot \frac{y}{z}\right)\right) - 47.69379582500642 \cdot \frac{y}{z}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{+149}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{+16}:\\ \;\;\;\;y \cdot \left(\left(\frac{x}{y} - \frac{36.52704169880642 - \frac{t + 457.9610022158428}{z}}{z}\right) - -3.13060547623\right)\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{-27}:\\ \;\;\;\;x + \left(y \cdot 1.6453555072203998\right) \cdot \left(b + z \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + \left(y \cdot 3.13060547623 + 11.1667541262 \cdot \frac{y}{z}\right)\right) - \frac{y}{z} \cdot 47.69379582500642\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 49.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{-94}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -5.9 \cdot 10^{-120} \lor \neg \left(x \leq -4.8 \cdot 10^{-144}\right) \land x \leq 10^{+69}:\\ \;\;\;\;y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -2.9e-94)
   x
   (if (or (<= x -5.9e-120) (and (not (<= x -4.8e-144)) (<= x 1e+69)))
     (* y 3.13060547623)
     x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -2.9e-94) {
		tmp = x;
	} else if ((x <= -5.9e-120) || (!(x <= -4.8e-144) && (x <= 1e+69))) {
		tmp = y * 3.13060547623;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-2.9d-94)) then
        tmp = x
    else if ((x <= (-5.9d-120)) .or. (.not. (x <= (-4.8d-144))) .and. (x <= 1d+69)) then
        tmp = y * 3.13060547623d0
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -2.9e-94) {
		tmp = x;
	} else if ((x <= -5.9e-120) || (!(x <= -4.8e-144) && (x <= 1e+69))) {
		tmp = y * 3.13060547623;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -2.9e-94:
		tmp = x
	elif (x <= -5.9e-120) or (not (x <= -4.8e-144) and (x <= 1e+69)):
		tmp = y * 3.13060547623
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -2.9e-94)
		tmp = x;
	elseif ((x <= -5.9e-120) || (!(x <= -4.8e-144) && (x <= 1e+69)))
		tmp = Float64(y * 3.13060547623);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -2.9e-94)
		tmp = x;
	elseif ((x <= -5.9e-120) || (~((x <= -4.8e-144)) && (x <= 1e+69)))
		tmp = y * 3.13060547623;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -2.9e-94], x, If[Or[LessEqual[x, -5.9e-120], And[N[Not[LessEqual[x, -4.8e-144]], $MachinePrecision], LessEqual[x, 1e+69]]], N[(y * 3.13060547623), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -2.89999999999999995e-94 or -5.89999999999999979e-120 < x < -4.79999999999999988e-144 or 1.0000000000000001e69 < x

   1. Initial program 50.5%

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

   3. Simplified 52.7%

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

   5. Taylor expanded in y around 0 70.6%

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

   if -2.89999999999999995e-94 < x < -5.89999999999999979e-120 or -4.79999999999999988e-144 < x < 1.0000000000000001e69

   1. Initial program 50.2%

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

   3. Simplified 51.0%

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

   5. Taylor expanded in z around inf 53.6%

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

   6. Taylor expanded in y around inf 44.5%

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

4. Final simplification 57.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{-94}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -5.9 \cdot 10^{-120} \lor \neg \left(x \leq -4.8 \cdot 10^{-144}\right) \land x \leq 10^{+69}:\\ \;\;\;\;y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 89.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+23} \lor \neg \left(z \leq 1.06 \cdot 10^{-27}\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot 1.6453555072203998\right) \cdot \left(b + z \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2.6e+23) (not (<= z 1.06e-27)))
   (+ 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 <= -2.6e+23) || !(z <= 1.06e-27)) {
		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 <= (-2.6d+23)) .or. (.not. (z <= 1.06d-27))) 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 <= -2.6e+23) || !(z <= 1.06e-27)) {
		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 <= -2.6e+23) or not (z <= 1.06e-27):
		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 <= -2.6e+23) || !(z <= 1.06e-27))
		tmp = Float64(x + Float64(y * 3.13060547623));
	else
		tmp = Float64(x + Float64(Float64(y * 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 <= -2.6e+23) || ~((z <= 1.06e-27)))
		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, -2.6e+23], N[Not[LessEqual[z, 1.06e-27]], $MachinePrecision]], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * 1.6453555072203998), $MachinePrecision] * N[(b + N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.59999999999999992e23 or 1.05999999999999998e-27 < z

   1. Initial program 12.7%

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

   3. Simplified 15.3%

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

   5. Taylor expanded in z around inf 87.1%

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

      1. +-commutative 87.1%

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

      2. *-commutative 87.1%

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

   7. Simplified 87.1%

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

   if -2.59999999999999992e23 < z < 1.05999999999999998e-27

   1. Initial program 98.8%

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

   3. Taylor expanded in z around 0 82.4%

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

   4. Taylor expanded in a around inf 84.2%

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

      1. associate-*r* 84.2%

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

      2. *-commutative 84.2%

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

   6. Simplified 84.2%

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

   7. Taylor expanded in b around 0 86.7%

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

      1. associate-*r* 86.7%

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

      2. *-commutative 86.7%

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

      3. associate-*r* 86.7%

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

      4. associate-*r* 86.6%

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

      5. associate-*r* 86.6%

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

      6. distribute-rgt-in 90.2%

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

      7. +-commutative 90.2%

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

      8. distribute-lft-out 90.2%

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

      9. associate-*r* 90.3%

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

      10. *-commutative 90.3%

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

   9. Simplified 90.3%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+23} \lor \neg \left(z \leq 1.06 \cdot 10^{-27}\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot 1.6453555072203998\right) \cdot \left(b + z \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 88.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+22}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{elif}\;z \leq 6.1 \cdot 10^{-47}:\\ \;\;\;\;x + \left(y \cdot 1.6453555072203998\right) \cdot \left(b + z \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 - \frac{y \cdot 36.52704169880642}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -4.5e+22)
   (+ x (* y 3.13060547623))
   (if (<= z 6.1e-47)
     (+ 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 <= -4.5e+22) {
		tmp = x + (y * 3.13060547623);
	} else if (z <= 6.1e-47) {
		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 <= (-4.5d+22)) then
        tmp = x + (y * 3.13060547623d0)
    else if (z <= 6.1d-47) 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 <= -4.5e+22) {
		tmp = x + (y * 3.13060547623);
	} else if (z <= 6.1e-47) {
		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 <= -4.5e+22:
		tmp = x + (y * 3.13060547623)
	elif z <= 6.1e-47:
		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 <= -4.5e+22)
		tmp = Float64(x + Float64(y * 3.13060547623));
	elseif (z <= 6.1e-47)
		tmp = Float64(x + Float64(Float64(y * 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 <= -4.5e+22)
		tmp = x + (y * 3.13060547623);
	elseif (z <= 6.1e-47)
		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, -4.5e+22], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.1e-47], N[(x + N[(N[(y * 1.6453555072203998), $MachinePrecision] * N[(b + N[(z * a), $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 < -4.4999999999999998e22

   1. Initial program 8.3%

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

   3. Simplified 11.0%

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

   5. Taylor expanded in z around inf 88.0%

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

      1. +-commutative 88.0%

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

      2. *-commutative 88.0%

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

   7. Simplified 88.0%

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

   if -4.4999999999999998e22 < z < 6.1e-47

   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 83.6%

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

      1. associate-*r* 83.6%

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

      2. *-commutative 83.6%

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

   6. Simplified 83.6%

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

   7. Taylor expanded in b around 0 86.2%

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

      1. associate-*r* 86.2%

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

      2. *-commutative 86.2%

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

      3. associate-*r* 87.1%

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

      4. associate-*r* 87.1%

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

      5. associate-*r* 87.0%

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

      6. distribute-rgt-in 90.7%

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

      7. +-commutative 90.7%

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

      8. distribute-lft-out 90.7%

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

      9. associate-*r* 90.8%

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

      10. *-commutative 90.8%

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

   9. Simplified 90.8%

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

   if 6.1e-47 < z

   1. Initial program 20.2%

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

   3. Taylor expanded in z around -inf 85.7%

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

      1. +-commutative 85.7%

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

      2. mul-1-neg 85.7%

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

      3. unsub-neg 85.7%

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

      4. *-commutative 85.7%

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

      5. distribute-rgt-out-- 85.7%

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

      6. metadata-eval 85.7%

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

   5. Simplified 85.7%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+22}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{elif}\;z \leq 6.1 \cdot 10^{-47}:\\ \;\;\;\;x + \left(y \cdot 1.6453555072203998\right) \cdot \left(b + z \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 - \frac{y \cdot 36.52704169880642}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 82.5% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.6 \cdot 10^{+24} \lor \neg \left(z \leq 1.22 \cdot 10^{-23}\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(y \cdot 1.6453555072203998\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -9.6e+24) (not (<= z 1.22e-23)))
   (+ x (* y 3.13060547623))
   (+ x (* b (* y 1.6453555072203998)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -9.6e+24) || !(z <= 1.22e-23)) {
		tmp = x + (y * 3.13060547623);
	} else {
		tmp = x + (b * (y * 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 <= (-9.6d+24)) .or. (.not. (z <= 1.22d-23))) then
        tmp = x + (y * 3.13060547623d0)
    else
        tmp = x + (b * (y * 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 <= -9.6e+24) || !(z <= 1.22e-23)) {
		tmp = x + (y * 3.13060547623);
	} else {
		tmp = x + (b * (y * 1.6453555072203998));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -9.6e+24) or not (z <= 1.22e-23):
		tmp = x + (y * 3.13060547623)
	else:
		tmp = x + (b * (y * 1.6453555072203998))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -9.6e+24) || !(z <= 1.22e-23))
		tmp = Float64(x + Float64(y * 3.13060547623));
	else
		tmp = Float64(x + Float64(b * Float64(y * 1.6453555072203998)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -9.6e+24) || ~((z <= 1.22e-23)))
		tmp = x + (y * 3.13060547623);
	else
		tmp = x + (b * (y * 1.6453555072203998));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -9.6e+24], N[Not[LessEqual[z, 1.22e-23]], $MachinePrecision]], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision], N[(x + N[(b * N[(y * 1.6453555072203998), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.6000000000000003e24 or 1.22000000000000007e-23 < z

   1. Initial program 11.4%

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

   3. Simplified 14.1%

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

   5. Taylor expanded in z around inf 87.6%

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

      1. +-commutative 87.6%

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

      2. *-commutative 87.6%

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

   7. Simplified 87.6%

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

   if -9.6000000000000003e24 < z < 1.22000000000000007e-23

   1. Initial program 98.8%

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

   3. Taylor expanded in z around 0 93.8%

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

      1. *-commutative 93.7%

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

   5. Simplified 93.8%

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

   6. Taylor expanded in z around 0 79.8%

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

      1. *-commutative 79.8%

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

      2. associate-*l* 79.8%

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

   8. Simplified 79.8%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.6 \cdot 10^{+24} \lor \neg \left(z \leq 1.22 \cdot 10^{-23}\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(y \cdot 1.6453555072203998\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 62.3% accurate, 7.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 50.3%

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

3. Simplified 51.8%

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

5. Taylor expanded in z around inf 66.4%

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

   1. +-commutative 66.4%

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

   2. *-commutative 66.4%

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

7. Simplified 66.4%

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

8. Final simplification 66.4%

   \[\leadsto x + y \cdot 3.13060547623 \]
9. Add Preprocessing

Alternative 18: 44.9% 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 50.3%

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

3. Simplified 51.8%

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

5. Taylor expanded in y around 0 43.1%

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

Developer target: 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 2024107 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, D"
  :precision binary64

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

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