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

Percentage Accurate: 58.1% → 97.8%

Time: 19.2s

Alternatives: 20

Speedup: 2.5×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 58.1% 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, 0.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 92.7%

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

   3. Simplified 97.9%

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

   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%

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

      1. remove-double-neg 0.0%

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

      2. distribute-lft-neg-out 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in z around -inf 85.1%

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

   6. Taylor expanded in t around inf 85.1%

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

      1. mul-1-neg 85.1%

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

      2. associate-/l* 96.8%

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

      3. distribute-lft-neg-in 96.8%

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

   8. Simplified 96.8%

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

   9. Taylor expanded in y around -inf 97.9%

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

       1. associate-/l* 100.0%

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

       2. sub-neg 100.0%

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

       3. metadata-eval 100.0%

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

   11. Simplified 100.0%

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

4. Final simplification 98.6%

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

Alternative 2: 97.2% accurate, 0.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 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. Step-by-step derivation

      1. remove-double-neg 92.7%

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

      2. distribute-lft-neg-out 92.7%

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

   3. Simplified 92.7%

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

   5. Taylor expanded in y around 0 92.7%

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

   7. Simplified 96.2%

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

   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%

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

      1. remove-double-neg 0.0%

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

      2. distribute-lft-neg-out 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in z around -inf 85.1%

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

   6. Taylor expanded in t around inf 85.1%

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

      1. mul-1-neg 85.1%

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

      2. associate-/l* 96.8%

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

      3. distribute-lft-neg-in 96.8%

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

   8. Simplified 96.8%

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

   9. Taylor expanded in y around -inf 97.9%

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

       1. associate-/l* 100.0%

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

       2. sub-neg 100.0%

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

       3. metadata-eval 100.0%

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

   11. Simplified 100.0%

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

4. Final simplification 97.5%

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

Alternative 3: 96.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+52}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+55}:\\ \;\;\;\;x + \frac{y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \frac{\mathsf{fma}\left(z, z, -232.09570038900438\right)}{z + -15.234687407}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot \frac{\frac{t}{z} + -36.52704169880642}{z} + y \cdot 3.13060547623\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -9.2e+52)
   (+ x (* y 3.13060547623))
   (if (<= z 4.5e+55)
     (+
      x
      (/
       (*
        y
        (+
         (* z (+ (* z (+ (* z (+ (* z 3.13060547623) 11.1667541262)) t)) a))
         b))
       (+
        0.607771387771
        (*
         z
         (+
          11.9400905721
          (*
           z
           (+
            31.4690115749
            (* z (/ (fma z z -232.09570038900438) (+ z -15.234687407))))))))))
     (+
      x
      (+ (* y (/ (+ (/ t z) -36.52704169880642) z)) (* y 3.13060547623))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -9.2e+52) {
		tmp = x + (y * 3.13060547623);
	} else if (z <= 4.5e+55) {
		tmp = x + ((y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * (fma(z, z, -232.09570038900438) / (z + -15.234687407)))))))));
	} else {
		tmp = x + ((y * (((t / z) + -36.52704169880642) / z)) + (y * 3.13060547623));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -9.2e+52)
		tmp = Float64(x + Float64(y * 3.13060547623));
	elseif (z <= 4.5e+55)
		tmp = Float64(x + Float64(Float64(y * Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / Float64(0.607771387771 + Float64(z * Float64(11.9400905721 + Float64(z * Float64(31.4690115749 + Float64(z * Float64(fma(z, z, -232.09570038900438) / Float64(z + -15.234687407))))))))));
	else
		tmp = Float64(x + Float64(Float64(y * Float64(Float64(Float64(t / z) + -36.52704169880642) / z)) + Float64(y * 3.13060547623)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -9.2e+52], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.5e+55], N[(x + 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[(0.607771387771 + N[(z * N[(11.9400905721 + N[(z * N[(31.4690115749 + N[(z * N[(N[(z * z + -232.09570038900438), $MachinePrecision] / N[(z + -15.234687407), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * N[(N[(N[(t / z), $MachinePrecision] + -36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.1999999999999999e52

   1. Initial program 4.8%

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

   3. Simplified 9.5%

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

   5. Taylor expanded in z around inf 97.8%

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

      1. +-commutative 97.8%

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

   7. Simplified 97.8%

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

   if -9.1999999999999999e52 < z < 4.49999999999999998e55

   1. Initial program 96.6%

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

      1. flip-+ 96.6%

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

      2. div-inv 96.6%

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

      3. fmm-def 96.6%

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

      4. metadata-eval 96.6%

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

      5. metadata-eval 96.6%

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

      6. sub-neg 96.6%

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

      7. metadata-eval 96.6%

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

   4. Applied egg-rr 96.6%

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

      1. associate-*r/ 96.6%

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

      2. *-rgt-identity 96.6%

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

   6. Simplified 96.6%

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

   if 4.49999999999999998e55 < z

   1. Initial program 5.1%

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

      1. remove-double-neg 5.1%

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

      2. distribute-lft-neg-out 5.1%

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

   3. Simplified 5.1%

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

   5. Taylor expanded in z around -inf 87.2%

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

   6. Taylor expanded in t around inf 87.2%

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

      1. mul-1-neg 87.2%

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

      2. associate-/l* 95.2%

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

      3. distribute-lft-neg-in 95.2%

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

   8. Simplified 95.2%

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

   9. Taylor expanded in y around -inf 96.8%

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

       1. associate-/l* 100.0%

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

       2. sub-neg 100.0%

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

       3. metadata-eval 100.0%

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

   11. Simplified 100.0%

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

4. Final simplification 97.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+52}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+55}:\\ \;\;\;\;x + \frac{y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \frac{\mathsf{fma}\left(z, z, -232.09570038900438\right)}{z + -15.234687407}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot \frac{\frac{t}{z} + -36.52704169880642}{z} + y \cdot 3.13060547623\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 96.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+52}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+55}:\\ \;\;\;\;x + \frac{y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right)}{0.607771387771 + z \cdot \left(11.9400905721 - z \cdot \left(z \cdot \left(z \cdot \left(-1 - \frac{15.234687407}{z}\right)\right) - 31.4690115749\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot \frac{\frac{t}{z} + -36.52704169880642}{z} + y \cdot 3.13060547623\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.2e+52)
   (+ x (* y 3.13060547623))
   (if (<= z 7.8e+55)
     (+
      x
      (/
       (*
        y
        (+
         (* z (+ (* z (+ (* z (+ (* z 3.13060547623) 11.1667541262)) t)) a))
         b))
       (+
        0.607771387771
        (*
         z
         (-
          11.9400905721
          (* z (- (* z (* z (- -1.0 (/ 15.234687407 z)))) 31.4690115749)))))))
     (+
      x
      (+ (* y (/ (+ (/ t z) -36.52704169880642) z)) (* y 3.13060547623))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.2e+52) {
		tmp = x + (y * 3.13060547623);
	} else if (z <= 7.8e+55) {
		tmp = x + ((y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / (0.607771387771 + (z * (11.9400905721 - (z * ((z * (z * (-1.0 - (15.234687407 / z)))) - 31.4690115749))))));
	} else {
		tmp = x + ((y * (((t / z) + -36.52704169880642) / z)) + (y * 3.13060547623));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-1.2d+52)) then
        tmp = x + (y * 3.13060547623d0)
    else if (z <= 7.8d+55) then
        tmp = x + ((y * ((z * ((z * ((z * ((z * 3.13060547623d0) + 11.1667541262d0)) + t)) + a)) + b)) / (0.607771387771d0 + (z * (11.9400905721d0 - (z * ((z * (z * ((-1.0d0) - (15.234687407d0 / z)))) - 31.4690115749d0))))))
    else
        tmp = x + ((y * (((t / z) + (-36.52704169880642d0)) / z)) + (y * 3.13060547623d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.2e+52) {
		tmp = x + (y * 3.13060547623);
	} else if (z <= 7.8e+55) {
		tmp = x + ((y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / (0.607771387771 + (z * (11.9400905721 - (z * ((z * (z * (-1.0 - (15.234687407 / z)))) - 31.4690115749))))));
	} else {
		tmp = x + ((y * (((t / z) + -36.52704169880642) / z)) + (y * 3.13060547623));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.2e+52:
		tmp = x + (y * 3.13060547623)
	elif z <= 7.8e+55:
		tmp = x + ((y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / (0.607771387771 + (z * (11.9400905721 - (z * ((z * (z * (-1.0 - (15.234687407 / z)))) - 31.4690115749))))))
	else:
		tmp = x + ((y * (((t / z) + -36.52704169880642) / z)) + (y * 3.13060547623))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.2e+52)
		tmp = Float64(x + Float64(y * 3.13060547623));
	elseif (z <= 7.8e+55)
		tmp = Float64(x + Float64(Float64(y * Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / Float64(0.607771387771 + Float64(z * Float64(11.9400905721 - Float64(z * Float64(Float64(z * Float64(z * Float64(-1.0 - Float64(15.234687407 / z)))) - 31.4690115749)))))));
	else
		tmp = Float64(x + Float64(Float64(y * Float64(Float64(Float64(t / z) + -36.52704169880642) / z)) + Float64(y * 3.13060547623)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1.2e+52)
		tmp = x + (y * 3.13060547623);
	elseif (z <= 7.8e+55)
		tmp = x + ((y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / (0.607771387771 + (z * (11.9400905721 - (z * ((z * (z * (-1.0 - (15.234687407 / z)))) - 31.4690115749))))));
	else
		tmp = x + ((y * (((t / z) + -36.52704169880642) / z)) + (y * 3.13060547623));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.2e+52], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.8e+55], N[(x + 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[(0.607771387771 + N[(z * N[(11.9400905721 - N[(z * N[(N[(z * N[(z * N[(-1.0 - N[(15.234687407 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 31.4690115749), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * N[(N[(N[(t / z), $MachinePrecision] + -36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.2e52

   1. Initial program 4.8%

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

   3. Simplified 9.5%

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

   5. Taylor expanded in z around inf 97.8%

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

      1. +-commutative 97.8%

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

   7. Simplified 97.8%

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

   if -1.2e52 < z < 7.80000000000000054e55

   1. Initial program 96.6%

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

   3. Taylor expanded in z around inf 96.6%

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

      1. associate-*r/ 96.6%

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

      2. metadata-eval 96.6%

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

   5. Simplified 96.6%

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

   if 7.80000000000000054e55 < z

   1. Initial program 5.1%

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

      1. remove-double-neg 5.1%

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

      2. distribute-lft-neg-out 5.1%

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

   3. Simplified 5.1%

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

   5. Taylor expanded in z around -inf 87.2%

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

   6. Taylor expanded in t around inf 87.2%

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

      1. mul-1-neg 87.2%

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

      2. associate-/l* 95.2%

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

      3. distribute-lft-neg-in 95.2%

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

   8. Simplified 95.2%

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

   9. Taylor expanded in y around -inf 96.8%

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

       1. associate-/l* 100.0%

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

       2. sub-neg 100.0%

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

       3. metadata-eval 100.0%

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

   11. Simplified 100.0%

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

4. Final simplification 97.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+52}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+55}:\\ \;\;\;\;x + \frac{y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right)}{0.607771387771 + z \cdot \left(11.9400905721 - z \cdot \left(z \cdot \left(z \cdot \left(-1 - \frac{15.234687407}{z}\right)\right) - 31.4690115749\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot \frac{\frac{t}{z} + -36.52704169880642}{z} + y \cdot 3.13060547623\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 96.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+52}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+55}:\\ \;\;\;\;\frac{y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771} + x\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot \frac{\frac{t}{z} + -36.52704169880642}{z} + y \cdot 3.13060547623\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.55e+52)
   (+ x (* y 3.13060547623))
   (if (<= z 4.5e+55)
     (+
      (/
       (*
        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)
     (+
      x
      (+ (* y (/ (+ (/ t z) -36.52704169880642) z)) (* y 3.13060547623))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.55e+52) {
		tmp = x + (y * 3.13060547623);
	} else if (z <= 4.5e+55) {
		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;
	} else {
		tmp = x + ((y * (((t / z) + -36.52704169880642) / z)) + (y * 3.13060547623));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-1.55d+52)) then
        tmp = x + (y * 3.13060547623d0)
    else if (z <= 4.5d+55) then
        tmp = ((y * ((z * ((z * ((z * ((z * 3.13060547623d0) + 11.1667541262d0)) + t)) + a)) + b)) / ((z * ((z * ((z * (z + 15.234687407d0)) + 31.4690115749d0)) + 11.9400905721d0)) + 0.607771387771d0)) + x
    else
        tmp = x + ((y * (((t / z) + (-36.52704169880642d0)) / z)) + (y * 3.13060547623d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.55e+52) {
		tmp = x + (y * 3.13060547623);
	} else if (z <= 4.5e+55) {
		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;
	} else {
		tmp = x + ((y * (((t / z) + -36.52704169880642) / z)) + (y * 3.13060547623));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.55e+52:
		tmp = x + (y * 3.13060547623)
	elif z <= 4.5e+55:
		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
	else:
		tmp = x + ((y * (((t / z) + -36.52704169880642) / z)) + (y * 3.13060547623))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.55e+52)
		tmp = Float64(x + Float64(y * 3.13060547623));
	elseif (z <= 4.5e+55)
		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);
	else
		tmp = Float64(x + Float64(Float64(y * Float64(Float64(Float64(t / z) + -36.52704169880642) / z)) + Float64(y * 3.13060547623)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1.55e+52)
		tmp = x + (y * 3.13060547623);
	elseif (z <= 4.5e+55)
		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;
	else
		tmp = x + ((y * (((t / z) + -36.52704169880642) / z)) + (y * 3.13060547623));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.55e+52], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.5e+55], 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], N[(x + N[(N[(y * N[(N[(N[(t / z), $MachinePrecision] + -36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.55e52

   1. Initial program 4.8%

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

   3. Simplified 9.5%

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

   5. Taylor expanded in z around inf 97.8%

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

      1. +-commutative 97.8%

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

   7. Simplified 97.8%

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

   if -1.55e52 < z < 4.49999999999999998e55

   1. Initial program 96.6%

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

   if 4.49999999999999998e55 < z

   1. Initial program 5.1%

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

      1. remove-double-neg 5.1%

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

      2. distribute-lft-neg-out 5.1%

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

   3. Simplified 5.1%

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

   5. Taylor expanded in z around -inf 87.2%

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

   6. Taylor expanded in t around inf 87.2%

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

      1. mul-1-neg 87.2%

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

      2. associate-/l* 95.2%

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

      3. distribute-lft-neg-in 95.2%

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

   8. Simplified 95.2%

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

   9. Taylor expanded in y around -inf 96.8%

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

       1. associate-/l* 100.0%

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

       2. sub-neg 100.0%

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

       3. metadata-eval 100.0%

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

   11. Simplified 100.0%

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

4. Final simplification 97.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+52}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+55}:\\ \;\;\;\;\frac{y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771} + x\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot \frac{\frac{t}{z} + -36.52704169880642}{z} + y \cdot 3.13060547623\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 95.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+51}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+55}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot 11.1667541262\right)\right)\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot \frac{\frac{t}{z} + -36.52704169880642}{z} + y \cdot 3.13060547623\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -4.6e+51)
   (+ x (* y 3.13060547623))
   (if (<= z 4.5e+55)
     (+
      x
      (/
       (* y (+ b (* z (+ a (* z (+ t (* z 11.1667541262)))))))
       (+
        (*
         z
         (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721))
        0.607771387771)))
     (+
      x
      (+ (* y (/ (+ (/ t z) -36.52704169880642) z)) (* y 3.13060547623))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -4.6e+51) {
		tmp = x + (y * 3.13060547623);
	} else if (z <= 4.5e+55) {
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771));
	} else {
		tmp = x + ((y * (((t / z) + -36.52704169880642) / z)) + (y * 3.13060547623));
	}
	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 <= (-4.6d+51)) then
        tmp = x + (y * 3.13060547623d0)
    else if (z <= 4.5d+55) then
        tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262d0))))))) / ((z * ((z * ((z * (z + 15.234687407d0)) + 31.4690115749d0)) + 11.9400905721d0)) + 0.607771387771d0))
    else
        tmp = x + ((y * (((t / z) + (-36.52704169880642d0)) / z)) + (y * 3.13060547623d0))
    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 <= -4.6e+51) {
		tmp = x + (y * 3.13060547623);
	} else if (z <= 4.5e+55) {
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771));
	} else {
		tmp = x + ((y * (((t / z) + -36.52704169880642) / z)) + (y * 3.13060547623));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -4.6e+51:
		tmp = x + (y * 3.13060547623)
	elif z <= 4.5e+55:
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771))
	else:
		tmp = x + ((y * (((t / z) + -36.52704169880642) / z)) + (y * 3.13060547623))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -4.6e+51)
		tmp = Float64(x + Float64(y * 3.13060547623));
	elseif (z <= 4.5e+55)
		tmp = Float64(x + Float64(Float64(y * Float64(b + Float64(z * Float64(a + Float64(z * Float64(t + Float64(z * 11.1667541262))))))) / Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)));
	else
		tmp = Float64(x + Float64(Float64(y * Float64(Float64(Float64(t / z) + -36.52704169880642) / z)) + Float64(y * 3.13060547623)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -4.6e+51)
		tmp = x + (y * 3.13060547623);
	elseif (z <= 4.5e+55)
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * 11.1667541262))))))) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771));
	else
		tmp = x + ((y * (((t / z) + -36.52704169880642) / z)) + (y * 3.13060547623));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -4.6e+51], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.5e+55], N[(x + N[(N[(y * N[(b + N[(z * N[(a + N[(z * N[(t + N[(z * 11.1667541262), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(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[(x + N[(N[(y * N[(N[(N[(t / z), $MachinePrecision] + -36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.6000000000000001e51

   1. Initial program 4.8%

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

   3. Simplified 9.5%

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

   5. Taylor expanded in z around inf 97.8%

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

      1. +-commutative 97.8%

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

   7. Simplified 97.8%

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

   if -4.6000000000000001e51 < z < 4.49999999999999998e55

   1. Initial program 96.6%

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

   3. Taylor expanded in z around 0 94.9%

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

      1. *-commutative 94.9%

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

   5. Simplified 94.9%

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

   if 4.49999999999999998e55 < z

   1. Initial program 5.1%

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

      1. remove-double-neg 5.1%

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

      2. distribute-lft-neg-out 5.1%

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

   3. Simplified 5.1%

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

   5. Taylor expanded in z around -inf 87.2%

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

   6. Taylor expanded in t around inf 87.2%

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

      1. mul-1-neg 87.2%

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

      2. associate-/l* 95.2%

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

      3. distribute-lft-neg-in 95.2%

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

   8. Simplified 95.2%

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

   9. Taylor expanded in y around -inf 96.8%

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

       1. associate-/l* 100.0%

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

       2. sub-neg 100.0%

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

       3. metadata-eval 100.0%

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

   11. Simplified 100.0%

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

4. Final simplification 96.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+51}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+55}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot 11.1667541262\right)\right)\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot \frac{\frac{t}{z} + -36.52704169880642}{z} + y \cdot 3.13060547623\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 95.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -15600:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 + \frac{t \cdot \frac{y}{z}}{z}\right)\\ \mathbf{elif}\;z \leq 5800000:\\ \;\;\;\;x + \frac{y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot 31.4690115749\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot \frac{\frac{t}{z} + -36.52704169880642}{z} + y \cdot 3.13060547623\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -15600.0)
   (+ x (+ (* y 3.13060547623) (/ (* t (/ y z)) z)))
   (if (<= z 5800000.0)
     (+
      x
      (/
       (*
        y
        (+
         (* z (+ (* z (+ (* z (+ (* z 3.13060547623) 11.1667541262)) t)) a))
         b))
       (+ 0.607771387771 (* z (+ 11.9400905721 (* z 31.4690115749))))))
     (+
      x
      (+ (* y (/ (+ (/ t z) -36.52704169880642) z)) (* y 3.13060547623))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -15600.0) {
		tmp = x + ((y * 3.13060547623) + ((t * (y / z)) / z));
	} else if (z <= 5800000.0) {
		tmp = x + ((y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / (0.607771387771 + (z * (11.9400905721 + (z * 31.4690115749)))));
	} else {
		tmp = x + ((y * (((t / z) + -36.52704169880642) / z)) + (y * 3.13060547623));
	}
	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 <= (-15600.0d0)) then
        tmp = x + ((y * 3.13060547623d0) + ((t * (y / z)) / z))
    else if (z <= 5800000.0d0) then
        tmp = x + ((y * ((z * ((z * ((z * ((z * 3.13060547623d0) + 11.1667541262d0)) + t)) + a)) + b)) / (0.607771387771d0 + (z * (11.9400905721d0 + (z * 31.4690115749d0)))))
    else
        tmp = x + ((y * (((t / z) + (-36.52704169880642d0)) / z)) + (y * 3.13060547623d0))
    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 <= -15600.0) {
		tmp = x + ((y * 3.13060547623) + ((t * (y / z)) / z));
	} else if (z <= 5800000.0) {
		tmp = x + ((y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / (0.607771387771 + (z * (11.9400905721 + (z * 31.4690115749)))));
	} else {
		tmp = x + ((y * (((t / z) + -36.52704169880642) / z)) + (y * 3.13060547623));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -15600.0:
		tmp = x + ((y * 3.13060547623) + ((t * (y / z)) / z))
	elif z <= 5800000.0:
		tmp = x + ((y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / (0.607771387771 + (z * (11.9400905721 + (z * 31.4690115749)))))
	else:
		tmp = x + ((y * (((t / z) + -36.52704169880642) / z)) + (y * 3.13060547623))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -15600.0)
		tmp = Float64(x + Float64(Float64(y * 3.13060547623) + Float64(Float64(t * Float64(y / z)) / z)));
	elseif (z <= 5800000.0)
		tmp = Float64(x + Float64(Float64(y * Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / Float64(0.607771387771 + Float64(z * Float64(11.9400905721 + Float64(z * 31.4690115749))))));
	else
		tmp = Float64(x + Float64(Float64(y * Float64(Float64(Float64(t / z) + -36.52704169880642) / z)) + Float64(y * 3.13060547623)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -15600.0)
		tmp = x + ((y * 3.13060547623) + ((t * (y / z)) / z));
	elseif (z <= 5800000.0)
		tmp = x + ((y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / (0.607771387771 + (z * (11.9400905721 + (z * 31.4690115749)))));
	else
		tmp = x + ((y * (((t / z) + -36.52704169880642) / z)) + (y * 3.13060547623));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -15600.0], N[(x + N[(N[(y * 3.13060547623), $MachinePrecision] + N[(N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5800000.0], N[(x + 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[(0.607771387771 + N[(z * N[(11.9400905721 + N[(z * 31.4690115749), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * N[(N[(N[(t / z), $MachinePrecision] + -36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -15600

   1. Initial program 19.0%

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

      1. remove-double-neg 19.0%

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

      2. distribute-lft-neg-out 19.0%

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

   3. Simplified 19.0%

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

   5. Taylor expanded in z around -inf 75.2%

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

   6. Taylor expanded in t around inf 75.2%

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

      1. mul-1-neg 75.2%

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

      2. associate-/l* 87.5%

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

      3. distribute-lft-neg-in 87.5%

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

   8. Simplified 87.5%

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

   9. Taylor expanded in t around inf 75.2%

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

       1. mul-1-neg 75.2%

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

       2. associate-*r/ 87.5%

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

       3. distribute-lft-neg-in 87.5%

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

       4. *-commutative 87.5%

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

   11. Simplified 87.5%

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

   if -15600 < z < 5.8e6

   1. Initial program 99.6%

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

   3. Taylor expanded in z around 0 97.8%

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

      1. *-commutative 97.8%

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

   5. Simplified 97.8%

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

   if 5.8e6 < z

   1. Initial program 16.1%

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

      1. remove-double-neg 16.1%

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

      2. distribute-lft-neg-out 16.1%

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

   3. Simplified 16.2%

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

   5. Taylor expanded in z around -inf 81.4%

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

   6. Taylor expanded in t around inf 81.4%

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

      1. mul-1-neg 81.4%

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

      2. associate-/l* 88.4%

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

      3. distribute-lft-neg-in 88.4%

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

   8. Simplified 88.4%

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

   9. Taylor expanded in y around -inf 89.8%

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

       1. associate-/l* 92.5%

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

       2. sub-neg 92.5%

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

       3. metadata-eval 92.5%

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

   11. Simplified 92.5%

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

4. Final simplification 94.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -15600:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 + \frac{t \cdot \frac{y}{z}}{z}\right)\\ \mathbf{elif}\;z \leq 5800000:\\ \;\;\;\;x + \frac{y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot 31.4690115749\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot \frac{\frac{t}{z} + -36.52704169880642}{z} + y \cdot 3.13060547623\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 95.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -13:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 + \frac{y \cdot -47.69379582500642 + \left(t \cdot \frac{y}{z} - y \cdot -11.1667541262\right)}{z}\right)\\ \mathbf{elif}\;z \leq 128000:\\ \;\;\;\;x + \frac{y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot \frac{\frac{t}{z} + -36.52704169880642}{z} + y \cdot 3.13060547623\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -13.0)
   (+
    x
    (+
     (* y 3.13060547623)
     (/
      (+ (* y -47.69379582500642) (- (* t (/ y z)) (* y -11.1667541262)))
      z)))
   (if (<= z 128000.0)
     (+
      x
      (/
       (*
        y
        (+
         (* z (+ (* z (+ (* z (+ (* z 3.13060547623) 11.1667541262)) t)) a))
         b))
       (+ 0.607771387771 (* z 11.9400905721))))
     (+
      x
      (+ (* y (/ (+ (/ t z) -36.52704169880642) z)) (* y 3.13060547623))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -13.0) {
		tmp = x + ((y * 3.13060547623) + (((y * -47.69379582500642) + ((t * (y / z)) - (y * -11.1667541262))) / z));
	} else if (z <= 128000.0) {
		tmp = x + ((y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / (0.607771387771 + (z * 11.9400905721)));
	} else {
		tmp = x + ((y * (((t / z) + -36.52704169880642) / z)) + (y * 3.13060547623));
	}
	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 <= (-13.0d0)) then
        tmp = x + ((y * 3.13060547623d0) + (((y * (-47.69379582500642d0)) + ((t * (y / z)) - (y * (-11.1667541262d0)))) / z))
    else if (z <= 128000.0d0) then
        tmp = x + ((y * ((z * ((z * ((z * ((z * 3.13060547623d0) + 11.1667541262d0)) + t)) + a)) + b)) / (0.607771387771d0 + (z * 11.9400905721d0)))
    else
        tmp = x + ((y * (((t / z) + (-36.52704169880642d0)) / z)) + (y * 3.13060547623d0))
    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 <= -13.0) {
		tmp = x + ((y * 3.13060547623) + (((y * -47.69379582500642) + ((t * (y / z)) - (y * -11.1667541262))) / z));
	} else if (z <= 128000.0) {
		tmp = x + ((y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / (0.607771387771 + (z * 11.9400905721)));
	} else {
		tmp = x + ((y * (((t / z) + -36.52704169880642) / z)) + (y * 3.13060547623));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -13.0:
		tmp = x + ((y * 3.13060547623) + (((y * -47.69379582500642) + ((t * (y / z)) - (y * -11.1667541262))) / z))
	elif z <= 128000.0:
		tmp = x + ((y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / (0.607771387771 + (z * 11.9400905721)))
	else:
		tmp = x + ((y * (((t / z) + -36.52704169880642) / z)) + (y * 3.13060547623))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -13.0)
		tmp = Float64(x + Float64(Float64(y * 3.13060547623) + Float64(Float64(Float64(y * -47.69379582500642) + Float64(Float64(t * Float64(y / z)) - Float64(y * -11.1667541262))) / z)));
	elseif (z <= 128000.0)
		tmp = Float64(x + Float64(Float64(y * Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / Float64(0.607771387771 + Float64(z * 11.9400905721))));
	else
		tmp = Float64(x + Float64(Float64(y * Float64(Float64(Float64(t / z) + -36.52704169880642) / z)) + Float64(y * 3.13060547623)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -13.0)
		tmp = x + ((y * 3.13060547623) + (((y * -47.69379582500642) + ((t * (y / z)) - (y * -11.1667541262))) / z));
	elseif (z <= 128000.0)
		tmp = x + ((y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / (0.607771387771 + (z * 11.9400905721)));
	else
		tmp = x + ((y * (((t / z) + -36.52704169880642) / z)) + (y * 3.13060547623));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -13.0], N[(x + N[(N[(y * 3.13060547623), $MachinePrecision] + N[(N[(N[(y * -47.69379582500642), $MachinePrecision] + N[(N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision] - N[(y * -11.1667541262), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 128000.0], N[(x + 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[(0.607771387771 + N[(z * 11.9400905721), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * N[(N[(N[(t / z), $MachinePrecision] + -36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -13

   1. Initial program 20.5%

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

      1. remove-double-neg 20.5%

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

      2. distribute-lft-neg-out 20.5%

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

   3. Simplified 20.5%

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

   5. Taylor expanded in z around -inf 73.9%

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

   6. Taylor expanded in t around inf 73.9%

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

      1. mul-1-neg 73.9%

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

      2. associate-/l* 86.1%

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

      3. distribute-lft-neg-in 86.1%

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

   8. Simplified 86.1%

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

   if -13 < z < 128000

   1. Initial program 99.6%

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

   3. Taylor expanded in z around 0 97.8%

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

      1. *-commutative 97.8%

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

   5. Simplified 97.8%

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

   if 128000 < z

   1. Initial program 16.1%

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

      1. remove-double-neg 16.1%

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

      2. distribute-lft-neg-out 16.1%

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

   3. Simplified 16.2%

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

   5. Taylor expanded in z around -inf 81.4%

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

   6. Taylor expanded in t around inf 81.4%

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

      1. mul-1-neg 81.4%

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

      2. associate-/l* 88.4%

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

      3. distribute-lft-neg-in 88.4%

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

   8. Simplified 88.4%

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

   9. Taylor expanded in y around -inf 89.8%

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

       1. associate-/l* 92.5%

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

       2. sub-neg 92.5%

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

       3. metadata-eval 92.5%

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

   11. Simplified 92.5%

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

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -13:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 + \frac{y \cdot -47.69379582500642 + \left(t \cdot \frac{y}{z} - y \cdot -11.1667541262\right)}{z}\right)\\ \mathbf{elif}\;z \leq 128000:\\ \;\;\;\;x + \frac{y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot \frac{\frac{t}{z} + -36.52704169880642}{z} + y \cdot 3.13060547623\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 92.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -20500:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 + \frac{t \cdot \frac{y}{z}}{z}\right)\\ \mathbf{elif}\;z \leq 4.1:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998 - z \cdot \left(b \cdot 32.324150453290734 - a \cdot 1.6453555072203998\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot \frac{\frac{t}{z} + -36.52704169880642}{z} + y \cdot 3.13060547623\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -20500.0)
   (+ x (+ (* y 3.13060547623) (/ (* t (/ y z)) z)))
   (if (<= z 4.1)
     (+
      x
      (*
       y
       (-
        (* b 1.6453555072203998)
        (* z (- (* b 32.324150453290734) (* a 1.6453555072203998))))))
     (+
      x
      (+ (* y (/ (+ (/ t z) -36.52704169880642) z)) (* y 3.13060547623))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -20500.0) {
		tmp = x + ((y * 3.13060547623) + ((t * (y / z)) / z));
	} else if (z <= 4.1) {
		tmp = x + (y * ((b * 1.6453555072203998) - (z * ((b * 32.324150453290734) - (a * 1.6453555072203998)))));
	} else {
		tmp = x + ((y * (((t / z) + -36.52704169880642) / z)) + (y * 3.13060547623));
	}
	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 <= (-20500.0d0)) then
        tmp = x + ((y * 3.13060547623d0) + ((t * (y / z)) / z))
    else if (z <= 4.1d0) then
        tmp = x + (y * ((b * 1.6453555072203998d0) - (z * ((b * 32.324150453290734d0) - (a * 1.6453555072203998d0)))))
    else
        tmp = x + ((y * (((t / z) + (-36.52704169880642d0)) / z)) + (y * 3.13060547623d0))
    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 <= -20500.0) {
		tmp = x + ((y * 3.13060547623) + ((t * (y / z)) / z));
	} else if (z <= 4.1) {
		tmp = x + (y * ((b * 1.6453555072203998) - (z * ((b * 32.324150453290734) - (a * 1.6453555072203998)))));
	} else {
		tmp = x + ((y * (((t / z) + -36.52704169880642) / z)) + (y * 3.13060547623));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -20500.0:
		tmp = x + ((y * 3.13060547623) + ((t * (y / z)) / z))
	elif z <= 4.1:
		tmp = x + (y * ((b * 1.6453555072203998) - (z * ((b * 32.324150453290734) - (a * 1.6453555072203998)))))
	else:
		tmp = x + ((y * (((t / z) + -36.52704169880642) / z)) + (y * 3.13060547623))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -20500.0)
		tmp = Float64(x + Float64(Float64(y * 3.13060547623) + Float64(Float64(t * Float64(y / z)) / z)));
	elseif (z <= 4.1)
		tmp = Float64(x + Float64(y * Float64(Float64(b * 1.6453555072203998) - Float64(z * Float64(Float64(b * 32.324150453290734) - Float64(a * 1.6453555072203998))))));
	else
		tmp = Float64(x + Float64(Float64(y * Float64(Float64(Float64(t / z) + -36.52704169880642) / z)) + Float64(y * 3.13060547623)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -20500.0)
		tmp = x + ((y * 3.13060547623) + ((t * (y / z)) / z));
	elseif (z <= 4.1)
		tmp = x + (y * ((b * 1.6453555072203998) - (z * ((b * 32.324150453290734) - (a * 1.6453555072203998)))));
	else
		tmp = x + ((y * (((t / z) + -36.52704169880642) / z)) + (y * 3.13060547623));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -20500.0], N[(x + N[(N[(y * 3.13060547623), $MachinePrecision] + N[(N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.1], N[(x + N[(y * N[(N[(b * 1.6453555072203998), $MachinePrecision] - N[(z * N[(N[(b * 32.324150453290734), $MachinePrecision] - N[(a * 1.6453555072203998), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * N[(N[(N[(t / z), $MachinePrecision] + -36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -20500

   1. Initial program 19.0%

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

      1. remove-double-neg 19.0%

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

      2. distribute-lft-neg-out 19.0%

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

   3. Simplified 19.0%

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

   5. Taylor expanded in z around -inf 75.2%

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

   6. Taylor expanded in t around inf 75.2%

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

      1. mul-1-neg 75.2%

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

      2. associate-/l* 87.5%

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

      3. distribute-lft-neg-in 87.5%

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

   8. Simplified 87.5%

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

   9. Taylor expanded in t around inf 75.2%

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

       1. mul-1-neg 75.2%

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

       2. associate-*r/ 87.5%

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

       3. distribute-lft-neg-in 87.5%

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

       4. *-commutative 87.5%

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

   11. Simplified 87.5%

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

   if -20500 < z < 4.0999999999999996

   1. Initial program 99.6%

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

      1. remove-double-neg 99.6%

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

      2. distribute-lft-neg-out 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in z around 0 81.0%

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

   6. Taylor expanded in y around 0 91.4%

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

   if 4.0999999999999996 < z

   1. Initial program 18.5%

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

      1. remove-double-neg 18.5%

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

      2. distribute-lft-neg-out 18.5%

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

   3. Simplified 18.5%

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

   5. Taylor expanded in z around -inf 79.2%

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

   6. Taylor expanded in t around inf 79.2%

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

      1. mul-1-neg 79.2%

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

      2. associate-/l* 85.9%

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

      3. distribute-lft-neg-in 85.9%

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

   8. Simplified 85.9%

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

   9. Taylor expanded in y around -inf 87.3%

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

       1. associate-/l* 90.0%

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

       2. sub-neg 90.0%

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

       3. metadata-eval 90.0%

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

   11. Simplified 90.0%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -20500:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 + \frac{t \cdot \frac{y}{z}}{z}\right)\\ \mathbf{elif}\;z \leq 4.1:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998 - z \cdot \left(b \cdot 32.324150453290734 - a \cdot 1.6453555072203998\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot \frac{\frac{t}{z} + -36.52704169880642}{z} + y \cdot 3.13060547623\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 92.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -29500 \lor \neg \left(z \leq 320000\right):\\ \;\;\;\;x + \left(y \cdot \frac{\frac{t}{z} + -36.52704169880642}{z} + y \cdot 3.13060547623\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(1.6453555072203998 \cdot \left(y \cdot b\right) + 1.6453555072203998 \cdot \left(a \cdot \left(y \cdot z\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -29500.0) (not (<= z 320000.0)))
   (+ x (+ (* y (/ (+ (/ t z) -36.52704169880642) z)) (* y 3.13060547623)))
   (+
    x
    (+ (* 1.6453555072203998 (* y b)) (* 1.6453555072203998 (* a (* y z)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -29500.0) || !(z <= 320000.0)) {
		tmp = x + ((y * (((t / z) + -36.52704169880642) / z)) + (y * 3.13060547623));
	} else {
		tmp = x + ((1.6453555072203998 * (y * b)) + (1.6453555072203998 * (a * (y * 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 <= (-29500.0d0)) .or. (.not. (z <= 320000.0d0))) then
        tmp = x + ((y * (((t / z) + (-36.52704169880642d0)) / z)) + (y * 3.13060547623d0))
    else
        tmp = x + ((1.6453555072203998d0 * (y * b)) + (1.6453555072203998d0 * (a * (y * 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 <= -29500.0) || !(z <= 320000.0)) {
		tmp = x + ((y * (((t / z) + -36.52704169880642) / z)) + (y * 3.13060547623));
	} else {
		tmp = x + ((1.6453555072203998 * (y * b)) + (1.6453555072203998 * (a * (y * z))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -29500.0) or not (z <= 320000.0):
		tmp = x + ((y * (((t / z) + -36.52704169880642) / z)) + (y * 3.13060547623))
	else:
		tmp = x + ((1.6453555072203998 * (y * b)) + (1.6453555072203998 * (a * (y * z))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -29500.0) || !(z <= 320000.0))
		tmp = Float64(x + Float64(Float64(y * Float64(Float64(Float64(t / z) + -36.52704169880642) / z)) + Float64(y * 3.13060547623)));
	else
		tmp = Float64(x + Float64(Float64(1.6453555072203998 * Float64(y * b)) + Float64(1.6453555072203998 * Float64(a * Float64(y * z)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -29500.0) || ~((z <= 320000.0)))
		tmp = x + ((y * (((t / z) + -36.52704169880642) / z)) + (y * 3.13060547623));
	else
		tmp = x + ((1.6453555072203998 * (y * b)) + (1.6453555072203998 * (a * (y * z))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -29500.0], N[Not[LessEqual[z, 320000.0]], $MachinePrecision]], N[(x + N[(N[(y * N[(N[(N[(t / z), $MachinePrecision] + -36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(1.6453555072203998 * N[(y * b), $MachinePrecision]), $MachinePrecision] + N[(1.6453555072203998 * N[(a * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -29500 or 3.2e5 < z

   1. Initial program 17.4%

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

      1. remove-double-neg 17.4%

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

      2. distribute-lft-neg-out 17.4%

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

   3. Simplified 17.4%

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

   5. Taylor expanded in z around -inf 78.7%

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

   6. Taylor expanded in t around inf 78.7%

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

      1. mul-1-neg 78.7%

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

      2. associate-/l* 88.0%

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

      3. distribute-lft-neg-in 88.0%

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

   8. Simplified 88.0%

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

   9. Taylor expanded in y around -inf 88.8%

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

       1. associate-/l* 90.3%

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

       2. sub-neg 90.3%

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

       3. metadata-eval 90.3%

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

   11. Simplified 90.3%

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

   if -29500 < z < 3.2e5

   1. Initial program 99.6%

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

      1. remove-double-neg 99.6%

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

      2. distribute-lft-neg-out 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in z around 0 79.8%

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

   6. Taylor expanded in a around inf 88.4%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -29500 \lor \neg \left(z \leq 320000\right):\\ \;\;\;\;x + \left(y \cdot \frac{\frac{t}{z} + -36.52704169880642}{z} + y \cdot 3.13060547623\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(1.6453555072203998 \cdot \left(y \cdot b\right) + 1.6453555072203998 \cdot \left(a \cdot \left(y \cdot z\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 92.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -10500:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 + \frac{t \cdot \frac{y}{z}}{z}\right)\\ \mathbf{elif}\;z \leq 105000:\\ \;\;\;\;x + \left(1.6453555072203998 \cdot \left(y \cdot b\right) + 1.6453555072203998 \cdot \left(a \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot \frac{\frac{t}{z} + -36.52704169880642}{z} + y \cdot 3.13060547623\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -10500.0)
   (+ x (+ (* y 3.13060547623) (/ (* t (/ y z)) z)))
   (if (<= z 105000.0)
     (+
      x
      (+ (* 1.6453555072203998 (* y b)) (* 1.6453555072203998 (* a (* y z)))))
     (+
      x
      (+ (* y (/ (+ (/ t z) -36.52704169880642) z)) (* y 3.13060547623))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -10500.0) {
		tmp = x + ((y * 3.13060547623) + ((t * (y / z)) / z));
	} else if (z <= 105000.0) {
		tmp = x + ((1.6453555072203998 * (y * b)) + (1.6453555072203998 * (a * (y * z))));
	} else {
		tmp = x + ((y * (((t / z) + -36.52704169880642) / z)) + (y * 3.13060547623));
	}
	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 <= (-10500.0d0)) then
        tmp = x + ((y * 3.13060547623d0) + ((t * (y / z)) / z))
    else if (z <= 105000.0d0) then
        tmp = x + ((1.6453555072203998d0 * (y * b)) + (1.6453555072203998d0 * (a * (y * z))))
    else
        tmp = x + ((y * (((t / z) + (-36.52704169880642d0)) / z)) + (y * 3.13060547623d0))
    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 <= -10500.0) {
		tmp = x + ((y * 3.13060547623) + ((t * (y / z)) / z));
	} else if (z <= 105000.0) {
		tmp = x + ((1.6453555072203998 * (y * b)) + (1.6453555072203998 * (a * (y * z))));
	} else {
		tmp = x + ((y * (((t / z) + -36.52704169880642) / z)) + (y * 3.13060547623));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -10500.0:
		tmp = x + ((y * 3.13060547623) + ((t * (y / z)) / z))
	elif z <= 105000.0:
		tmp = x + ((1.6453555072203998 * (y * b)) + (1.6453555072203998 * (a * (y * z))))
	else:
		tmp = x + ((y * (((t / z) + -36.52704169880642) / z)) + (y * 3.13060547623))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -10500.0)
		tmp = Float64(x + Float64(Float64(y * 3.13060547623) + Float64(Float64(t * Float64(y / z)) / z)));
	elseif (z <= 105000.0)
		tmp = Float64(x + Float64(Float64(1.6453555072203998 * Float64(y * b)) + Float64(1.6453555072203998 * Float64(a * Float64(y * z)))));
	else
		tmp = Float64(x + Float64(Float64(y * Float64(Float64(Float64(t / z) + -36.52704169880642) / z)) + Float64(y * 3.13060547623)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -10500.0)
		tmp = x + ((y * 3.13060547623) + ((t * (y / z)) / z));
	elseif (z <= 105000.0)
		tmp = x + ((1.6453555072203998 * (y * b)) + (1.6453555072203998 * (a * (y * z))));
	else
		tmp = x + ((y * (((t / z) + -36.52704169880642) / z)) + (y * 3.13060547623));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -10500.0], N[(x + N[(N[(y * 3.13060547623), $MachinePrecision] + N[(N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 105000.0], N[(x + N[(N[(1.6453555072203998 * N[(y * b), $MachinePrecision]), $MachinePrecision] + N[(1.6453555072203998 * N[(a * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * N[(N[(N[(t / z), $MachinePrecision] + -36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -10500

   1. Initial program 19.0%

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

      1. remove-double-neg 19.0%

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

      2. distribute-lft-neg-out 19.0%

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

   3. Simplified 19.0%

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

   5. Taylor expanded in z around -inf 75.2%

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

   6. Taylor expanded in t around inf 75.2%

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

      1. mul-1-neg 75.2%

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

      2. associate-/l* 87.5%

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

      3. distribute-lft-neg-in 87.5%

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

   8. Simplified 87.5%

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

   9. Taylor expanded in t around inf 75.2%

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

       1. mul-1-neg 75.2%

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

       2. associate-*r/ 87.5%

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

       3. distribute-lft-neg-in 87.5%

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

       4. *-commutative 87.5%

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

   11. Simplified 87.5%

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

   if -10500 < z < 105000

   1. Initial program 99.6%

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

      1. remove-double-neg 99.6%

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

      2. distribute-lft-neg-out 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in z around 0 79.8%

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

   6. Taylor expanded in a around inf 88.4%

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

   if 105000 < z

   1. Initial program 16.1%

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

      1. remove-double-neg 16.1%

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

      2. distribute-lft-neg-out 16.1%

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

   3. Simplified 16.2%

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

   5. Taylor expanded in z around -inf 81.4%

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

   6. Taylor expanded in t around inf 81.4%

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

      1. mul-1-neg 81.4%

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

      2. associate-/l* 88.4%

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

      3. distribute-lft-neg-in 88.4%

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

   8. Simplified 88.4%

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

   9. Taylor expanded in y around -inf 89.8%

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

       1. associate-/l* 92.5%

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

       2. sub-neg 92.5%

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

       3. metadata-eval 92.5%

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

   11. Simplified 92.5%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -10500:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 + \frac{t \cdot \frac{y}{z}}{z}\right)\\ \mathbf{elif}\;z \leq 105000:\\ \;\;\;\;x + \left(1.6453555072203998 \cdot \left(y \cdot b\right) + 1.6453555072203998 \cdot \left(a \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot \frac{\frac{t}{z} + -36.52704169880642}{z} + y \cdot 3.13060547623\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 92.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -38000:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 - \frac{y \cdot \left(36.52704169880642 - \frac{t}{z}\right)}{z}\right)\\ \mathbf{elif}\;z \leq 1450000:\\ \;\;\;\;x + \left(1.6453555072203998 \cdot \left(y \cdot b\right) + 1.6453555072203998 \cdot \left(a \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot \frac{\frac{t}{z} + -36.52704169880642}{z} + y \cdot 3.13060547623\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -38000.0)
   (+ x (- (* y 3.13060547623) (/ (* y (- 36.52704169880642 (/ t z))) z)))
   (if (<= z 1450000.0)
     (+
      x
      (+ (* 1.6453555072203998 (* y b)) (* 1.6453555072203998 (* a (* y z)))))
     (+
      x
      (+ (* y (/ (+ (/ t z) -36.52704169880642) z)) (* y 3.13060547623))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -38000.0) {
		tmp = x + ((y * 3.13060547623) - ((y * (36.52704169880642 - (t / z))) / z));
	} else if (z <= 1450000.0) {
		tmp = x + ((1.6453555072203998 * (y * b)) + (1.6453555072203998 * (a * (y * z))));
	} else {
		tmp = x + ((y * (((t / z) + -36.52704169880642) / z)) + (y * 3.13060547623));
	}
	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 <= (-38000.0d0)) then
        tmp = x + ((y * 3.13060547623d0) - ((y * (36.52704169880642d0 - (t / z))) / z))
    else if (z <= 1450000.0d0) then
        tmp = x + ((1.6453555072203998d0 * (y * b)) + (1.6453555072203998d0 * (a * (y * z))))
    else
        tmp = x + ((y * (((t / z) + (-36.52704169880642d0)) / z)) + (y * 3.13060547623d0))
    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 <= -38000.0) {
		tmp = x + ((y * 3.13060547623) - ((y * (36.52704169880642 - (t / z))) / z));
	} else if (z <= 1450000.0) {
		tmp = x + ((1.6453555072203998 * (y * b)) + (1.6453555072203998 * (a * (y * z))));
	} else {
		tmp = x + ((y * (((t / z) + -36.52704169880642) / z)) + (y * 3.13060547623));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -38000.0:
		tmp = x + ((y * 3.13060547623) - ((y * (36.52704169880642 - (t / z))) / z))
	elif z <= 1450000.0:
		tmp = x + ((1.6453555072203998 * (y * b)) + (1.6453555072203998 * (a * (y * z))))
	else:
		tmp = x + ((y * (((t / z) + -36.52704169880642) / z)) + (y * 3.13060547623))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -38000.0)
		tmp = Float64(x + Float64(Float64(y * 3.13060547623) - Float64(Float64(y * Float64(36.52704169880642 - Float64(t / z))) / z)));
	elseif (z <= 1450000.0)
		tmp = Float64(x + Float64(Float64(1.6453555072203998 * Float64(y * b)) + Float64(1.6453555072203998 * Float64(a * Float64(y * z)))));
	else
		tmp = Float64(x + Float64(Float64(y * Float64(Float64(Float64(t / z) + -36.52704169880642) / z)) + Float64(y * 3.13060547623)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -38000.0)
		tmp = x + ((y * 3.13060547623) - ((y * (36.52704169880642 - (t / z))) / z));
	elseif (z <= 1450000.0)
		tmp = x + ((1.6453555072203998 * (y * b)) + (1.6453555072203998 * (a * (y * z))));
	else
		tmp = x + ((y * (((t / z) + -36.52704169880642) / z)) + (y * 3.13060547623));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -38000.0], N[(x + N[(N[(y * 3.13060547623), $MachinePrecision] - N[(N[(y * N[(36.52704169880642 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1450000.0], N[(x + N[(N[(1.6453555072203998 * N[(y * b), $MachinePrecision]), $MachinePrecision] + N[(1.6453555072203998 * N[(a * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * N[(N[(N[(t / z), $MachinePrecision] + -36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -38000

   1. Initial program 19.0%

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

      1. remove-double-neg 19.0%

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

      2. distribute-lft-neg-out 19.0%

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

   3. Simplified 19.0%

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

   5. Taylor expanded in z around -inf 75.2%

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

   6. Taylor expanded in t around inf 75.2%

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

      1. mul-1-neg 75.2%

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

      2. associate-/l* 87.5%

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

      3. distribute-lft-neg-in 87.5%

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

   8. Simplified 87.5%

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

   9. Taylor expanded in y around -inf 87.5%

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

   if -38000 < z < 1.45e6

   1. Initial program 99.6%

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

      1. remove-double-neg 99.6%

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

      2. distribute-lft-neg-out 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in z around 0 79.8%

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

   6. Taylor expanded in a around inf 88.4%

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

   if 1.45e6 < z

   1. Initial program 16.1%

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

      1. remove-double-neg 16.1%

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

      2. distribute-lft-neg-out 16.1%

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

   3. Simplified 16.2%

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

   5. Taylor expanded in z around -inf 81.4%

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

   6. Taylor expanded in t around inf 81.4%

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

      1. mul-1-neg 81.4%

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

      2. associate-/l* 88.4%

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

      3. distribute-lft-neg-in 88.4%

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

   8. Simplified 88.4%

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

   9. Taylor expanded in y around -inf 89.8%

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

       1. associate-/l* 92.5%

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

       2. sub-neg 92.5%

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

       3. metadata-eval 92.5%

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

   11. Simplified 92.5%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -38000:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 - \frac{y \cdot \left(36.52704169880642 - \frac{t}{z}\right)}{z}\right)\\ \mathbf{elif}\;z \leq 1450000:\\ \;\;\;\;x + \left(1.6453555072203998 \cdot \left(y \cdot b\right) + 1.6453555072203998 \cdot \left(a \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot \frac{\frac{t}{z} + -36.52704169880642}{z} + y \cdot 3.13060547623\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 88.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+51}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{elif}\;z \leq 14500000:\\ \;\;\;\;x + \left(1.6453555072203998 \cdot \left(y \cdot b\right) + 1.6453555072203998 \cdot \left(a \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(3.13060547623 + \frac{-36.52704169880642}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -4.4e+51)
   (+ x (* y 3.13060547623))
   (if (<= z 14500000.0)
     (+
      x
      (+ (* 1.6453555072203998 (* y b)) (* 1.6453555072203998 (* a (* y z)))))
     (+ x (* y (+ 3.13060547623 (/ -36.52704169880642 z)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -4.4e+51) {
		tmp = x + (y * 3.13060547623);
	} else if (z <= 14500000.0) {
		tmp = x + ((1.6453555072203998 * (y * b)) + (1.6453555072203998 * (a * (y * z))));
	} else {
		tmp = x + (y * (3.13060547623 + (-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 <= (-4.4d+51)) then
        tmp = x + (y * 3.13060547623d0)
    else if (z <= 14500000.0d0) then
        tmp = x + ((1.6453555072203998d0 * (y * b)) + (1.6453555072203998d0 * (a * (y * z))))
    else
        tmp = x + (y * (3.13060547623d0 + ((-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 <= -4.4e+51) {
		tmp = x + (y * 3.13060547623);
	} else if (z <= 14500000.0) {
		tmp = x + ((1.6453555072203998 * (y * b)) + (1.6453555072203998 * (a * (y * z))));
	} else {
		tmp = x + (y * (3.13060547623 + (-36.52704169880642 / z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -4.4e+51:
		tmp = x + (y * 3.13060547623)
	elif z <= 14500000.0:
		tmp = x + ((1.6453555072203998 * (y * b)) + (1.6453555072203998 * (a * (y * z))))
	else:
		tmp = x + (y * (3.13060547623 + (-36.52704169880642 / z)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -4.4e+51)
		tmp = Float64(x + Float64(y * 3.13060547623));
	elseif (z <= 14500000.0)
		tmp = Float64(x + Float64(Float64(1.6453555072203998 * Float64(y * b)) + Float64(1.6453555072203998 * Float64(a * Float64(y * z)))));
	else
		tmp = Float64(x + Float64(y * Float64(3.13060547623 + Float64(-36.52704169880642 / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -4.4e+51)
		tmp = x + (y * 3.13060547623);
	elseif (z <= 14500000.0)
		tmp = x + ((1.6453555072203998 * (y * b)) + (1.6453555072203998 * (a * (y * z))));
	else
		tmp = x + (y * (3.13060547623 + (-36.52704169880642 / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -4.4e+51], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 14500000.0], N[(x + N[(N[(1.6453555072203998 * N[(y * b), $MachinePrecision]), $MachinePrecision] + N[(1.6453555072203998 * N[(a * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(3.13060547623 + N[(-36.52704169880642 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.39999999999999984e51

   1. Initial program 4.8%

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

   3. Simplified 9.5%

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

   5. Taylor expanded in z around inf 97.8%

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

      1. +-commutative 97.8%

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

   7. Simplified 97.8%

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

   if -4.39999999999999984e51 < z < 1.45e7

   1. Initial program 97.1%

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

      1. remove-double-neg 97.1%

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

      2. distribute-lft-neg-out 97.1%

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

   3. Simplified 97.1%

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

   5. Taylor expanded in z around 0 74.6%

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

   6. Taylor expanded in a around inf 82.4%

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

   if 1.45e7 < z

   1. Initial program 13.7%

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

      1. remove-double-neg 13.7%

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

      2. distribute-lft-neg-out 13.7%

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

   3. Simplified 13.7%

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

   5. Taylor expanded in z around -inf 87.9%

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

      1. +-commutative 87.9%

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

      2. mul-1-neg 87.9%

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

      3. unsub-neg 87.9%

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

      4. distribute-rgt-out-- 87.9%

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

      5. metadata-eval 87.9%

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

   7. Simplified 87.9%

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

   8. Taylor expanded in y around 0 89.4%

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

      1. associate-*r/ 89.4%

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

      2. metadata-eval 89.4%

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

      3. sub-neg 89.4%

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

      4. distribute-neg-frac 89.4%

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

      5. metadata-eval 89.4%

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

   10. Simplified 89.4%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+51}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{elif}\;z \leq 14500000:\\ \;\;\;\;x + \left(1.6453555072203998 \cdot \left(y \cdot b\right) + 1.6453555072203998 \cdot \left(a \cdot \left(y \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(3.13060547623 + \frac{-36.52704169880642}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 83.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -22 \lor \neg \left(z \leq 19000000\right):\\ \;\;\;\;x + y \cdot \left(3.13060547623 + \frac{-36.52704169880642}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot b}{0.607771387771 + z \cdot 11.9400905721}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -22.0) (not (<= z 19000000.0)))
   (+ x (* y (+ 3.13060547623 (/ -36.52704169880642 z))))
   (+ x (/ (* y b) (+ 0.607771387771 (* z 11.9400905721))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -22.0) || !(z <= 19000000.0)) {
		tmp = x + (y * (3.13060547623 + (-36.52704169880642 / z)));
	} else {
		tmp = x + ((y * b) / (0.607771387771 + (z * 11.9400905721)));
	}
	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 <= (-22.0d0)) .or. (.not. (z <= 19000000.0d0))) then
        tmp = x + (y * (3.13060547623d0 + ((-36.52704169880642d0) / z)))
    else
        tmp = x + ((y * b) / (0.607771387771d0 + (z * 11.9400905721d0)))
    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 <= -22.0) || !(z <= 19000000.0)) {
		tmp = x + (y * (3.13060547623 + (-36.52704169880642 / z)));
	} else {
		tmp = x + ((y * b) / (0.607771387771 + (z * 11.9400905721)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -22.0) or not (z <= 19000000.0):
		tmp = x + (y * (3.13060547623 + (-36.52704169880642 / z)))
	else:
		tmp = x + ((y * b) / (0.607771387771 + (z * 11.9400905721)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -22.0) || !(z <= 19000000.0))
		tmp = Float64(x + Float64(y * Float64(3.13060547623 + Float64(-36.52704169880642 / z))));
	else
		tmp = Float64(x + Float64(Float64(y * b) / Float64(0.607771387771 + Float64(z * 11.9400905721))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -22.0) || ~((z <= 19000000.0)))
		tmp = x + (y * (3.13060547623 + (-36.52704169880642 / z)));
	else
		tmp = x + ((y * b) / (0.607771387771 + (z * 11.9400905721)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -22.0], N[Not[LessEqual[z, 19000000.0]], $MachinePrecision]], N[(x + N[(y * N[(3.13060547623 + N[(-36.52704169880642 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * b), $MachinePrecision] / N[(0.607771387771 + N[(z * 11.9400905721), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -22 or 1.9e7 < z

   1. Initial program 16.7%

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

      1. remove-double-neg 16.7%

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

      2. distribute-lft-neg-out 16.7%

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

   3. Simplified 16.8%

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

   5. Taylor expanded in z around -inf 83.9%

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

      1. +-commutative 83.9%

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

      2. mul-1-neg 83.9%

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

      3. unsub-neg 83.9%

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

      4. distribute-rgt-out-- 83.9%

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

      5. metadata-eval 83.9%

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

   7. Simplified 83.9%

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

   8. Taylor expanded in y around 0 84.7%

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

      1. associate-*r/ 84.7%

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

      2. metadata-eval 84.7%

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

      3. sub-neg 84.7%

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

      4. distribute-neg-frac 84.7%

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

      5. metadata-eval 84.7%

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

   10. Simplified 84.7%

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

   if -22 < z < 1.9e7

   1. Initial program 99.6%

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

      1. remove-double-neg 99.6%

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

      2. distribute-lft-neg-out 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in b around inf 80.6%

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

   6. Taylor expanded in z around 0 79.2%

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

      1. *-commutative 79.2%

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

   8. Simplified 79.2%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -22 \lor \neg \left(z \leq 19000000\right):\\ \;\;\;\;x + y \cdot \left(3.13060547623 + \frac{-36.52704169880642}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot b}{0.607771387771 + z \cdot 11.9400905721}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 83.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+51}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{elif}\;z \leq 13500000:\\ \;\;\;\;x + 1.6453555072203998 \cdot \left(y \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(3.13060547623 + \frac{-36.52704169880642}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -4.4e+51)
   (+ x (* y 3.13060547623))
   (if (<= z 13500000.0)
     (+ x (* 1.6453555072203998 (* y b)))
     (+ x (* y (+ 3.13060547623 (/ -36.52704169880642 z)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -4.4e+51) {
		tmp = x + (y * 3.13060547623);
	} else if (z <= 13500000.0) {
		tmp = x + (1.6453555072203998 * (y * b));
	} else {
		tmp = x + (y * (3.13060547623 + (-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 <= (-4.4d+51)) then
        tmp = x + (y * 3.13060547623d0)
    else if (z <= 13500000.0d0) then
        tmp = x + (1.6453555072203998d0 * (y * b))
    else
        tmp = x + (y * (3.13060547623d0 + ((-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 <= -4.4e+51) {
		tmp = x + (y * 3.13060547623);
	} else if (z <= 13500000.0) {
		tmp = x + (1.6453555072203998 * (y * b));
	} else {
		tmp = x + (y * (3.13060547623 + (-36.52704169880642 / z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -4.4e+51:
		tmp = x + (y * 3.13060547623)
	elif z <= 13500000.0:
		tmp = x + (1.6453555072203998 * (y * b))
	else:
		tmp = x + (y * (3.13060547623 + (-36.52704169880642 / z)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -4.4e+51)
		tmp = Float64(x + Float64(y * 3.13060547623));
	elseif (z <= 13500000.0)
		tmp = Float64(x + Float64(1.6453555072203998 * Float64(y * b)));
	else
		tmp = Float64(x + Float64(y * Float64(3.13060547623 + Float64(-36.52704169880642 / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -4.4e+51)
		tmp = x + (y * 3.13060547623);
	elseif (z <= 13500000.0)
		tmp = x + (1.6453555072203998 * (y * b));
	else
		tmp = x + (y * (3.13060547623 + (-36.52704169880642 / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -4.4e+51], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 13500000.0], N[(x + N[(1.6453555072203998 * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(3.13060547623 + N[(-36.52704169880642 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.39999999999999984e51

   1. Initial program 4.8%

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

   3. Simplified 9.5%

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

   5. Taylor expanded in z around inf 97.8%

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

      1. +-commutative 97.8%

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

   7. Simplified 97.8%

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

   if -4.39999999999999984e51 < z < 1.35e7

   1. Initial program 97.1%

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

   3. Simplified 99.0%

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

   5. Taylor expanded in z around 0 73.7%

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

      1. +-commutative 73.7%

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

      2. *-commutative 73.7%

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

   7. Simplified 73.7%

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

   if 1.35e7 < z

   1. Initial program 13.7%

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

      1. remove-double-neg 13.7%

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

      2. distribute-lft-neg-out 13.7%

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

   3. Simplified 13.7%

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

   5. Taylor expanded in z around -inf 87.9%

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

      1. +-commutative 87.9%

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

      2. mul-1-neg 87.9%

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

      3. unsub-neg 87.9%

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

      4. distribute-rgt-out-- 87.9%

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

      5. metadata-eval 87.9%

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

   7. Simplified 87.9%

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

   8. Taylor expanded in y around 0 89.4%

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

      1. associate-*r/ 89.4%

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

      2. metadata-eval 89.4%

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

      3. sub-neg 89.4%

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

      4. distribute-neg-frac 89.4%

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

      5. metadata-eval 89.4%

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

   10. Simplified 89.4%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+51}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{elif}\;z \leq 13500000:\\ \;\;\;\;x + 1.6453555072203998 \cdot \left(y \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(3.13060547623 + \frac{-36.52704169880642}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 83.0% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+51} \lor \neg \left(z \leq 18000000\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x + 1.6453555072203998 \cdot \left(y \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -4.4e+51) (not (<= z 18000000.0)))
   (+ x (* y 3.13060547623))
   (+ x (* 1.6453555072203998 (* y b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -4.4e+51) || !(z <= 18000000.0)) {
		tmp = x + (y * 3.13060547623);
	} else {
		tmp = x + (1.6453555072203998 * (y * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-4.4d+51)) .or. (.not. (z <= 18000000.0d0))) then
        tmp = x + (y * 3.13060547623d0)
    else
        tmp = x + (1.6453555072203998d0 * (y * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -4.4e+51) || !(z <= 18000000.0)) {
		tmp = x + (y * 3.13060547623);
	} else {
		tmp = x + (1.6453555072203998 * (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -4.4e+51) or not (z <= 18000000.0):
		tmp = x + (y * 3.13060547623)
	else:
		tmp = x + (1.6453555072203998 * (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -4.4e+51) || !(z <= 18000000.0))
		tmp = Float64(x + Float64(y * 3.13060547623));
	else
		tmp = Float64(x + Float64(1.6453555072203998 * Float64(y * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -4.4e+51) || ~((z <= 18000000.0)))
		tmp = x + (y * 3.13060547623);
	else
		tmp = x + (1.6453555072203998 * (y * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -4.4e+51], N[Not[LessEqual[z, 18000000.0]], $MachinePrecision]], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision], N[(x + N[(1.6453555072203998 * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.39999999999999984e51 or 1.8e7 < z

   1. Initial program 10.3%

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

   3. Simplified 15.6%

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

   5. Taylor expanded in z around inf 92.6%

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

      1. +-commutative 92.6%

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

   7. Simplified 92.6%

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

   if -4.39999999999999984e51 < z < 1.8e7

   1. Initial program 97.1%

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

   3. Simplified 99.0%

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

   5. Taylor expanded in z around 0 73.7%

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

      1. +-commutative 73.7%

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

      2. *-commutative 73.7%

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

   7. Simplified 73.7%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+51} \lor \neg \left(z \leq 18000000\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x + 1.6453555072203998 \cdot \left(y \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 83.0% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+51} \lor \neg \left(z \leq 23000000\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(y \cdot 1.6453555072203998\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -4.4e+51) (not (<= z 23000000.0)))
   (+ 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 <= -4.4e+51) || !(z <= 23000000.0)) {
		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 <= (-4.4d+51)) .or. (.not. (z <= 23000000.0d0))) 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 <= -4.4e+51) || !(z <= 23000000.0)) {
		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 <= -4.4e+51) or not (z <= 23000000.0):
		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 <= -4.4e+51) || !(z <= 23000000.0))
		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 <= -4.4e+51) || ~((z <= 23000000.0)))
		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, -4.4e+51], N[Not[LessEqual[z, 23000000.0]], $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 < -4.39999999999999984e51 or 2.3e7 < z

   1. Initial program 10.3%

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

   3. Simplified 15.6%

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

   5. Taylor expanded in z around inf 92.6%

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

      1. +-commutative 92.6%

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

   7. Simplified 92.6%

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

   if -4.39999999999999984e51 < z < 2.3e7

   1. Initial program 97.1%

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

      1. remove-double-neg 97.1%

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

      2. distribute-lft-neg-out 97.1%

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

   3. Simplified 97.1%

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

   5. Taylor expanded in z around 0 74.6%

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

   6. Taylor expanded in b around inf 73.1%

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

   7. Taylor expanded in z around 0 73.7%

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

      1. *-commutative 73.7%

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

      2. associate-*r* 73.6%

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

   9. Simplified 73.6%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+51} \lor \neg \left(z \leq 23000000\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(y \cdot 1.6453555072203998\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 63.1% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.4 \cdot 10^{-128} \lor \neg \left(z \leq 13200\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;1.6453555072203998 \cdot \left(y \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -7.4e-128) (not (<= z 13200.0)))
   (+ x (* y 3.13060547623))
   (* 1.6453555072203998 (* y b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -7.4e-128) || !(z <= 13200.0)) {
		tmp = x + (y * 3.13060547623);
	} else {
		tmp = 1.6453555072203998 * (y * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-7.4d-128)) .or. (.not. (z <= 13200.0d0))) then
        tmp = x + (y * 3.13060547623d0)
    else
        tmp = 1.6453555072203998d0 * (y * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -7.4e-128) || !(z <= 13200.0)) {
		tmp = x + (y * 3.13060547623);
	} else {
		tmp = 1.6453555072203998 * (y * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -7.4e-128) or not (z <= 13200.0):
		tmp = x + (y * 3.13060547623)
	else:
		tmp = 1.6453555072203998 * (y * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -7.4e-128) || !(z <= 13200.0))
		tmp = Float64(x + Float64(y * 3.13060547623));
	else
		tmp = Float64(1.6453555072203998 * Float64(y * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -7.4e-128) || ~((z <= 13200.0)))
		tmp = x + (y * 3.13060547623);
	else
		tmp = 1.6453555072203998 * (y * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -7.4e-128], N[Not[LessEqual[z, 13200.0]], $MachinePrecision]], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision], N[(1.6453555072203998 * N[(y * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.4e-128 or 13200 < z

   1. Initial program 33.5%

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

   3. Simplified 39.1%

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

   5. Taylor expanded in z around inf 75.8%

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

      1. +-commutative 75.8%

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

   7. Simplified 75.8%

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

   if -7.4e-128 < z < 13200

   1. Initial program 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around 0 81.3%

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

      1. *-commutative 81.3%

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

   7. Simplified 81.3%

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

   8. Taylor expanded in y around inf 45.0%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.4 \cdot 10^{-128} \lor \neg \left(z \leq 13200\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;1.6453555072203998 \cdot \left(y \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 50.4% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{+154} \lor \neg \left(y \leq 1.4 \cdot 10^{+34}\right):\\ \;\;\;\;1.6453555072203998 \cdot \left(y \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -3.3e+154) (not (<= y 1.4e+34)))
   (* 1.6453555072203998 (* y b))
   x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -3.3e+154) || !(y <= 1.4e+34)) {
		tmp = 1.6453555072203998 * (y * b);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-3.3d+154)) .or. (.not. (y <= 1.4d+34))) then
        tmp = 1.6453555072203998d0 * (y * b)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -3.3e+154) || !(y <= 1.4e+34)) {
		tmp = 1.6453555072203998 * (y * b);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -3.3e+154) or not (y <= 1.4e+34):
		tmp = 1.6453555072203998 * (y * b)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -3.3e+154) || !(y <= 1.4e+34))
		tmp = Float64(1.6453555072203998 * Float64(y * b));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -3.3e+154) || ~((y <= 1.4e+34)))
		tmp = 1.6453555072203998 * (y * b);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -3.3e+154], N[Not[LessEqual[y, 1.4e+34]], $MachinePrecision]], N[(1.6453555072203998 * N[(y * b), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -3.3e154 or 1.40000000000000004e34 < y

   1. Initial program 61.7%

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

   3. Simplified 67.2%

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

   5. Taylor expanded in z around 0 45.6%

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

      1. *-commutative 45.6%

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

   7. Simplified 45.6%

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

   8. Taylor expanded in y around inf 39.1%

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

   if -3.3e154 < y < 1.40000000000000004e34

   1. Initial program 59.3%

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

   3. Simplified 61.5%

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

   5. Taylor expanded in y around 0 59.7%

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

4. Final simplification 52.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{+154} \lor \neg \left(y \leq 1.4 \cdot 10^{+34}\right):\\ \;\;\;\;1.6453555072203998 \cdot \left(y \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 46.0% 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 60.1%

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

3. Simplified 63.5%

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

5. Taylor expanded in y around 0 43.1%

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

Developer Target 1: 98.3% 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 2024151 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, D"
  :precision binary64

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

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