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

Percentage Accurate: 59.1% → 97.8%

Time: 16.7s

Alternatives: 18

Speedup: 7.4×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 59.1% 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

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771} \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right)}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \mathsf{fma}\left(-36.52704169880642, \frac{y}{z}, \mathsf{fma}\left(3.13060547623, y, y \cdot \frac{t + 457.9610022158428}{{z}^{2}}\right)\right)\\ \end{array} \end{array} \]

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
    (fma
     -36.52704169880642
     (/ y z)
     (fma 3.13060547623 y (* y (/ (+ t 457.9610022158428) (pow z 2.0))))))))

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 + fma(-36.52704169880642, (y / z), fma(3.13060547623, y, (y * ((t + 457.9610022158428) / pow(z, 2.0)))));
	}
	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 + fma(-36.52704169880642, Float64(y / z), fma(3.13060547623, y, Float64(y * Float64(Float64(t + 457.9610022158428) / (z ^ 2.0))))));
	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[(-36.52704169880642 * N[(y / z), $MachinePrecision] + N[(3.13060547623 * y + N[(y * N[(N[(t + 457.9610022158428), $MachinePrecision] / N[Power[z, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 97.2%

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

   3. Simplified 97.8%

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

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

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in z around -inf 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in z around inf 85.9%

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

      1. fma-define 85.9%

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

      2. fma-define 85.9%

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

      3. associate-/l* 100.0%

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

      4. +-commutative 100.0%

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

   10. Simplified 100.0%

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

4. Final simplification 98.7%

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

Alternative 2: 95.8% accurate, 0.1× speedup

Math

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

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (/
          (*
           y
           (+
            (* z (+ (* z (+ (* z (+ (* z 3.13060547623) 11.1667541262)) t)) a))
            b))
          (+
           (*
            z
            (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721))
           0.607771387771))))
   (if (<= t_1 INFINITY)
     (+ t_1 x)
     (+
      x
      (fma
       -36.52704169880642
       (/ y z)
       (fma 3.13060547623 y (* y (/ (+ t 457.9610022158428) (pow z 2.0)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771);
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1 + x;
	} else {
		tmp = x + fma(-36.52704169880642, (y / z), fma(3.13060547623, y, (y * ((t + 457.9610022158428) / pow(z, 2.0)))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y * Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = Float64(t_1 + x);
	else
		tmp = Float64(x + fma(-36.52704169880642, Float64(y / z), fma(3.13060547623, y, Float64(y * Float64(Float64(t + 457.9610022158428) / (z ^ 2.0))))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y * N[(N[(z * N[(N[(z * N[(N[(z * N[(N[(z * 3.13060547623), $MachinePrecision] + 11.1667541262), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(N[(z * N[(N[(z * N[(N[(z * N[(z + 15.234687407), $MachinePrecision]), $MachinePrecision] + 31.4690115749), $MachinePrecision]), $MachinePrecision] + 11.9400905721), $MachinePrecision]), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], N[(t$95$1 + x), $MachinePrecision], N[(x + N[(-36.52704169880642 * N[(y / z), $MachinePrecision] + N[(3.13060547623 * y + N[(y * N[(N[(t + 457.9610022158428), $MachinePrecision] / N[Power[z, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 97.2%

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

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

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in z around -inf 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in z around inf 85.9%

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

      1. fma-define 85.9%

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

      2. fma-define 85.9%

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

      3. associate-/l* 100.0%

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

      4. +-commutative 100.0%

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

   10. Simplified 100.0%

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

4. Final simplification 98.3%

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

Alternative 3: 95.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\\ \mathbf{if}\;t\_1 \leq \infty:\\ \;\;\;\;t\_1 + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623 - {\left(\sqrt[3]{\frac{36.52704169880642 - \frac{t + 457.9610022158428}{z}}{z}}\right)}^{3}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (/
          (*
           y
           (+
            (* z (+ (* z (+ (* z (+ (* z 3.13060547623) 11.1667541262)) t)) a))
            b))
          (+
           (*
            z
            (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721))
           0.607771387771))))
   (if (<= t_1 INFINITY)
     (+ t_1 x)
     (fma
      y
      (-
       3.13060547623
       (pow
        (cbrt (/ (- 36.52704169880642 (/ (+ t 457.9610022158428) z)) z))
        3.0))
      x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771);
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1 + x;
	} else {
		tmp = fma(y, (3.13060547623 - pow(cbrt(((36.52704169880642 - ((t + 457.9610022158428) / z)) / z)), 3.0)), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y * Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / Float64(Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = Float64(t_1 + x);
	else
		tmp = fma(y, Float64(3.13060547623 - (cbrt(Float64(Float64(36.52704169880642 - Float64(Float64(t + 457.9610022158428) / z)) / z)) ^ 3.0)), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y * N[(N[(z * N[(N[(z * N[(N[(z * N[(N[(z * 3.13060547623), $MachinePrecision] + 11.1667541262), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision] + a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(N[(z * N[(N[(z * N[(N[(z * N[(z + 15.234687407), $MachinePrecision]), $MachinePrecision] + 31.4690115749), $MachinePrecision]), $MachinePrecision] + 11.9400905721), $MachinePrecision]), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], N[(t$95$1 + x), $MachinePrecision], N[(y * N[(3.13060547623 - N[Power[N[Power[N[(N[(36.52704169880642 - N[(N[(t + 457.9610022158428), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], 1/3], $MachinePrecision], 3.0], $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 97.2%

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

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

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in z around -inf 99.9%

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

      1. mul-1-neg 99.9%

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

      2. unsub-neg 99.9%

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

      3. mul-1-neg 99.9%

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

      4. unsub-neg 99.9%

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

      5. +-commutative 99.9%

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

   7. Simplified 99.9%

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

      1. add-cube-cbrt 99.9%

         \[\leadsto \mathsf{fma}\left(y, 3.13060547623 - \color{blue}{\left(\sqrt[3]{\frac{36.52704169880642 - \frac{t + 457.9610022158428}{z}}{z}} \cdot \sqrt[3]{\frac{36.52704169880642 - \frac{t + 457.9610022158428}{z}}{z}}\right) \cdot \sqrt[3]{\frac{36.52704169880642 - \frac{t + 457.9610022158428}{z}}{z}}}, x\right) \]

      2. pow3 99.9%

         \[\leadsto \mathsf{fma}\left(y, 3.13060547623 - \color{blue}{{\left(\sqrt[3]{\frac{36.52704169880642 - \frac{t + 457.9610022158428}{z}}{z}}\right)}^{3}}, x\right) \]

   9. Applied egg-rr 99.9%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771} \leq \infty:\\ \;\;\;\;\frac{y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771} + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623 - {\left(\sqrt[3]{\frac{36.52704169880642 - \frac{t + 457.9610022158428}{z}}{z}}\right)}^{3}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 95.8% accurate, 0.5× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771);
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1 + x;
	} else {
		tmp = x + (y * (3.13060547623 - ((36.52704169880642 - ((t + 457.9610022158428) / z)) / z)));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771);
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1 + x;
	} else {
		tmp = x + (y * (3.13060547623 - ((36.52704169880642 - ((t + 457.9610022158428) / z)) / z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / ((z * ((z * ((z * (z + 15.234687407)) + 31.4690115749)) + 11.9400905721)) + 0.607771387771)
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1 + x
	else:
		tmp = x + (y * (3.13060547623 - ((36.52704169880642 - ((t + 457.9610022158428) / z)) / z)))
	return tmp

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 97.2%

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

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

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in z around -inf 99.9%

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

      1. mul-1-neg 99.9%

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

      2. unsub-neg 99.9%

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

      3. mul-1-neg 99.9%

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

      4. unsub-neg 99.9%

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

      5. +-commutative 99.9%

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

   7. Simplified 99.9%

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

      1. fma-undefine 99.9%

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

   9. Applied egg-rr 99.9%

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

4. Final simplification 98.3%

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

Alternative 5: 96.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t + 457.9610022158428}{z}\\ \mathbf{if}\;z \leq -1.28 \cdot 10^{+45}:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 + \frac{y \cdot t\_1 - y \cdot 36.52704169880642}{z}\right)\\ \mathbf{elif}\;z \leq 1520000000:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot 11.1667541262\right)\right)\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(3.13060547623 - \frac{36.52704169880642 - t\_1}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ t 457.9610022158428) z)))
   (if (<= z -1.28e+45)
     (+ x (+ (* y 3.13060547623) (/ (- (* y t_1) (* y 36.52704169880642)) z)))
     (if (<= z 1520000000.0)
       (+
        x
        (/
         (* y (+ b (* z (+ a (* z (+ t (* z 11.1667541262)))))))
         (+
          (*
           z
           (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721))
          0.607771387771)))
       (+ x (* y (- 3.13060547623 (/ (- 36.52704169880642 t_1) z))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t + 457.9610022158428) / z;
	double tmp;
	if (z <= -1.28e+45) {
		tmp = x + ((y * 3.13060547623) + (((y * t_1) - (y * 36.52704169880642)) / z));
	} else if (z <= 1520000000.0) {
		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 * (3.13060547623 - ((36.52704169880642 - t_1) / z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t + 457.9610022158428d0) / z
    if (z <= (-1.28d+45)) then
        tmp = x + ((y * 3.13060547623d0) + (((y * t_1) - (y * 36.52704169880642d0)) / z))
    else if (z <= 1520000000.0d0) 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 * (3.13060547623d0 - ((36.52704169880642d0 - t_1) / z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t + 457.9610022158428) / z;
	double tmp;
	if (z <= -1.28e+45) {
		tmp = x + ((y * 3.13060547623) + (((y * t_1) - (y * 36.52704169880642)) / z));
	} else if (z <= 1520000000.0) {
		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 * (3.13060547623 - ((36.52704169880642 - t_1) / z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t + 457.9610022158428) / z
	tmp = 0
	if z <= -1.28e+45:
		tmp = x + ((y * 3.13060547623) + (((y * t_1) - (y * 36.52704169880642)) / z))
	elif z <= 1520000000.0:
		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 * (3.13060547623 - ((36.52704169880642 - t_1) / z)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t + 457.9610022158428) / z)
	tmp = 0.0
	if (z <= -1.28e+45)
		tmp = Float64(x + Float64(Float64(y * 3.13060547623) + Float64(Float64(Float64(y * t_1) - Float64(y * 36.52704169880642)) / z)));
	elseif (z <= 1520000000.0)
		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(y * Float64(3.13060547623 - Float64(Float64(36.52704169880642 - t_1) / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t + 457.9610022158428) / z;
	tmp = 0.0;
	if (z <= -1.28e+45)
		tmp = x + ((y * 3.13060547623) + (((y * t_1) - (y * 36.52704169880642)) / z));
	elseif (z <= 1520000000.0)
		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 * (3.13060547623 - ((36.52704169880642 - t_1) / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t + 457.9610022158428), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[z, -1.28e+45], N[(x + N[(N[(y * 3.13060547623), $MachinePrecision] + N[(N[(N[(y * t$95$1), $MachinePrecision] - N[(y * 36.52704169880642), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1520000000.0], 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[(y * N[(3.13060547623 - N[(N[(36.52704169880642 - t$95$1), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.28000000000000002e45

   1. Initial program 12.0%

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

   3. Simplified 12.0%

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

   5. Taylor expanded in z around -inf 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in z around -inf 88.5%

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

      1. +-commutative 88.5%

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

      2. mul-1-neg 88.5%

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

      3. unsub-neg 88.5%

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

      4. +-commutative 88.5%

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

      5. mul-1-neg 88.5%

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

      6. unsub-neg 88.5%

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

      7. *-commutative 88.5%

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

      8. associate-/l* 98.4%

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

      9. +-commutative 98.4%

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

   10. Simplified 98.4%

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

   if -1.28000000000000002e45 < z < 1.52e9

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0 98.8%

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

      1. *-commutative 98.8%

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

   5. Simplified 98.8%

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

   if 1.52e9 < z

   1. Initial program 13.7%

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

   3. Simplified 15.1%

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

   5. Taylor expanded in z around -inf 97.1%

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

      1. mul-1-neg 97.1%

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

      2. unsub-neg 97.1%

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

      3. mul-1-neg 97.1%

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

      4. unsub-neg 97.1%

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

      5. +-commutative 97.1%

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

   7. Simplified 97.1%

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

      1. fma-undefine 97.1%

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

   9. Applied egg-rr 97.1%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.28 \cdot 10^{+45}:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 + \frac{y \cdot \frac{t + 457.9610022158428}{z} - y \cdot 36.52704169880642}{z}\right)\\ \mathbf{elif}\;z \leq 1520000000:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot 11.1667541262\right)\right)\right)}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(3.13060547623 - \frac{36.52704169880642 - \frac{t + 457.9610022158428}{z}}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 96.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t + 457.9610022158428}{z}\\ \mathbf{if}\;z \leq -22000:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 + \frac{y \cdot t\_1 - y \cdot 36.52704169880642}{z}\right)\\ \mathbf{elif}\;z \leq 4100000:\\ \;\;\;\;x + \frac{y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot 31.4690115749\right)}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(3.13060547623 - \frac{36.52704169880642 - t\_1}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ t 457.9610022158428) z)))
   (if (<= z -22000.0)
     (+ x (+ (* y 3.13060547623) (/ (- (* y t_1) (* y 36.52704169880642)) z)))
     (if (<= z 4100000.0)
       (+
        x
        (/
         (*
          y
          (+
           (* z (+ (* z (+ (* z (+ (* z 3.13060547623) 11.1667541262)) t)) a))
           b))
         (+ 0.607771387771 (* z (+ 11.9400905721 (* z 31.4690115749))))))
       (+ x (* y (- 3.13060547623 (/ (- 36.52704169880642 t_1) z))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t + 457.9610022158428) / z;
	double tmp;
	if (z <= -22000.0) {
		tmp = x + ((y * 3.13060547623) + (((y * t_1) - (y * 36.52704169880642)) / z));
	} else if (z <= 4100000.0) {
		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 * (3.13060547623 - ((36.52704169880642 - t_1) / z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t + 457.9610022158428d0) / z
    if (z <= (-22000.0d0)) then
        tmp = x + ((y * 3.13060547623d0) + (((y * t_1) - (y * 36.52704169880642d0)) / z))
    else if (z <= 4100000.0d0) 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 * (3.13060547623d0 - ((36.52704169880642d0 - t_1) / z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t + 457.9610022158428) / z;
	double tmp;
	if (z <= -22000.0) {
		tmp = x + ((y * 3.13060547623) + (((y * t_1) - (y * 36.52704169880642)) / z));
	} else if (z <= 4100000.0) {
		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 * (3.13060547623 - ((36.52704169880642 - t_1) / z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t + 457.9610022158428) / z
	tmp = 0
	if z <= -22000.0:
		tmp = x + ((y * 3.13060547623) + (((y * t_1) - (y * 36.52704169880642)) / z))
	elif z <= 4100000.0:
		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 * (3.13060547623 - ((36.52704169880642 - t_1) / z)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t + 457.9610022158428) / z)
	tmp = 0.0
	if (z <= -22000.0)
		tmp = Float64(x + Float64(Float64(y * 3.13060547623) + Float64(Float64(Float64(y * t_1) - Float64(y * 36.52704169880642)) / z)));
	elseif (z <= 4100000.0)
		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(y * Float64(3.13060547623 - Float64(Float64(36.52704169880642 - t_1) / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t + 457.9610022158428) / z;
	tmp = 0.0;
	if (z <= -22000.0)
		tmp = x + ((y * 3.13060547623) + (((y * t_1) - (y * 36.52704169880642)) / z));
	elseif (z <= 4100000.0)
		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 * (3.13060547623 - ((36.52704169880642 - t_1) / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t + 457.9610022158428), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[z, -22000.0], N[(x + N[(N[(y * 3.13060547623), $MachinePrecision] + N[(N[(N[(y * t$95$1), $MachinePrecision] - N[(y * 36.52704169880642), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4100000.0], 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[(y * N[(3.13060547623 - N[(N[(36.52704169880642 - t$95$1), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -22000

   1. Initial program 24.7%

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

   3. Simplified 24.7%

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

   5. Taylor expanded in z around -inf 98.6%

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

   7. Simplified 98.6%

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

   8. Taylor expanded in z around -inf 83.4%

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

      1. +-commutative 83.4%

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

      2. mul-1-neg 83.4%

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

      3. unsub-neg 83.4%

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

      4. +-commutative 83.4%

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

      5. mul-1-neg 83.4%

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

      6. unsub-neg 83.4%

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

      7. *-commutative 83.4%

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

      8. associate-/l* 91.8%

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

      9. +-commutative 91.8%

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

   10. Simplified 91.8%

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

   if -22000 < z < 4.1e6

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0 98.3%

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

   if 4.1e6 < z

   1. Initial program 13.7%

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

   3. Simplified 15.1%

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

   5. Taylor expanded in z around -inf 97.1%

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

      1. mul-1-neg 97.1%

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

      2. unsub-neg 97.1%

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

      3. mul-1-neg 97.1%

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

      4. unsub-neg 97.1%

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

      5. +-commutative 97.1%

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

   7. Simplified 97.1%

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

      1. fma-undefine 97.1%

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

   9. Applied egg-rr 97.1%

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

4. Final simplification 96.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -22000:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 + \frac{y \cdot \frac{t + 457.9610022158428}{z} - y \cdot 36.52704169880642}{z}\right)\\ \mathbf{elif}\;z \leq 4100000:\\ \;\;\;\;x + \frac{y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot 31.4690115749\right)}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(3.13060547623 - \frac{36.52704169880642 - \frac{t + 457.9610022158428}{z}}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 95.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t + 457.9610022158428}{z}\\ \mathbf{if}\;z \leq -980:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 + \frac{y \cdot t\_1 - y \cdot 36.52704169880642}{z}\right)\\ \mathbf{elif}\;z \leq 3200000:\\ \;\;\;\;x + \frac{y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(3.13060547623 - \frac{36.52704169880642 - t\_1}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ t 457.9610022158428) z)))
   (if (<= z -980.0)
     (+ x (+ (* y 3.13060547623) (/ (- (* y t_1) (* y 36.52704169880642)) z)))
     (if (<= z 3200000.0)
       (+
        x
        (/
         (*
          y
          (+
           (* z (+ (* z (+ (* z (+ (* z 3.13060547623) 11.1667541262)) t)) a))
           b))
         (+ 0.607771387771 (* z 11.9400905721))))
       (+ x (* y (- 3.13060547623 (/ (- 36.52704169880642 t_1) z))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t + 457.9610022158428) / z;
	double tmp;
	if (z <= -980.0) {
		tmp = x + ((y * 3.13060547623) + (((y * t_1) - (y * 36.52704169880642)) / z));
	} else if (z <= 3200000.0) {
		tmp = x + ((y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / (0.607771387771 + (z * 11.9400905721)));
	} else {
		tmp = x + (y * (3.13060547623 - ((36.52704169880642 - t_1) / z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t + 457.9610022158428d0) / z
    if (z <= (-980.0d0)) then
        tmp = x + ((y * 3.13060547623d0) + (((y * t_1) - (y * 36.52704169880642d0)) / z))
    else if (z <= 3200000.0d0) then
        tmp = x + ((y * ((z * ((z * ((z * ((z * 3.13060547623d0) + 11.1667541262d0)) + t)) + a)) + b)) / (0.607771387771d0 + (z * 11.9400905721d0)))
    else
        tmp = x + (y * (3.13060547623d0 - ((36.52704169880642d0 - t_1) / z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t + 457.9610022158428) / z;
	double tmp;
	if (z <= -980.0) {
		tmp = x + ((y * 3.13060547623) + (((y * t_1) - (y * 36.52704169880642)) / z));
	} else if (z <= 3200000.0) {
		tmp = x + ((y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / (0.607771387771 + (z * 11.9400905721)));
	} else {
		tmp = x + (y * (3.13060547623 - ((36.52704169880642 - t_1) / z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t + 457.9610022158428) / z
	tmp = 0
	if z <= -980.0:
		tmp = x + ((y * 3.13060547623) + (((y * t_1) - (y * 36.52704169880642)) / z))
	elif z <= 3200000.0:
		tmp = x + ((y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / (0.607771387771 + (z * 11.9400905721)))
	else:
		tmp = x + (y * (3.13060547623 - ((36.52704169880642 - t_1) / z)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t + 457.9610022158428) / z)
	tmp = 0.0
	if (z <= -980.0)
		tmp = Float64(x + Float64(Float64(y * 3.13060547623) + Float64(Float64(Float64(y * t_1) - Float64(y * 36.52704169880642)) / z)));
	elseif (z <= 3200000.0)
		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(y * Float64(3.13060547623 - Float64(Float64(36.52704169880642 - t_1) / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t + 457.9610022158428) / z;
	tmp = 0.0;
	if (z <= -980.0)
		tmp = x + ((y * 3.13060547623) + (((y * t_1) - (y * 36.52704169880642)) / z));
	elseif (z <= 3200000.0)
		tmp = x + ((y * ((z * ((z * ((z * ((z * 3.13060547623) + 11.1667541262)) + t)) + a)) + b)) / (0.607771387771 + (z * 11.9400905721)));
	else
		tmp = x + (y * (3.13060547623 - ((36.52704169880642 - t_1) / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t + 457.9610022158428), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[z, -980.0], N[(x + N[(N[(y * 3.13060547623), $MachinePrecision] + N[(N[(N[(y * t$95$1), $MachinePrecision] - N[(y * 36.52704169880642), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3200000.0], 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[(y * N[(3.13060547623 - N[(N[(36.52704169880642 - t$95$1), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -980

   1. Initial program 24.7%

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

   3. Simplified 24.7%

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

   5. Taylor expanded in z around -inf 98.6%

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

   7. Simplified 98.6%

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

   8. Taylor expanded in z around -inf 83.4%

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

      1. +-commutative 83.4%

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

      2. mul-1-neg 83.4%

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

      3. unsub-neg 83.4%

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

      4. +-commutative 83.4%

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

      5. mul-1-neg 83.4%

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

      6. unsub-neg 83.4%

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

      7. *-commutative 83.4%

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

      8. associate-/l* 91.8%

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

      9. +-commutative 91.8%

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

   10. Simplified 91.8%

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

   if -980 < z < 3.2e6

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0 98.1%

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

      1. *-commutative 98.1%

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

   5. Simplified 98.1%

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

   if 3.2e6 < z

   1. Initial program 13.7%

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

   3. Simplified 15.1%

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

   5. Taylor expanded in z around -inf 97.1%

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

      1. mul-1-neg 97.1%

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

      2. unsub-neg 97.1%

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

      3. mul-1-neg 97.1%

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

      4. unsub-neg 97.1%

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

      5. +-commutative 97.1%

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

   7. Simplified 97.1%

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

      1. fma-undefine 97.1%

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

   9. Applied egg-rr 97.1%

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

4. Final simplification 96.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -980:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 + \frac{y \cdot \frac{t + 457.9610022158428}{z} - y \cdot 36.52704169880642}{z}\right)\\ \mathbf{elif}\;z \leq 3200000:\\ \;\;\;\;x + \frac{y \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(3.13060547623 - \frac{36.52704169880642 - \frac{t + 457.9610022158428}{z}}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 85.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t + 457.9610022158428}{z}\\ \mathbf{if}\;z \leq -1150:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 + \frac{y \cdot t\_1 - y \cdot 36.52704169880642}{z}\right)\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-52}:\\ \;\;\;\;x + \left(1.6453555072203998 \cdot \left(y \cdot b\right) + z \cdot \left(1.6453555072203998 \cdot \left(y \cdot a\right) - \left(y \cdot b\right) \cdot 32.324150453290734\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(3.13060547623 - \frac{36.52704169880642 - t\_1}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ t 457.9610022158428) z)))
   (if (<= z -1150.0)
     (+ x (+ (* y 3.13060547623) (/ (- (* y t_1) (* y 36.52704169880642)) z)))
     (if (<= z 2.5e-52)
       (+
        x
        (+
         (* 1.6453555072203998 (* y b))
         (*
          z
          (- (* 1.6453555072203998 (* y a)) (* (* y b) 32.324150453290734)))))
       (+ x (* y (- 3.13060547623 (/ (- 36.52704169880642 t_1) z))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t + 457.9610022158428) / z;
	double tmp;
	if (z <= -1150.0) {
		tmp = x + ((y * 3.13060547623) + (((y * t_1) - (y * 36.52704169880642)) / z));
	} else if (z <= 2.5e-52) {
		tmp = x + ((1.6453555072203998 * (y * b)) + (z * ((1.6453555072203998 * (y * a)) - ((y * b) * 32.324150453290734))));
	} else {
		tmp = x + (y * (3.13060547623 - ((36.52704169880642 - t_1) / z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t + 457.9610022158428d0) / z
    if (z <= (-1150.0d0)) then
        tmp = x + ((y * 3.13060547623d0) + (((y * t_1) - (y * 36.52704169880642d0)) / z))
    else if (z <= 2.5d-52) then
        tmp = x + ((1.6453555072203998d0 * (y * b)) + (z * ((1.6453555072203998d0 * (y * a)) - ((y * b) * 32.324150453290734d0))))
    else
        tmp = x + (y * (3.13060547623d0 - ((36.52704169880642d0 - t_1) / z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t + 457.9610022158428) / z;
	double tmp;
	if (z <= -1150.0) {
		tmp = x + ((y * 3.13060547623) + (((y * t_1) - (y * 36.52704169880642)) / z));
	} else if (z <= 2.5e-52) {
		tmp = x + ((1.6453555072203998 * (y * b)) + (z * ((1.6453555072203998 * (y * a)) - ((y * b) * 32.324150453290734))));
	} else {
		tmp = x + (y * (3.13060547623 - ((36.52704169880642 - t_1) / z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t + 457.9610022158428) / z
	tmp = 0
	if z <= -1150.0:
		tmp = x + ((y * 3.13060547623) + (((y * t_1) - (y * 36.52704169880642)) / z))
	elif z <= 2.5e-52:
		tmp = x + ((1.6453555072203998 * (y * b)) + (z * ((1.6453555072203998 * (y * a)) - ((y * b) * 32.324150453290734))))
	else:
		tmp = x + (y * (3.13060547623 - ((36.52704169880642 - t_1) / z)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t + 457.9610022158428) / z)
	tmp = 0.0
	if (z <= -1150.0)
		tmp = Float64(x + Float64(Float64(y * 3.13060547623) + Float64(Float64(Float64(y * t_1) - Float64(y * 36.52704169880642)) / z)));
	elseif (z <= 2.5e-52)
		tmp = Float64(x + Float64(Float64(1.6453555072203998 * Float64(y * b)) + Float64(z * Float64(Float64(1.6453555072203998 * Float64(y * a)) - Float64(Float64(y * b) * 32.324150453290734)))));
	else
		tmp = Float64(x + Float64(y * Float64(3.13060547623 - Float64(Float64(36.52704169880642 - t_1) / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t + 457.9610022158428) / z;
	tmp = 0.0;
	if (z <= -1150.0)
		tmp = x + ((y * 3.13060547623) + (((y * t_1) - (y * 36.52704169880642)) / z));
	elseif (z <= 2.5e-52)
		tmp = x + ((1.6453555072203998 * (y * b)) + (z * ((1.6453555072203998 * (y * a)) - ((y * b) * 32.324150453290734))));
	else
		tmp = x + (y * (3.13060547623 - ((36.52704169880642 - t_1) / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t + 457.9610022158428), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[z, -1150.0], N[(x + N[(N[(y * 3.13060547623), $MachinePrecision] + N[(N[(N[(y * t$95$1), $MachinePrecision] - N[(y * 36.52704169880642), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.5e-52], N[(x + N[(N[(1.6453555072203998 * N[(y * b), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(1.6453555072203998 * N[(y * a), $MachinePrecision]), $MachinePrecision] - N[(N[(y * b), $MachinePrecision] * 32.324150453290734), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(3.13060547623 - N[(N[(36.52704169880642 - t$95$1), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1150

   1. Initial program 24.7%

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

   3. Simplified 24.7%

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

   5. Taylor expanded in z around -inf 98.6%

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

   7. Simplified 98.6%

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

   8. Taylor expanded in z around -inf 83.4%

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

      1. +-commutative 83.4%

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

      2. mul-1-neg 83.4%

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

      3. unsub-neg 83.4%

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

      4. +-commutative 83.4%

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

      5. mul-1-neg 83.4%

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

      6. unsub-neg 83.4%

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

      7. *-commutative 83.4%

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

      8. associate-/l* 91.8%

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

      9. +-commutative 91.8%

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

   10. Simplified 91.8%

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

   if -1150 < z < 2.5e-52

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0 88.6%

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

   if 2.5e-52 < z

   1. Initial program 26.0%

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

   3. Simplified 27.2%

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

   5. Taylor expanded in z around -inf 91.3%

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

      1. mul-1-neg 91.3%

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

      2. unsub-neg 91.3%

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

      3. mul-1-neg 91.3%

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

      4. unsub-neg 91.3%

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

      5. +-commutative 91.3%

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

   7. Simplified 91.3%

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

      1. fma-undefine 91.3%

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

   9. Applied egg-rr 91.3%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1150:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 + \frac{y \cdot \frac{t + 457.9610022158428}{z} - y \cdot 36.52704169880642}{z}\right)\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-52}:\\ \;\;\;\;x + \left(1.6453555072203998 \cdot \left(y \cdot b\right) + z \cdot \left(1.6453555072203998 \cdot \left(y \cdot a\right) - \left(y \cdot b\right) \cdot 32.324150453290734\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(3.13060547623 - \frac{36.52704169880642 - \frac{t + 457.9610022158428}{z}}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 82.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+38}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{elif}\;z \leq -4.3 \cdot 10^{-58}:\\ \;\;\;\;x + \left(z \cdot a\right) \cdot \left(y \cdot 1.6453555072203998\right)\\ \mathbf{elif}\;z \leq 25000000:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 + -36.52704169880642 \cdot \frac{y}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -1.9e+38)
   (+ x (* y 3.13060547623))
   (if (<= z -4.3e-58)
     (+ x (* (* z a) (* y 1.6453555072203998)))
     (if (<= z 25000000.0)
       (+ x (* y (* b 1.6453555072203998)))
       (+ x (+ (* y 3.13060547623) (* -36.52704169880642 (/ y z))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -1.9e+38) {
		tmp = x + (y * 3.13060547623);
	} else if (z <= -4.3e-58) {
		tmp = x + ((z * a) * (y * 1.6453555072203998));
	} else if (z <= 25000000.0) {
		tmp = x + (y * (b * 1.6453555072203998));
	} else {
		tmp = x + ((y * 3.13060547623) + (-36.52704169880642 * (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 <= (-1.9d+38)) then
        tmp = x + (y * 3.13060547623d0)
    else if (z <= (-4.3d-58)) then
        tmp = x + ((z * a) * (y * 1.6453555072203998d0))
    else if (z <= 25000000.0d0) then
        tmp = x + (y * (b * 1.6453555072203998d0))
    else
        tmp = x + ((y * 3.13060547623d0) + ((-36.52704169880642d0) * (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 <= -1.9e+38) {
		tmp = x + (y * 3.13060547623);
	} else if (z <= -4.3e-58) {
		tmp = x + ((z * a) * (y * 1.6453555072203998));
	} else if (z <= 25000000.0) {
		tmp = x + (y * (b * 1.6453555072203998));
	} else {
		tmp = x + ((y * 3.13060547623) + (-36.52704169880642 * (y / z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -1.9e+38:
		tmp = x + (y * 3.13060547623)
	elif z <= -4.3e-58:
		tmp = x + ((z * a) * (y * 1.6453555072203998))
	elif z <= 25000000.0:
		tmp = x + (y * (b * 1.6453555072203998))
	else:
		tmp = x + ((y * 3.13060547623) + (-36.52704169880642 * (y / z)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -1.9e+38)
		tmp = Float64(x + Float64(y * 3.13060547623));
	elseif (z <= -4.3e-58)
		tmp = Float64(x + Float64(Float64(z * a) * Float64(y * 1.6453555072203998)));
	elseif (z <= 25000000.0)
		tmp = Float64(x + Float64(y * Float64(b * 1.6453555072203998)));
	else
		tmp = Float64(x + Float64(Float64(y * 3.13060547623) + Float64(-36.52704169880642 * Float64(y / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -1.9e+38)
		tmp = x + (y * 3.13060547623);
	elseif (z <= -4.3e-58)
		tmp = x + ((z * a) * (y * 1.6453555072203998));
	elseif (z <= 25000000.0)
		tmp = x + (y * (b * 1.6453555072203998));
	else
		tmp = x + ((y * 3.13060547623) + (-36.52704169880642 * (y / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -1.9e+38], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.3e-58], N[(x + N[(N[(z * a), $MachinePrecision] * N[(y * 1.6453555072203998), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 25000000.0], N[(x + N[(y * N[(b * 1.6453555072203998), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * 3.13060547623), $MachinePrecision] + N[(-36.52704169880642 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.8999999999999999e38

   1. Initial program 14.9%

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

   3. Taylor expanded in z around inf 93.8%

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

      1. *-commutative 93.8%

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

   5. Simplified 93.8%

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

   if -1.8999999999999999e38 < z < -4.2999999999999999e-58

   1. Initial program 99.5%

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

   3. Taylor expanded in a around inf 69.1%

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

   4. Taylor expanded in z around 0 51.2%

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

      1. *-commutative 53.9%

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

   6. Simplified 51.2%

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

   7. Taylor expanded in z around 0 60.6%

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

      1. associate-*r* 60.7%

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

      2. *-commutative 60.7%

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

      3. *-commutative 60.7%

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

      4. associate-*r* 60.8%

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

      5. associate-*l* 60.8%

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

      6. *-commutative 60.8%

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

   9. Simplified 60.8%

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

   if -4.2999999999999999e-58 < z < 2.5e7

   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 83.2%

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

      1. *-commutative 83.2%

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

   7. Simplified 83.2%

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

      1. fma-undefine 83.2%

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

   9. Applied egg-rr 83.2%

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

   if 2.5e7 < z

   1. Initial program 13.7%

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

   3. Simplified 15.1%

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

   5. Taylor expanded in z around -inf 97.1%

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

   7. Simplified 97.1%

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

   8. Taylor expanded in z around inf 94.0%

      \[\leadsto \color{blue}{x + \left(-36.52704169880642 \cdot \frac{y}{z} + 3.13060547623 \cdot y\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+38}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{elif}\;z \leq -4.3 \cdot 10^{-58}:\\ \;\;\;\;x + \left(z \cdot a\right) \cdot \left(y \cdot 1.6453555072203998\right)\\ \mathbf{elif}\;z \leq 25000000:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 + -36.52704169880642 \cdot \frac{y}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 86.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{-29} \lor \neg \left(z \leq 2600000\right):\\ \;\;\;\;x + y \cdot \left(3.13060547623 - \frac{36.52704169880642 - \frac{t + 457.9610022158428}{z}}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -4e-29) (not (<= z 2600000.0)))
   (+
    x
    (*
     y
     (-
      3.13060547623
      (/ (- 36.52704169880642 (/ (+ t 457.9610022158428) z)) z))))
   (+ x (* y (* b 1.6453555072203998)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -4e-29) || !(z <= 2600000.0)) {
		tmp = x + (y * (3.13060547623 - ((36.52704169880642 - ((t + 457.9610022158428) / z)) / z)));
	} else {
		tmp = x + (y * (b * 1.6453555072203998));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-4d-29)) .or. (.not. (z <= 2600000.0d0))) then
        tmp = x + (y * (3.13060547623d0 - ((36.52704169880642d0 - ((t + 457.9610022158428d0) / z)) / z)))
    else
        tmp = x + (y * (b * 1.6453555072203998d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -4e-29) || !(z <= 2600000.0)) {
		tmp = x + (y * (3.13060547623 - ((36.52704169880642 - ((t + 457.9610022158428) / z)) / z)));
	} else {
		tmp = x + (y * (b * 1.6453555072203998));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -4e-29) or not (z <= 2600000.0):
		tmp = x + (y * (3.13060547623 - ((36.52704169880642 - ((t + 457.9610022158428) / z)) / z)))
	else:
		tmp = x + (y * (b * 1.6453555072203998))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -4e-29) || !(z <= 2600000.0))
		tmp = Float64(x + Float64(y * Float64(3.13060547623 - Float64(Float64(36.52704169880642 - Float64(Float64(t + 457.9610022158428) / z)) / z))));
	else
		tmp = Float64(x + Float64(y * Float64(b * 1.6453555072203998)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -4e-29) || ~((z <= 2600000.0)))
		tmp = x + (y * (3.13060547623 - ((36.52704169880642 - ((t + 457.9610022158428) / z)) / z)));
	else
		tmp = x + (y * (b * 1.6453555072203998));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -4e-29], N[Not[LessEqual[z, 2600000.0]], $MachinePrecision]], N[(x + N[(y * N[(3.13060547623 - N[(N[(36.52704169880642 - N[(N[(t + 457.9610022158428), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(b * 1.6453555072203998), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.99999999999999977e-29 or 2.6e6 < z

   1. Initial program 22.2%

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

   3. Simplified 22.9%

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

   5. Taylor expanded in z around -inf 92.5%

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

      1. mul-1-neg 92.5%

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

      2. unsub-neg 92.5%

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

      3. mul-1-neg 92.5%

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

      4. unsub-neg 92.5%

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

      5. +-commutative 92.5%

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

   7. Simplified 92.5%

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

      1. fma-undefine 92.5%

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

   9. Applied egg-rr 92.5%

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

   if -3.99999999999999977e-29 < z < 2.6e6

   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. Step-by-step derivation

      1. fma-undefine 81.3%

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

   9. Applied egg-rr 81.3%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{-29} \lor \neg \left(z \leq 2600000\right):\\ \;\;\;\;x + y \cdot \left(3.13060547623 - \frac{36.52704169880642 - \frac{t + 457.9610022158428}{z}}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 85.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t + 457.9610022158428}{z}\\ \mathbf{if}\;z \leq -6.5 \cdot 10^{-29}:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 + \frac{y \cdot t\_1 - y \cdot 36.52704169880642}{z}\right)\\ \mathbf{elif}\;z \leq 3800000:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(3.13060547623 - \frac{36.52704169880642 - t\_1}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ t 457.9610022158428) z)))
   (if (<= z -6.5e-29)
     (+ x (+ (* y 3.13060547623) (/ (- (* y t_1) (* y 36.52704169880642)) z)))
     (if (<= z 3800000.0)
       (+ x (* y (* b 1.6453555072203998)))
       (+ x (* y (- 3.13060547623 (/ (- 36.52704169880642 t_1) z))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t + 457.9610022158428) / z;
	double tmp;
	if (z <= -6.5e-29) {
		tmp = x + ((y * 3.13060547623) + (((y * t_1) - (y * 36.52704169880642)) / z));
	} else if (z <= 3800000.0) {
		tmp = x + (y * (b * 1.6453555072203998));
	} else {
		tmp = x + (y * (3.13060547623 - ((36.52704169880642 - t_1) / z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t + 457.9610022158428d0) / z
    if (z <= (-6.5d-29)) then
        tmp = x + ((y * 3.13060547623d0) + (((y * t_1) - (y * 36.52704169880642d0)) / z))
    else if (z <= 3800000.0d0) then
        tmp = x + (y * (b * 1.6453555072203998d0))
    else
        tmp = x + (y * (3.13060547623d0 - ((36.52704169880642d0 - t_1) / z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t + 457.9610022158428) / z;
	double tmp;
	if (z <= -6.5e-29) {
		tmp = x + ((y * 3.13060547623) + (((y * t_1) - (y * 36.52704169880642)) / z));
	} else if (z <= 3800000.0) {
		tmp = x + (y * (b * 1.6453555072203998));
	} else {
		tmp = x + (y * (3.13060547623 - ((36.52704169880642 - t_1) / z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t + 457.9610022158428) / z
	tmp = 0
	if z <= -6.5e-29:
		tmp = x + ((y * 3.13060547623) + (((y * t_1) - (y * 36.52704169880642)) / z))
	elif z <= 3800000.0:
		tmp = x + (y * (b * 1.6453555072203998))
	else:
		tmp = x + (y * (3.13060547623 - ((36.52704169880642 - t_1) / z)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t + 457.9610022158428) / z)
	tmp = 0.0
	if (z <= -6.5e-29)
		tmp = Float64(x + Float64(Float64(y * 3.13060547623) + Float64(Float64(Float64(y * t_1) - Float64(y * 36.52704169880642)) / z)));
	elseif (z <= 3800000.0)
		tmp = Float64(x + Float64(y * Float64(b * 1.6453555072203998)));
	else
		tmp = Float64(x + Float64(y * Float64(3.13060547623 - Float64(Float64(36.52704169880642 - t_1) / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t + 457.9610022158428) / z;
	tmp = 0.0;
	if (z <= -6.5e-29)
		tmp = x + ((y * 3.13060547623) + (((y * t_1) - (y * 36.52704169880642)) / z));
	elseif (z <= 3800000.0)
		tmp = x + (y * (b * 1.6453555072203998));
	else
		tmp = x + (y * (3.13060547623 - ((36.52704169880642 - t_1) / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t + 457.9610022158428), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[z, -6.5e-29], N[(x + N[(N[(y * 3.13060547623), $MachinePrecision] + N[(N[(N[(y * t$95$1), $MachinePrecision] - N[(y * 36.52704169880642), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3800000.0], N[(x + N[(y * N[(b * 1.6453555072203998), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(3.13060547623 - N[(N[(36.52704169880642 - t$95$1), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.5e-29

   1. Initial program 29.7%

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

   3. Simplified 29.8%

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

   5. Taylor expanded in z around -inf 94.9%

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

   7. Simplified 94.9%

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

   8. Taylor expanded in z around -inf 80.6%

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

      1. +-commutative 80.6%

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

      2. mul-1-neg 80.6%

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

      3. unsub-neg 80.6%

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

      4. +-commutative 80.6%

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

      5. mul-1-neg 80.6%

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

      6. unsub-neg 80.6%

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

      7. *-commutative 80.6%

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

      8. associate-/l* 88.5%

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

      9. +-commutative 88.5%

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

   10. Simplified 88.5%

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

   if -6.5e-29 < z < 3.8e6

   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. Step-by-step derivation

      1. fma-undefine 81.3%

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

   9. Applied egg-rr 81.3%

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

   if 3.8e6 < z

   1. Initial program 13.7%

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

   3. Simplified 15.1%

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

   5. Taylor expanded in z around -inf 97.1%

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

      1. mul-1-neg 97.1%

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

      2. unsub-neg 97.1%

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

      3. mul-1-neg 97.1%

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

      4. unsub-neg 97.1%

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

      5. +-commutative 97.1%

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

   7. Simplified 97.1%

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

      1. fma-undefine 97.1%

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

   9. Applied egg-rr 97.1%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{-29}:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 + \frac{y \cdot \frac{t + 457.9610022158428}{z} - y \cdot 36.52704169880642}{z}\right)\\ \mathbf{elif}\;z \leq 3800000:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(3.13060547623 - \frac{36.52704169880642 - \frac{t + 457.9610022158428}{z}}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 82.8% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot 3.13060547623\\ \mathbf{if}\;z \leq -1.9 \cdot 10^{+38}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-55}:\\ \;\;\;\;x + \left(z \cdot a\right) \cdot \left(y \cdot 1.6453555072203998\right)\\ \mathbf{elif}\;z \leq 800000000:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* y 3.13060547623))))
   (if (<= z -1.9e+38)
     t_1
     (if (<= z -2.3e-55)
       (+ x (* (* z a) (* y 1.6453555072203998)))
       (if (<= z 800000000.0) (+ x (* y (* b 1.6453555072203998))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * 3.13060547623);
	double tmp;
	if (z <= -1.9e+38) {
		tmp = t_1;
	} else if (z <= -2.3e-55) {
		tmp = x + ((z * a) * (y * 1.6453555072203998));
	} else if (z <= 800000000.0) {
		tmp = x + (y * (b * 1.6453555072203998));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * 3.13060547623d0)
    if (z <= (-1.9d+38)) then
        tmp = t_1
    else if (z <= (-2.3d-55)) then
        tmp = x + ((z * a) * (y * 1.6453555072203998d0))
    else if (z <= 800000000.0d0) then
        tmp = x + (y * (b * 1.6453555072203998d0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * 3.13060547623);
	double tmp;
	if (z <= -1.9e+38) {
		tmp = t_1;
	} else if (z <= -2.3e-55) {
		tmp = x + ((z * a) * (y * 1.6453555072203998));
	} else if (z <= 800000000.0) {
		tmp = x + (y * (b * 1.6453555072203998));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y * 3.13060547623)
	tmp = 0
	if z <= -1.9e+38:
		tmp = t_1
	elif z <= -2.3e-55:
		tmp = x + ((z * a) * (y * 1.6453555072203998))
	elif z <= 800000000.0:
		tmp = x + (y * (b * 1.6453555072203998))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y * 3.13060547623))
	tmp = 0.0
	if (z <= -1.9e+38)
		tmp = t_1;
	elseif (z <= -2.3e-55)
		tmp = Float64(x + Float64(Float64(z * a) * Float64(y * 1.6453555072203998)));
	elseif (z <= 800000000.0)
		tmp = Float64(x + Float64(y * Float64(b * 1.6453555072203998)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (y * 3.13060547623);
	tmp = 0.0;
	if (z <= -1.9e+38)
		tmp = t_1;
	elseif (z <= -2.3e-55)
		tmp = x + ((z * a) * (y * 1.6453555072203998));
	elseif (z <= 800000000.0)
		tmp = x + (y * (b * 1.6453555072203998));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.9e+38], t$95$1, If[LessEqual[z, -2.3e-55], N[(x + N[(N[(z * a), $MachinePrecision] * N[(y * 1.6453555072203998), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 800000000.0], N[(x + N[(y * N[(b * 1.6453555072203998), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.8999999999999999e38 or 8e8 < z

   1. Initial program 14.3%

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

   3. Taylor expanded in z around inf 93.4%

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

      1. *-commutative 93.4%

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

   5. Simplified 93.4%

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

   if -1.8999999999999999e38 < z < -2.30000000000000011e-55

   1. Initial program 99.5%

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

   3. Taylor expanded in a around inf 69.1%

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

   4. Taylor expanded in z around 0 51.2%

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

      1. *-commutative 53.9%

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

   6. Simplified 51.2%

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

   7. Taylor expanded in z around 0 60.6%

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

      1. associate-*r* 60.7%

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

      2. *-commutative 60.7%

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

      3. *-commutative 60.7%

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

      4. associate-*r* 60.8%

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

      5. associate-*l* 60.8%

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

      6. *-commutative 60.8%

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

   9. Simplified 60.8%

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

   if -2.30000000000000011e-55 < z < 8e8

   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 83.2%

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

      1. *-commutative 83.2%

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

   7. Simplified 83.2%

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

      1. fma-undefine 83.2%

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

   9. Applied egg-rr 83.2%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+38}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-55}:\\ \;\;\;\;x + \left(z \cdot a\right) \cdot \left(y \cdot 1.6453555072203998\right)\\ \mathbf{elif}\;z \leq 800000000:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 82.8% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot 3.13060547623\\ \mathbf{if}\;z \leq -1.9 \cdot 10^{+38}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-55}:\\ \;\;\;\;x + 1.6453555072203998 \cdot \left(a \cdot \left(y \cdot z\right)\right)\\ \mathbf{elif}\;z \leq 920000000:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* y 3.13060547623))))
   (if (<= z -1.9e+38)
     t_1
     (if (<= z -3.4e-55)
       (+ x (* 1.6453555072203998 (* a (* y z))))
       (if (<= z 920000000.0) (+ x (* y (* b 1.6453555072203998))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * 3.13060547623);
	double tmp;
	if (z <= -1.9e+38) {
		tmp = t_1;
	} else if (z <= -3.4e-55) {
		tmp = x + (1.6453555072203998 * (a * (y * z)));
	} else if (z <= 920000000.0) {
		tmp = x + (y * (b * 1.6453555072203998));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * 3.13060547623d0)
    if (z <= (-1.9d+38)) then
        tmp = t_1
    else if (z <= (-3.4d-55)) then
        tmp = x + (1.6453555072203998d0 * (a * (y * z)))
    else if (z <= 920000000.0d0) then
        tmp = x + (y * (b * 1.6453555072203998d0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * 3.13060547623);
	double tmp;
	if (z <= -1.9e+38) {
		tmp = t_1;
	} else if (z <= -3.4e-55) {
		tmp = x + (1.6453555072203998 * (a * (y * z)));
	} else if (z <= 920000000.0) {
		tmp = x + (y * (b * 1.6453555072203998));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y * 3.13060547623)
	tmp = 0
	if z <= -1.9e+38:
		tmp = t_1
	elif z <= -3.4e-55:
		tmp = x + (1.6453555072203998 * (a * (y * z)))
	elif z <= 920000000.0:
		tmp = x + (y * (b * 1.6453555072203998))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y * 3.13060547623))
	tmp = 0.0
	if (z <= -1.9e+38)
		tmp = t_1;
	elseif (z <= -3.4e-55)
		tmp = Float64(x + Float64(1.6453555072203998 * Float64(a * Float64(y * z))));
	elseif (z <= 920000000.0)
		tmp = Float64(x + Float64(y * Float64(b * 1.6453555072203998)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (y * 3.13060547623);
	tmp = 0.0;
	if (z <= -1.9e+38)
		tmp = t_1;
	elseif (z <= -3.4e-55)
		tmp = x + (1.6453555072203998 * (a * (y * z)));
	elseif (z <= 920000000.0)
		tmp = x + (y * (b * 1.6453555072203998));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.9e+38], t$95$1, If[LessEqual[z, -3.4e-55], N[(x + N[(1.6453555072203998 * N[(a * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 920000000.0], N[(x + N[(y * N[(b * 1.6453555072203998), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.8999999999999999e38 or 9.2e8 < z

   1. Initial program 14.3%

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

   3. Taylor expanded in z around inf 93.4%

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

      1. *-commutative 93.4%

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

   5. Simplified 93.4%

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

   if -1.8999999999999999e38 < z < -3.39999999999999973e-55

   1. Initial program 99.5%

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

   3. Taylor expanded in a around inf 69.1%

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

   4. Taylor expanded in z around 0 60.6%

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

      1. *-commutative 60.6%

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

   6. Simplified 60.6%

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

   if -3.39999999999999973e-55 < z < 9.2e8

   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 83.2%

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

      1. *-commutative 83.2%

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

   7. Simplified 83.2%

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

      1. fma-undefine 83.2%

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

   9. Applied egg-rr 83.2%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+38}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-55}:\\ \;\;\;\;x + 1.6453555072203998 \cdot \left(a \cdot \left(y \cdot z\right)\right)\\ \mathbf{elif}\;z \leq 920000000:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 82.0% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-55} \lor \neg \left(z \leq 1500000000\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -3.5e-55) (not (<= z 1500000000.0)))
   (+ x (* y 3.13060547623))
   (+ x (* y (* b 1.6453555072203998)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3.5e-55) || !(z <= 1500000000.0)) {
		tmp = x + (y * 3.13060547623);
	} else {
		tmp = x + (y * (b * 1.6453555072203998));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-3.5d-55)) .or. (.not. (z <= 1500000000.0d0))) then
        tmp = x + (y * 3.13060547623d0)
    else
        tmp = x + (y * (b * 1.6453555072203998d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3.5e-55) || !(z <= 1500000000.0)) {
		tmp = x + (y * 3.13060547623);
	} else {
		tmp = x + (y * (b * 1.6453555072203998));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -3.5e-55) or not (z <= 1500000000.0):
		tmp = x + (y * 3.13060547623)
	else:
		tmp = x + (y * (b * 1.6453555072203998))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -3.5e-55) || !(z <= 1500000000.0))
		tmp = Float64(x + Float64(y * 3.13060547623));
	else
		tmp = Float64(x + Float64(y * Float64(b * 1.6453555072203998)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -3.5e-55) || ~((z <= 1500000000.0)))
		tmp = x + (y * 3.13060547623);
	else
		tmp = x + (y * (b * 1.6453555072203998));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -3.5e-55], N[Not[LessEqual[z, 1500000000.0]], $MachinePrecision]], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(b * 1.6453555072203998), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.50000000000000025e-55 or 1.5e9 < z

   1. Initial program 24.3%

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

   3. Taylor expanded in z around inf 86.5%

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

      1. *-commutative 86.5%

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

   5. Simplified 86.5%

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

   if -3.50000000000000025e-55 < z < 1.5e9

   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 83.2%

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

      1. *-commutative 83.2%

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

   7. Simplified 83.2%

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

      1. fma-undefine 83.2%

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

   9. Applied egg-rr 83.2%

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

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-55} \lor \neg \left(z \leq 1500000000\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 82.1% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-55} \lor \neg \left(z \leq 186000000\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x + 1.6453555072203998 \cdot \left(y \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -3.5e-55) (not (<= z 186000000.0)))
   (+ 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 <= -3.5e-55) || !(z <= 186000000.0)) {
		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 <= (-3.5d-55)) .or. (.not. (z <= 186000000.0d0))) 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 <= -3.5e-55) || !(z <= 186000000.0)) {
		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 <= -3.5e-55) or not (z <= 186000000.0):
		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 <= -3.5e-55) || !(z <= 186000000.0))
		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 <= -3.5e-55) || ~((z <= 186000000.0)))
		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, -3.5e-55], N[Not[LessEqual[z, 186000000.0]], $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 < -3.50000000000000025e-55 or 1.86e8 < z

   1. Initial program 24.3%

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

   3. Taylor expanded in z around inf 86.5%

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

      1. *-commutative 86.5%

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

   5. Simplified 86.5%

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

   if -3.50000000000000025e-55 < z < 1.86e8

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0 83.1%

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

      1. *-commutative 83.1%

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

   5. Simplified 83.1%

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

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-55} \lor \neg \left(z \leq 186000000\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x + 1.6453555072203998 \cdot \left(y \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 50.6% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{-45} \lor \neg \left(x \leq 3.2 \cdot 10^{-104}\right):\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot 3.13060547623\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= x -2.5e-45) (not (<= x 3.2e-104))) x (* y 3.13060547623)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((x <= -2.5e-45) || !(x <= 3.2e-104)) {
		tmp = x;
	} else {
		tmp = 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 ((x <= (-2.5d-45)) .or. (.not. (x <= 3.2d-104))) then
        tmp = x
    else
        tmp = 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 ((x <= -2.5e-45) || !(x <= 3.2e-104)) {
		tmp = x;
	} else {
		tmp = y * 3.13060547623;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (x <= -2.5e-45) or not (x <= 3.2e-104):
		tmp = x
	else:
		tmp = y * 3.13060547623
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((x <= -2.5e-45) || !(x <= 3.2e-104))
		tmp = x;
	else
		tmp = Float64(y * 3.13060547623);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((x <= -2.5e-45) || ~((x <= 3.2e-104)))
		tmp = x;
	else
		tmp = y * 3.13060547623;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[x, -2.5e-45], N[Not[LessEqual[x, 3.2e-104]], $MachinePrecision]], x, N[(y * 3.13060547623), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.49999999999999988e-45 or 3.19999999999999989e-104 < x

   1. Initial program 54.9%

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

   3. Simplified 54.9%

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

   5. Taylor expanded in y around 0 73.6%

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

   if -2.49999999999999988e-45 < x < 3.19999999999999989e-104

   1. Initial program 61.6%

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

   3. Taylor expanded in z around inf 47.8%

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

      1. *-commutative 47.8%

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

   5. Simplified 47.8%

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

   6. Taylor expanded in y around inf 47.8%

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

   7. Taylor expanded in x around 0 39.7%

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

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{-45} \lor \neg \left(x \leq 3.2 \cdot 10^{-104}\right):\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot 3.13060547623\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 61.9% accurate, 7.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 57.3%

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

3. Taylor expanded in z around inf 69.3%

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

   1. *-commutative 69.3%

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

5. Simplified 69.3%

   \[\leadsto x + \color{blue}{y \cdot 3.13060547623} \]
6. Add Preprocessing

Alternative 18: 45.3% accurate, 37.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 57.3%

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

3. Simplified 57.7%

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

5. Taylor expanded in y around 0 52.2%

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

Developer target: 98.4% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024096 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, D"
  :precision binary64

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

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