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

Percentage Accurate: 58.7% → 98.5%

Time: 21.5s

Alternatives: 12

Speedup: 2.5×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 58.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.5% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+45}:\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623 + \frac{\frac{t + 457.9610022158428}{z} - 36.52704169880642}{z}, x\right)\\ \mathbf{elif}\;z \leq 2600000:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right)}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 - y \cdot \frac{36.52704169880642 - \frac{457.9610022158428 + \left(t + \frac{a + \left(1112.0901850848957 + \left(-6976.8927133548 + t \cdot -15.234687407\right)\right)}{z}\right)}{z}}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -2.9e+45)
   (fma
    y
    (+ 3.13060547623 (/ (- (/ (+ t 457.9610022158428) z) 36.52704169880642) z))
    x)
   (if (<= z 2600000.0)
     (fma
      y
      (/
       (fma z (fma z (fma z (fma z 3.13060547623 11.1667541262) t) a) b)
       (fma
        z
        (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721)
        0.607771387771))
      x)
     (+
      x
      (-
       (* y 3.13060547623)
       (*
        y
        (/
         (-
          36.52704169880642
          (/
           (+
            457.9610022158428
            (+
             t
             (/
              (+
               a
               (+ 1112.0901850848957 (+ -6976.8927133548 (* t -15.234687407))))
              z)))
           z))
         z)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.9e+45) {
		tmp = fma(y, (3.13060547623 + ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)), x);
	} else if (z <= 2600000.0) {
		tmp = fma(y, (fma(z, fma(z, fma(z, fma(z, 3.13060547623, 11.1667541262), t), a), b) / fma(z, fma(z, fma(z, (z + 15.234687407), 31.4690115749), 11.9400905721), 0.607771387771)), x);
	} else {
		tmp = x + ((y * 3.13060547623) - (y * ((36.52704169880642 - ((457.9610022158428 + (t + ((a + (1112.0901850848957 + (-6976.8927133548 + (t * -15.234687407)))) / z))) / z)) / z)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -2.9e+45)
		tmp = fma(y, Float64(3.13060547623 + Float64(Float64(Float64(Float64(t + 457.9610022158428) / z) - 36.52704169880642) / z)), x);
	elseif (z <= 2600000.0)
		tmp = fma(y, Float64(fma(z, fma(z, fma(z, fma(z, 3.13060547623, 11.1667541262), t), a), b) / fma(z, fma(z, fma(z, Float64(z + 15.234687407), 31.4690115749), 11.9400905721), 0.607771387771)), x);
	else
		tmp = Float64(x + Float64(Float64(y * 3.13060547623) - Float64(y * Float64(Float64(36.52704169880642 - Float64(Float64(457.9610022158428 + Float64(t + Float64(Float64(a + Float64(1112.0901850848957 + Float64(-6976.8927133548 + Float64(t * -15.234687407)))) / z))) / z)) / z))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -2.9e+45], N[(y * N[(3.13060547623 + N[(N[(N[(N[(t + 457.9610022158428), $MachinePrecision] / z), $MachinePrecision] - 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[z, 2600000.0], N[(y * N[(N[(z * N[(z * N[(z * N[(z * 3.13060547623 + 11.1667541262), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision] + b), $MachinePrecision] / N[(z * N[(z * N[(z * N[(z + 15.234687407), $MachinePrecision] + 31.4690115749), $MachinePrecision] + 11.9400905721), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(x + N[(N[(y * 3.13060547623), $MachinePrecision] - N[(y * N[(N[(36.52704169880642 - N[(N[(457.9610022158428 + N[(t + N[(N[(a + N[(1112.0901850848957 + N[(-6976.8927133548 + N[(t * -15.234687407), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.8999999999999997e45

   1. Initial program 6.2%

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

   3. Simplified 7.8%

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

   5. Taylor expanded in z around -inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. unsub-neg 100.0%

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

      3. mul-1-neg 100.0%

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

      4. unsub-neg 100.0%

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

      5. +-commutative 100.0%

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

   7. Simplified 100.0%

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

   if -2.8999999999999997e45 < 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

   if 2.6e6 < z

   1. Initial program 15.0%

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

   3. Taylor expanded in z around -inf 77.2%

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

   4. Taylor expanded in y around 0 94.0%

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

   6. Simplified 100.0%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+45}:\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623 + \frac{\frac{t + 457.9610022158428}{z} - 36.52704169880642}{z}, x\right)\\ \mathbf{elif}\;z \leq 2600000:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right)}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 - y \cdot \frac{36.52704169880642 - \frac{457.9610022158428 + \left(t + \frac{a + \left(1112.0901850848957 + \left(-6976.8927133548 + t \cdot -15.234687407\right)\right)}{z}\right)}{z}}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 98.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -48000000000000:\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623 - \frac{36.52704169880642 - \frac{457.9610022158428 + \left(t + \frac{a + \left(t \cdot -15.234687407 + -5864.8025282699045\right)}{z}\right)}{z}}{z}, x\right)\\ \mathbf{elif}\;z \leq 2600000:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 - y \cdot \frac{36.52704169880642 - \frac{457.9610022158428 + \left(t + \frac{a + \left(1112.0901850848957 + \left(-6976.8927133548 + t \cdot -15.234687407\right)\right)}{z}\right)}{z}}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -48000000000000.0)
   (fma
    y
    (-
     3.13060547623
     (/
      (-
       36.52704169880642
       (/
        (+
         457.9610022158428
         (+ t (/ (+ a (+ (* t -15.234687407) -5864.8025282699045)) z)))
        z))
      z))
    x)
   (if (<= z 2600000.0)
     (+
      x
      (/
       (*
        y
        (+
         b
         (* z (+ a (* z (+ t (* z (+ 11.1667541262 (* z 3.13060547623)))))))))
       (+
        0.607771387771
        (*
         z
         (+ 11.9400905721 (* z (+ 31.4690115749 (* z (+ z 15.234687407)))))))))
     (+
      x
      (-
       (* y 3.13060547623)
       (*
        y
        (/
         (-
          36.52704169880642
          (/
           (+
            457.9610022158428
            (+
             t
             (/
              (+
               a
               (+ 1112.0901850848957 (+ -6976.8927133548 (* t -15.234687407))))
              z)))
           z))
         z)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -48000000000000.0) {
		tmp = fma(y, (3.13060547623 - ((36.52704169880642 - ((457.9610022158428 + (t + ((a + ((t * -15.234687407) + -5864.8025282699045)) / z))) / z)) / z)), x);
	} else if (z <= 2600000.0) {
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * (11.1667541262 + (z * 3.13060547623))))))))) / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * (z + 15.234687407))))))));
	} else {
		tmp = x + ((y * 3.13060547623) - (y * ((36.52704169880642 - ((457.9610022158428 + (t + ((a + (1112.0901850848957 + (-6976.8927133548 + (t * -15.234687407)))) / z))) / z)) / z)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -48000000000000.0)
		tmp = fma(y, Float64(3.13060547623 - Float64(Float64(36.52704169880642 - Float64(Float64(457.9610022158428 + Float64(t + Float64(Float64(a + Float64(Float64(t * -15.234687407) + -5864.8025282699045)) / z))) / z)) / z)), x);
	elseif (z <= 2600000.0)
		tmp = Float64(x + Float64(Float64(y * Float64(b + Float64(z * Float64(a + Float64(z * Float64(t + Float64(z * Float64(11.1667541262 + Float64(z * 3.13060547623))))))))) / Float64(0.607771387771 + Float64(z * Float64(11.9400905721 + Float64(z * Float64(31.4690115749 + Float64(z * Float64(z + 15.234687407)))))))));
	else
		tmp = Float64(x + Float64(Float64(y * 3.13060547623) - Float64(y * Float64(Float64(36.52704169880642 - Float64(Float64(457.9610022158428 + Float64(t + Float64(Float64(a + Float64(1112.0901850848957 + Float64(-6976.8927133548 + Float64(t * -15.234687407)))) / z))) / z)) / z))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -48000000000000.0], N[(y * N[(3.13060547623 - N[(N[(36.52704169880642 - N[(N[(457.9610022158428 + N[(t + N[(N[(a + N[(N[(t * -15.234687407), $MachinePrecision] + -5864.8025282699045), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[z, 2600000.0], N[(x + N[(N[(y * N[(b + N[(z * N[(a + N[(z * N[(t + N[(z * N[(11.1667541262 + N[(z * 3.13060547623), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(0.607771387771 + N[(z * N[(11.9400905721 + N[(z * N[(31.4690115749 + N[(z * N[(z + 15.234687407), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * 3.13060547623), $MachinePrecision] - N[(y * N[(N[(36.52704169880642 - N[(N[(457.9610022158428 + N[(t + N[(N[(a + N[(1112.0901850848957 + N[(-6976.8927133548 + N[(t * -15.234687407), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.8e13

   1. Initial program 17.3%

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

   3. Simplified 18.8%

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

   5. Taylor expanded in z around -inf 100.0%

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

   7. Simplified 100.0%

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

   if -4.8e13 < z < 2.6e6

   1. Initial program 99.7%

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

   if 2.6e6 < z

   1. Initial program 15.0%

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

   3. Taylor expanded in z around -inf 77.2%

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

   4. Taylor expanded in y around 0 94.0%

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

   6. Simplified 100.0%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -48000000000000:\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623 - \frac{36.52704169880642 - \frac{457.9610022158428 + \left(t + \frac{a + \left(t \cdot -15.234687407 + -5864.8025282699045\right)}{z}\right)}{z}}{z}, x\right)\\ \mathbf{elif}\;z \leq 2600000:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 - y \cdot \frac{36.52704169880642 - \frac{457.9610022158428 + \left(t + \frac{a + \left(1112.0901850848957 + \left(-6976.8927133548 + t \cdot -15.234687407\right)\right)}{z}\right)}{z}}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 90.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y \cdot 3.13060547623 - y \cdot \frac{36.52704169880642 - \frac{457.9610022158428 + \left(t + \frac{a + \left(1112.0901850848957 + \left(-6976.8927133548 + t \cdot -15.234687407\right)\right)}{z}\right)}{z}}{z}\right)\\ \mathbf{if}\;z \leq -0.74:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-251}:\\ \;\;\;\;x + \left(1.6453555072203998 \cdot \left(y \cdot b\right) + z \cdot \left(1.6453555072203998 \cdot \left(y \cdot a\right) - \left(y \cdot b\right) \cdot 32.324150453290734\right)\right)\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-113}:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998\right)\\ \mathbf{elif}\;z \leq 16:\\ \;\;\;\;x + \frac{y \cdot \left(z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot 15.234687407\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+
          x
          (-
           (* y 3.13060547623)
           (*
            y
            (/
             (-
              36.52704169880642
              (/
               (+
                457.9610022158428
                (+
                 t
                 (/
                  (+
                   a
                   (+
                    1112.0901850848957
                    (+ -6976.8927133548 (* t -15.234687407))))
                  z)))
               z))
             z))))))
   (if (<= z -0.74)
     t_1
     (if (<= z -2e-251)
       (+
        x
        (+
         (* 1.6453555072203998 (* y b))
         (*
          z
          (- (* 1.6453555072203998 (* y a)) (* (* y b) 32.324150453290734)))))
       (if (<= z 2.5e-113)
         (+ x (* y (* b 1.6453555072203998)))
         (if (<= z 16.0)
           (+
            x
            (/
             (*
              y
              (*
               z
               (+ a (* z (+ t (* z (+ 11.1667541262 (* z 3.13060547623))))))))
             (+
              0.607771387771
              (*
               z
               (+ 11.9400905721 (* z (+ 31.4690115749 (* z 15.234687407))))))))
           t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((y * 3.13060547623) - (y * ((36.52704169880642 - ((457.9610022158428 + (t + ((a + (1112.0901850848957 + (-6976.8927133548 + (t * -15.234687407)))) / z))) / z)) / z)));
	double tmp;
	if (z <= -0.74) {
		tmp = t_1;
	} else if (z <= -2e-251) {
		tmp = x + ((1.6453555072203998 * (y * b)) + (z * ((1.6453555072203998 * (y * a)) - ((y * b) * 32.324150453290734))));
	} else if (z <= 2.5e-113) {
		tmp = x + (y * (b * 1.6453555072203998));
	} else if (z <= 16.0) {
		tmp = x + ((y * (z * (a + (z * (t + (z * (11.1667541262 + (z * 3.13060547623)))))))) / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * 15.234687407)))))));
	} 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) - (y * ((36.52704169880642d0 - ((457.9610022158428d0 + (t + ((a + (1112.0901850848957d0 + ((-6976.8927133548d0) + (t * (-15.234687407d0))))) / z))) / z)) / z)))
    if (z <= (-0.74d0)) then
        tmp = t_1
    else if (z <= (-2d-251)) then
        tmp = x + ((1.6453555072203998d0 * (y * b)) + (z * ((1.6453555072203998d0 * (y * a)) - ((y * b) * 32.324150453290734d0))))
    else if (z <= 2.5d-113) then
        tmp = x + (y * (b * 1.6453555072203998d0))
    else if (z <= 16.0d0) then
        tmp = x + ((y * (z * (a + (z * (t + (z * (11.1667541262d0 + (z * 3.13060547623d0)))))))) / (0.607771387771d0 + (z * (11.9400905721d0 + (z * (31.4690115749d0 + (z * 15.234687407d0)))))))
    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) - (y * ((36.52704169880642 - ((457.9610022158428 + (t + ((a + (1112.0901850848957 + (-6976.8927133548 + (t * -15.234687407)))) / z))) / z)) / z)));
	double tmp;
	if (z <= -0.74) {
		tmp = t_1;
	} else if (z <= -2e-251) {
		tmp = x + ((1.6453555072203998 * (y * b)) + (z * ((1.6453555072203998 * (y * a)) - ((y * b) * 32.324150453290734))));
	} else if (z <= 2.5e-113) {
		tmp = x + (y * (b * 1.6453555072203998));
	} else if (z <= 16.0) {
		tmp = x + ((y * (z * (a + (z * (t + (z * (11.1667541262 + (z * 3.13060547623)))))))) / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * 15.234687407)))))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + ((y * 3.13060547623) - (y * ((36.52704169880642 - ((457.9610022158428 + (t + ((a + (1112.0901850848957 + (-6976.8927133548 + (t * -15.234687407)))) / z))) / z)) / z)))
	tmp = 0
	if z <= -0.74:
		tmp = t_1
	elif z <= -2e-251:
		tmp = x + ((1.6453555072203998 * (y * b)) + (z * ((1.6453555072203998 * (y * a)) - ((y * b) * 32.324150453290734))))
	elif z <= 2.5e-113:
		tmp = x + (y * (b * 1.6453555072203998))
	elif z <= 16.0:
		tmp = x + ((y * (z * (a + (z * (t + (z * (11.1667541262 + (z * 3.13060547623)))))))) / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * 15.234687407)))))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(y * 3.13060547623) - Float64(y * Float64(Float64(36.52704169880642 - Float64(Float64(457.9610022158428 + Float64(t + Float64(Float64(a + Float64(1112.0901850848957 + Float64(-6976.8927133548 + Float64(t * -15.234687407)))) / z))) / z)) / z))))
	tmp = 0.0
	if (z <= -0.74)
		tmp = t_1;
	elseif (z <= -2e-251)
		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)))));
	elseif (z <= 2.5e-113)
		tmp = Float64(x + Float64(y * Float64(b * 1.6453555072203998)));
	elseif (z <= 16.0)
		tmp = Float64(x + Float64(Float64(y * Float64(z * Float64(a + Float64(z * Float64(t + Float64(z * Float64(11.1667541262 + Float64(z * 3.13060547623)))))))) / Float64(0.607771387771 + Float64(z * Float64(11.9400905721 + Float64(z * Float64(31.4690115749 + Float64(z * 15.234687407))))))));
	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) - (y * ((36.52704169880642 - ((457.9610022158428 + (t + ((a + (1112.0901850848957 + (-6976.8927133548 + (t * -15.234687407)))) / z))) / z)) / z)));
	tmp = 0.0;
	if (z <= -0.74)
		tmp = t_1;
	elseif (z <= -2e-251)
		tmp = x + ((1.6453555072203998 * (y * b)) + (z * ((1.6453555072203998 * (y * a)) - ((y * b) * 32.324150453290734))));
	elseif (z <= 2.5e-113)
		tmp = x + (y * (b * 1.6453555072203998));
	elseif (z <= 16.0)
		tmp = x + ((y * (z * (a + (z * (t + (z * (11.1667541262 + (z * 3.13060547623)))))))) / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * 15.234687407)))))));
	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[(y * 3.13060547623), $MachinePrecision] - N[(y * N[(N[(36.52704169880642 - N[(N[(457.9610022158428 + N[(t + N[(N[(a + N[(1112.0901850848957 + N[(-6976.8927133548 + N[(t * -15.234687407), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.74], t$95$1, If[LessEqual[z, -2e-251], 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], If[LessEqual[z, 2.5e-113], N[(x + N[(y * N[(b * 1.6453555072203998), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 16.0], N[(x + N[(N[(y * N[(z * N[(a + N[(z * N[(t + N[(z * N[(11.1667541262 + N[(z * 3.13060547623), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(0.607771387771 + N[(z * N[(11.9400905721 + N[(z * N[(31.4690115749 + N[(z * 15.234687407), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -0.73999999999999999 or 16 < z

   1. Initial program 16.1%

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

   3. Taylor expanded in z around -inf 80.2%

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

   4. Taylor expanded in y around 0 96.2%

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

   6. Simplified 100.0%

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

   if -0.73999999999999999 < z < -2.00000000000000003e-251

   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 z around 0 88.4%

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

   if -2.00000000000000003e-251 < z < 2.4999999999999999e-113

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 92.3%

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

      1. *-commutative 92.3%

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

      2. *-commutative 92.3%

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

      3. associate-*l* 92.3%

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

   5. Simplified 92.3%

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

   if 2.4999999999999999e-113 < z < 16

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 99.9%

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

      1. *-commutative 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in b around 0 85.7%

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

4. Final simplification 94.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.74:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 - y \cdot \frac{36.52704169880642 - \frac{457.9610022158428 + \left(t + \frac{a + \left(1112.0901850848957 + \left(-6976.8927133548 + t \cdot -15.234687407\right)\right)}{z}\right)}{z}}{z}\right)\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-251}:\\ \;\;\;\;x + \left(1.6453555072203998 \cdot \left(y \cdot b\right) + z \cdot \left(1.6453555072203998 \cdot \left(y \cdot a\right) - \left(y \cdot b\right) \cdot 32.324150453290734\right)\right)\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-113}:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998\right)\\ \mathbf{elif}\;z \leq 16:\\ \;\;\;\;x + \frac{y \cdot \left(z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot 15.234687407\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 - y \cdot \frac{36.52704169880642 - \frac{457.9610022158428 + \left(t + \frac{a + \left(1112.0901850848957 + \left(-6976.8927133548 + t \cdot -15.234687407\right)\right)}{z}\right)}{z}}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+14} \lor \neg \left(z \leq 2600000\right):\\ \;\;\;\;x + \left(y \cdot 3.13060547623 - y \cdot \frac{36.52704169880642 - \frac{457.9610022158428 + \left(t + \frac{a + \left(1112.0901850848957 + \left(-6976.8927133548 + t \cdot -15.234687407\right)\right)}{z}\right)}{z}}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2.8e+14) (not (<= z 2600000.0)))
   (+
    x
    (-
     (* y 3.13060547623)
     (*
      y
      (/
       (-
        36.52704169880642
        (/
         (+
          457.9610022158428
          (+
           t
           (/
            (+
             a
             (+ 1112.0901850848957 (+ -6976.8927133548 (* t -15.234687407))))
            z)))
         z))
       z))))
   (+
    x
    (/
     (*
      y
      (+
       b
       (* z (+ a (* z (+ t (* z (+ 11.1667541262 (* z 3.13060547623)))))))))
     (+
      0.607771387771
      (*
       z
       (+ 11.9400905721 (* z (+ 31.4690115749 (* z (+ z 15.234687407)))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.8e+14) || !(z <= 2600000.0)) {
		tmp = x + ((y * 3.13060547623) - (y * ((36.52704169880642 - ((457.9610022158428 + (t + ((a + (1112.0901850848957 + (-6976.8927133548 + (t * -15.234687407)))) / z))) / z)) / z)));
	} else {
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * (11.1667541262 + (z * 3.13060547623))))))))) / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * (z + 15.234687407))))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-2.8d+14)) .or. (.not. (z <= 2600000.0d0))) then
        tmp = x + ((y * 3.13060547623d0) - (y * ((36.52704169880642d0 - ((457.9610022158428d0 + (t + ((a + (1112.0901850848957d0 + ((-6976.8927133548d0) + (t * (-15.234687407d0))))) / z))) / z)) / z)))
    else
        tmp = x + ((y * (b + (z * (a + (z * (t + (z * (11.1667541262d0 + (z * 3.13060547623d0))))))))) / (0.607771387771d0 + (z * (11.9400905721d0 + (z * (31.4690115749d0 + (z * (z + 15.234687407d0))))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.8e+14) || !(z <= 2600000.0)) {
		tmp = x + ((y * 3.13060547623) - (y * ((36.52704169880642 - ((457.9610022158428 + (t + ((a + (1112.0901850848957 + (-6976.8927133548 + (t * -15.234687407)))) / z))) / z)) / z)));
	} else {
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * (11.1667541262 + (z * 3.13060547623))))))))) / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * (z + 15.234687407))))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -2.8e+14) or not (z <= 2600000.0):
		tmp = x + ((y * 3.13060547623) - (y * ((36.52704169880642 - ((457.9610022158428 + (t + ((a + (1112.0901850848957 + (-6976.8927133548 + (t * -15.234687407)))) / z))) / z)) / z)))
	else:
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * (11.1667541262 + (z * 3.13060547623))))))))) / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * (z + 15.234687407))))))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2.8e+14) || !(z <= 2600000.0))
		tmp = Float64(x + Float64(Float64(y * 3.13060547623) - Float64(y * Float64(Float64(36.52704169880642 - Float64(Float64(457.9610022158428 + Float64(t + Float64(Float64(a + Float64(1112.0901850848957 + Float64(-6976.8927133548 + Float64(t * -15.234687407)))) / z))) / z)) / z))));
	else
		tmp = Float64(x + Float64(Float64(y * Float64(b + Float64(z * Float64(a + Float64(z * Float64(t + Float64(z * Float64(11.1667541262 + Float64(z * 3.13060547623))))))))) / Float64(0.607771387771 + Float64(z * Float64(11.9400905721 + Float64(z * Float64(31.4690115749 + Float64(z * Float64(z + 15.234687407)))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -2.8e+14) || ~((z <= 2600000.0)))
		tmp = x + ((y * 3.13060547623) - (y * ((36.52704169880642 - ((457.9610022158428 + (t + ((a + (1112.0901850848957 + (-6976.8927133548 + (t * -15.234687407)))) / z))) / z)) / z)));
	else
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * (11.1667541262 + (z * 3.13060547623))))))))) / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * (z + 15.234687407))))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2.8e+14], N[Not[LessEqual[z, 2600000.0]], $MachinePrecision]], N[(x + N[(N[(y * 3.13060547623), $MachinePrecision] - N[(y * N[(N[(36.52704169880642 - N[(N[(457.9610022158428 + N[(t + N[(N[(a + N[(1112.0901850848957 + N[(-6976.8927133548 + N[(t * -15.234687407), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * N[(b + N[(z * N[(a + N[(z * N[(t + N[(z * N[(11.1667541262 + N[(z * 3.13060547623), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(0.607771387771 + N[(z * N[(11.9400905721 + N[(z * N[(31.4690115749 + N[(z * N[(z + 15.234687407), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.8e14 or 2.6e6 < z

   1. Initial program 16.1%

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

   3. Taylor expanded in z around -inf 80.2%

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

   4. Taylor expanded in y around 0 96.2%

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

   6. Simplified 100.0%

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

   if -2.8e14 < z < 2.6e6

   1. Initial program 99.7%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+14} \lor \neg \left(z \leq 2600000\right):\\ \;\;\;\;x + \left(y \cdot 3.13060547623 - y \cdot \frac{36.52704169880642 - \frac{457.9610022158428 + \left(t + \frac{a + \left(1112.0901850848957 + \left(-6976.8927133548 + t \cdot -15.234687407\right)\right)}{z}\right)}{z}}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 98.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -12.8 \lor \neg \left(z \leq 116000\right):\\ \;\;\;\;x + \left(y \cdot 3.13060547623 - y \cdot \frac{36.52704169880642 - \frac{457.9610022158428 + \left(t + \frac{a + \left(1112.0901850848957 + \left(-6976.8927133548 + t \cdot -15.234687407\right)\right)}{z}\right)}{z}}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot 15.234687407\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -12.8) (not (<= z 116000.0)))
   (+
    x
    (-
     (* y 3.13060547623)
     (*
      y
      (/
       (-
        36.52704169880642
        (/
         (+
          457.9610022158428
          (+
           t
           (/
            (+
             a
             (+ 1112.0901850848957 (+ -6976.8927133548 (* t -15.234687407))))
            z)))
         z))
       z))))
   (+
    x
    (/
     (*
      y
      (+
       b
       (* z (+ a (* z (+ t (* z (+ 11.1667541262 (* z 3.13060547623)))))))))
     (+
      0.607771387771
      (* z (+ 11.9400905721 (* z (+ 31.4690115749 (* z 15.234687407))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -12.8) || !(z <= 116000.0)) {
		tmp = x + ((y * 3.13060547623) - (y * ((36.52704169880642 - ((457.9610022158428 + (t + ((a + (1112.0901850848957 + (-6976.8927133548 + (t * -15.234687407)))) / z))) / z)) / z)));
	} else {
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * (11.1667541262 + (z * 3.13060547623))))))))) / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * 15.234687407)))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-12.8d0)) .or. (.not. (z <= 116000.0d0))) then
        tmp = x + ((y * 3.13060547623d0) - (y * ((36.52704169880642d0 - ((457.9610022158428d0 + (t + ((a + (1112.0901850848957d0 + ((-6976.8927133548d0) + (t * (-15.234687407d0))))) / z))) / z)) / z)))
    else
        tmp = x + ((y * (b + (z * (a + (z * (t + (z * (11.1667541262d0 + (z * 3.13060547623d0))))))))) / (0.607771387771d0 + (z * (11.9400905721d0 + (z * (31.4690115749d0 + (z * 15.234687407d0)))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -12.8) || !(z <= 116000.0)) {
		tmp = x + ((y * 3.13060547623) - (y * ((36.52704169880642 - ((457.9610022158428 + (t + ((a + (1112.0901850848957 + (-6976.8927133548 + (t * -15.234687407)))) / z))) / z)) / z)));
	} else {
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * (11.1667541262 + (z * 3.13060547623))))))))) / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * 15.234687407)))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -12.8) or not (z <= 116000.0):
		tmp = x + ((y * 3.13060547623) - (y * ((36.52704169880642 - ((457.9610022158428 + (t + ((a + (1112.0901850848957 + (-6976.8927133548 + (t * -15.234687407)))) / z))) / z)) / z)))
	else:
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * (11.1667541262 + (z * 3.13060547623))))))))) / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * 15.234687407)))))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -12.8) || !(z <= 116000.0))
		tmp = Float64(x + Float64(Float64(y * 3.13060547623) - Float64(y * Float64(Float64(36.52704169880642 - Float64(Float64(457.9610022158428 + Float64(t + Float64(Float64(a + Float64(1112.0901850848957 + Float64(-6976.8927133548 + Float64(t * -15.234687407)))) / z))) / z)) / z))));
	else
		tmp = Float64(x + Float64(Float64(y * Float64(b + Float64(z * Float64(a + Float64(z * Float64(t + Float64(z * Float64(11.1667541262 + Float64(z * 3.13060547623))))))))) / Float64(0.607771387771 + Float64(z * Float64(11.9400905721 + Float64(z * Float64(31.4690115749 + Float64(z * 15.234687407))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -12.8) || ~((z <= 116000.0)))
		tmp = x + ((y * 3.13060547623) - (y * ((36.52704169880642 - ((457.9610022158428 + (t + ((a + (1112.0901850848957 + (-6976.8927133548 + (t * -15.234687407)))) / z))) / z)) / z)));
	else
		tmp = x + ((y * (b + (z * (a + (z * (t + (z * (11.1667541262 + (z * 3.13060547623))))))))) / (0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * 15.234687407)))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -12.8], N[Not[LessEqual[z, 116000.0]], $MachinePrecision]], N[(x + N[(N[(y * 3.13060547623), $MachinePrecision] - N[(y * N[(N[(36.52704169880642 - N[(N[(457.9610022158428 + N[(t + N[(N[(a + N[(1112.0901850848957 + N[(-6976.8927133548 + N[(t * -15.234687407), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * N[(b + N[(z * N[(a + N[(z * N[(t + N[(z * N[(11.1667541262 + N[(z * 3.13060547623), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(0.607771387771 + N[(z * N[(11.9400905721 + N[(z * N[(31.4690115749 + N[(z * 15.234687407), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -12.800000000000001 or 116000 < z

   1. Initial program 16.1%

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

   3. Taylor expanded in z around -inf 80.2%

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

   4. Taylor expanded in y around 0 96.2%

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

   6. Simplified 100.0%

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

   if -12.800000000000001 < z < 116000

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0 99.7%

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

      1. *-commutative 99.7%

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

   5. Simplified 99.7%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -12.8 \lor \neg \left(z \leq 116000\right):\\ \;\;\;\;x + \left(y \cdot 3.13060547623 - y \cdot \frac{36.52704169880642 - \frac{457.9610022158428 + \left(t + \frac{a + \left(1112.0901850848957 + \left(-6976.8927133548 + t \cdot -15.234687407\right)\right)}{z}\right)}{z}}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot 15.234687407\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 90.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y \cdot 3.13060547623 - y \cdot \frac{36.52704169880642 - \frac{457.9610022158428 + \left(t + \frac{a + \left(1112.0901850848957 + \left(-6976.8927133548 + t \cdot -15.234687407\right)\right)}{z}\right)}{z}}{z}\right)\\ \mathbf{if}\;z \leq -0.00375:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-246}:\\ \;\;\;\;x + \left(1.6453555072203998 \cdot \left(y \cdot b\right) + z \cdot \left(1.6453555072203998 \cdot \left(y \cdot a\right) - \left(y \cdot b\right) \cdot 32.324150453290734\right)\right)\\ \mathbf{elif}\;z \leq 12.2:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+
          x
          (-
           (* y 3.13060547623)
           (*
            y
            (/
             (-
              36.52704169880642
              (/
               (+
                457.9610022158428
                (+
                 t
                 (/
                  (+
                   a
                   (+
                    1112.0901850848957
                    (+ -6976.8927133548 (* t -15.234687407))))
                  z)))
               z))
             z))))))
   (if (<= z -0.00375)
     t_1
     (if (<= z -2e-246)
       (+
        x
        (+
         (* 1.6453555072203998 (* y b))
         (*
          z
          (- (* 1.6453555072203998 (* y a)) (* (* y b) 32.324150453290734)))))
       (if (<= z 12.2) (+ 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) - (y * ((36.52704169880642 - ((457.9610022158428 + (t + ((a + (1112.0901850848957 + (-6976.8927133548 + (t * -15.234687407)))) / z))) / z)) / z)));
	double tmp;
	if (z <= -0.00375) {
		tmp = t_1;
	} else if (z <= -2e-246) {
		tmp = x + ((1.6453555072203998 * (y * b)) + (z * ((1.6453555072203998 * (y * a)) - ((y * b) * 32.324150453290734))));
	} else if (z <= 12.2) {
		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) - (y * ((36.52704169880642d0 - ((457.9610022158428d0 + (t + ((a + (1112.0901850848957d0 + ((-6976.8927133548d0) + (t * (-15.234687407d0))))) / z))) / z)) / z)))
    if (z <= (-0.00375d0)) then
        tmp = t_1
    else if (z <= (-2d-246)) then
        tmp = x + ((1.6453555072203998d0 * (y * b)) + (z * ((1.6453555072203998d0 * (y * a)) - ((y * b) * 32.324150453290734d0))))
    else if (z <= 12.2d0) 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) - (y * ((36.52704169880642 - ((457.9610022158428 + (t + ((a + (1112.0901850848957 + (-6976.8927133548 + (t * -15.234687407)))) / z))) / z)) / z)));
	double tmp;
	if (z <= -0.00375) {
		tmp = t_1;
	} else if (z <= -2e-246) {
		tmp = x + ((1.6453555072203998 * (y * b)) + (z * ((1.6453555072203998 * (y * a)) - ((y * b) * 32.324150453290734))));
	} else if (z <= 12.2) {
		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) - (y * ((36.52704169880642 - ((457.9610022158428 + (t + ((a + (1112.0901850848957 + (-6976.8927133548 + (t * -15.234687407)))) / z))) / z)) / z)))
	tmp = 0
	if z <= -0.00375:
		tmp = t_1
	elif z <= -2e-246:
		tmp = x + ((1.6453555072203998 * (y * b)) + (z * ((1.6453555072203998 * (y * a)) - ((y * b) * 32.324150453290734))))
	elif z <= 12.2:
		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(Float64(y * 3.13060547623) - Float64(y * Float64(Float64(36.52704169880642 - Float64(Float64(457.9610022158428 + Float64(t + Float64(Float64(a + Float64(1112.0901850848957 + Float64(-6976.8927133548 + Float64(t * -15.234687407)))) / z))) / z)) / z))))
	tmp = 0.0
	if (z <= -0.00375)
		tmp = t_1;
	elseif (z <= -2e-246)
		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)))));
	elseif (z <= 12.2)
		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) - (y * ((36.52704169880642 - ((457.9610022158428 + (t + ((a + (1112.0901850848957 + (-6976.8927133548 + (t * -15.234687407)))) / z))) / z)) / z)));
	tmp = 0.0;
	if (z <= -0.00375)
		tmp = t_1;
	elseif (z <= -2e-246)
		tmp = x + ((1.6453555072203998 * (y * b)) + (z * ((1.6453555072203998 * (y * a)) - ((y * b) * 32.324150453290734))));
	elseif (z <= 12.2)
		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[(N[(y * 3.13060547623), $MachinePrecision] - N[(y * N[(N[(36.52704169880642 - N[(N[(457.9610022158428 + N[(t + N[(N[(a + N[(1112.0901850848957 + N[(-6976.8927133548 + N[(t * -15.234687407), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.00375], t$95$1, If[LessEqual[z, -2e-246], 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], If[LessEqual[z, 12.2], N[(x + N[(y * N[(b * 1.6453555072203998), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.0037499999999999999 or 12.199999999999999 < z

   1. Initial program 16.1%

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

   3. Taylor expanded in z around -inf 80.2%

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

   4. Taylor expanded in y around 0 96.2%

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

   6. Simplified 100.0%

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

   if -0.0037499999999999999 < z < -1.99999999999999991e-246

   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 z around 0 88.4%

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

   if -1.99999999999999991e-246 < z < 12.199999999999999

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 82.6%

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

      1. *-commutative 82.6%

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

      2. *-commutative 82.6%

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

      3. associate-*l* 82.6%

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

   5. Simplified 82.6%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.00375:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 - y \cdot \frac{36.52704169880642 - \frac{457.9610022158428 + \left(t + \frac{a + \left(1112.0901850848957 + \left(-6976.8927133548 + t \cdot -15.234687407\right)\right)}{z}\right)}{z}}{z}\right)\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-246}:\\ \;\;\;\;x + \left(1.6453555072203998 \cdot \left(y \cdot b\right) + z \cdot \left(1.6453555072203998 \cdot \left(y \cdot a\right) - \left(y \cdot b\right) \cdot 32.324150453290734\right)\right)\\ \mathbf{elif}\;z \leq 12.2:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 - y \cdot \frac{36.52704169880642 - \frac{457.9610022158428 + \left(t + \frac{a + \left(1112.0901850848957 + \left(-6976.8927133548 + t \cdot -15.234687407\right)\right)}{z}\right)}{z}}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 86.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y \cdot \frac{\frac{t + 457.9610022158428}{z} - 36.52704169880642}{z} + y \cdot 3.13060547623\right)\\ \mathbf{if}\;z \leq -2.95 \cdot 10^{+50}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-238}:\\ \;\;\;\;x + \left(1.6453555072203998 \cdot \left(y \cdot b\right) + z \cdot \left(1.6453555072203998 \cdot \left(y \cdot a\right) - \left(y \cdot b\right) \cdot 32.324150453290734\right)\right)\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-59}:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+
          x
          (+
           (* y (/ (- (/ (+ t 457.9610022158428) z) 36.52704169880642) z))
           (* y 3.13060547623)))))
   (if (<= z -2.95e+50)
     t_1
     (if (<= z -1.2e-238)
       (+
        x
        (+
         (* 1.6453555072203998 (* y b))
         (*
          z
          (- (* 1.6453555072203998 (* y a)) (* (* y b) 32.324150453290734)))))
       (if (<= z 5.5e-59) (+ 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 * ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)) + (y * 3.13060547623));
	double tmp;
	if (z <= -2.95e+50) {
		tmp = t_1;
	} else if (z <= -1.2e-238) {
		tmp = x + ((1.6453555072203998 * (y * b)) + (z * ((1.6453555072203998 * (y * a)) - ((y * b) * 32.324150453290734))));
	} else if (z <= 5.5e-59) {
		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 * ((((t + 457.9610022158428d0) / z) - 36.52704169880642d0) / z)) + (y * 3.13060547623d0))
    if (z <= (-2.95d+50)) then
        tmp = t_1
    else if (z <= (-1.2d-238)) then
        tmp = x + ((1.6453555072203998d0 * (y * b)) + (z * ((1.6453555072203998d0 * (y * a)) - ((y * b) * 32.324150453290734d0))))
    else if (z <= 5.5d-59) 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 * ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)) + (y * 3.13060547623));
	double tmp;
	if (z <= -2.95e+50) {
		tmp = t_1;
	} else if (z <= -1.2e-238) {
		tmp = x + ((1.6453555072203998 * (y * b)) + (z * ((1.6453555072203998 * (y * a)) - ((y * b) * 32.324150453290734))));
	} else if (z <= 5.5e-59) {
		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 * ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)) + (y * 3.13060547623))
	tmp = 0
	if z <= -2.95e+50:
		tmp = t_1
	elif z <= -1.2e-238:
		tmp = x + ((1.6453555072203998 * (y * b)) + (z * ((1.6453555072203998 * (y * a)) - ((y * b) * 32.324150453290734))))
	elif z <= 5.5e-59:
		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(Float64(y * Float64(Float64(Float64(Float64(t + 457.9610022158428) / z) - 36.52704169880642) / z)) + Float64(y * 3.13060547623)))
	tmp = 0.0
	if (z <= -2.95e+50)
		tmp = t_1;
	elseif (z <= -1.2e-238)
		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)))));
	elseif (z <= 5.5e-59)
		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 * ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)) + (y * 3.13060547623));
	tmp = 0.0;
	if (z <= -2.95e+50)
		tmp = t_1;
	elseif (z <= -1.2e-238)
		tmp = x + ((1.6453555072203998 * (y * b)) + (z * ((1.6453555072203998 * (y * a)) - ((y * b) * 32.324150453290734))));
	elseif (z <= 5.5e-59)
		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[(N[(y * N[(N[(N[(N[(t + 457.9610022158428), $MachinePrecision] / z), $MachinePrecision] - 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.95e+50], t$95$1, If[LessEqual[z, -1.2e-238], 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], If[LessEqual[z, 5.5e-59], N[(x + N[(y * N[(b * 1.6453555072203998), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.9499999999999999e50 or 5.50000000000000014e-59 < z

   1. Initial program 19.0%

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

   3. Taylor expanded in z around -inf 80.0%

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

   4. Taylor expanded in y around 0 88.9%

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

      1. associate-/l* 92.6%

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

      2. mul-1-neg 92.6%

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

      3. unsub-neg 92.6%

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

      4. +-commutative 92.6%

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

   6. Simplified 92.6%

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

   if -2.9499999999999999e50 < z < -1.1999999999999999e-238

   1. Initial program 98.0%

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

   3. Taylor expanded in z around 0 87.2%

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

   if -1.1999999999999999e-238 < z < 5.50000000000000014e-59

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 89.0%

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

      1. *-commutative 89.0%

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

      2. *-commutative 89.0%

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

      3. associate-*l* 89.0%

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

   5. Simplified 89.0%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.95 \cdot 10^{+50}:\\ \;\;\;\;x + \left(y \cdot \frac{\frac{t + 457.9610022158428}{z} - 36.52704169880642}{z} + y \cdot 3.13060547623\right)\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-238}:\\ \;\;\;\;x + \left(1.6453555072203998 \cdot \left(y \cdot b\right) + z \cdot \left(1.6453555072203998 \cdot \left(y \cdot a\right) - \left(y \cdot b\right) \cdot 32.324150453290734\right)\right)\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-59}:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot \frac{\frac{t + 457.9610022158428}{z} - 36.52704169880642}{z} + y \cdot 3.13060547623\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 85.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{-8} \lor \neg \left(z \leq 5.5 \cdot 10^{-59}\right):\\ \;\;\;\;x + \left(y \cdot \frac{\frac{t + 457.9610022158428}{z} - 36.52704169880642}{z} + y \cdot 3.13060547623\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -4.2e-8) (not (<= z 5.5e-59)))
   (+
    x
    (+
     (* y (/ (- (/ (+ t 457.9610022158428) z) 36.52704169880642) z))
     (* 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 <= -4.2e-8) || !(z <= 5.5e-59)) {
		tmp = x + ((y * ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)) + (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 <= (-4.2d-8)) .or. (.not. (z <= 5.5d-59))) then
        tmp = x + ((y * ((((t + 457.9610022158428d0) / z) - 36.52704169880642d0) / z)) + (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 <= -4.2e-8) || !(z <= 5.5e-59)) {
		tmp = x + ((y * ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)) + (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 <= -4.2e-8) or not (z <= 5.5e-59):
		tmp = x + ((y * ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)) + (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 <= -4.2e-8) || !(z <= 5.5e-59))
		tmp = Float64(x + Float64(Float64(y * Float64(Float64(Float64(Float64(t + 457.9610022158428) / z) - 36.52704169880642) / z)) + Float64(y * 3.13060547623)));
	else
		tmp = Float64(x + Float64(y * Float64(b * 1.6453555072203998)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -4.2e-8) || ~((z <= 5.5e-59)))
		tmp = x + ((y * ((((t + 457.9610022158428) / z) - 36.52704169880642) / z)) + (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, -4.2e-8], N[Not[LessEqual[z, 5.5e-59]], $MachinePrecision]], N[(x + N[(N[(y * N[(N[(N[(N[(t + 457.9610022158428), $MachinePrecision] / z), $MachinePrecision] - 36.52704169880642), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(b * 1.6453555072203998), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.19999999999999989e-8 or 5.50000000000000014e-59 < z

   1. Initial program 24.9%

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

   3. Taylor expanded in z around -inf 78.8%

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

   4. Taylor expanded in y around 0 87.0%

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

      1. associate-/l* 90.3%

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

      2. mul-1-neg 90.3%

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

      3. unsub-neg 90.3%

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

      4. +-commutative 90.3%

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

   6. Simplified 90.3%

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

   if -4.19999999999999989e-8 < z < 5.50000000000000014e-59

   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 84.3%

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

      1. *-commutative 84.3%

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

      2. *-commutative 84.3%

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

      3. associate-*l* 84.3%

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

   5. Simplified 84.3%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{-8} \lor \neg \left(z \leq 5.5 \cdot 10^{-59}\right):\\ \;\;\;\;x + \left(y \cdot \frac{\frac{t + 457.9610022158428}{z} - 36.52704169880642}{z} + y \cdot 3.13060547623\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 84.1% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.1 \cdot 10^{-6} \lor \neg \left(z \leq 5.2 \cdot 10^{-13}\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -5.1e-6) (not (<= z 5.2e-13)))
   (+ 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 <= -5.1e-6) || !(z <= 5.2e-13)) {
		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 <= (-5.1d-6)) .or. (.not. (z <= 5.2d-13))) 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 <= -5.1e-6) || !(z <= 5.2e-13)) {
		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 <= -5.1e-6) or not (z <= 5.2e-13):
		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 <= -5.1e-6) || !(z <= 5.2e-13))
		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 <= -5.1e-6) || ~((z <= 5.2e-13)))
		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, -5.1e-6], N[Not[LessEqual[z, 5.2e-13]], $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 < -5.1000000000000003e-6 or 5.2000000000000001e-13 < z

   1. Initial program 20.1%

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

   3. Simplified 22.3%

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

   5. Taylor expanded in z around inf 88.0%

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

      1. +-commutative 88.0%

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

      2. *-commutative 88.0%

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

   7. Simplified 88.0%

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

   if -5.1000000000000003e-6 < z < 5.2000000000000001e-13

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0 81.8%

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

      1. *-commutative 81.8%

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

      2. *-commutative 81.8%

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

      3. associate-*l* 81.8%

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

   5. Simplified 81.8%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.1 \cdot 10^{-6} \lor \neg \left(z \leq 5.2 \cdot 10^{-13}\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 64.7% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.057 \lor \neg \left(z \leq 1.1 \cdot 10^{-57}\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -0.057) (not (<= z 1.1e-57))) (+ x (* y 3.13060547623)) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -0.057) || !(z <= 1.1e-57)) {
		tmp = x + (y * 3.13060547623);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-0.057d0)) .or. (.not. (z <= 1.1d-57))) then
        tmp = x + (y * 3.13060547623d0)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -0.057) || !(z <= 1.1e-57)) {
		tmp = x + (y * 3.13060547623);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -0.057) or not (z <= 1.1e-57):
		tmp = x + (y * 3.13060547623)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -0.057) || !(z <= 1.1e-57))
		tmp = Float64(x + Float64(y * 3.13060547623));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -0.057) || ~((z <= 1.1e-57)))
		tmp = x + (y * 3.13060547623);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -0.057], N[Not[LessEqual[z, 1.1e-57]], $MachinePrecision]], N[(x + N[(y * 3.13060547623), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -0.0570000000000000021 or 1.09999999999999999e-57 < z

   1. Initial program 23.2%

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

   3. Simplified 25.3%

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

   5. Taylor expanded in z around inf 86.3%

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

      1. +-commutative 86.3%

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

      2. *-commutative 86.3%

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

   7. Simplified 86.3%

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

   if -0.0570000000000000021 < z < 1.09999999999999999e-57

   1. Initial program 99.6%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around 0 46.0%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.057 \lor \neg \left(z \leq 1.1 \cdot 10^{-57}\right):\\ \;\;\;\;x + y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 51.3% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{-122}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.65 \cdot 10^{-98}:\\ \;\;\;\;y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -6.2e-122) x (if (<= x 2.65e-98) (* y 3.13060547623) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -6.2e-122) {
		tmp = x;
	} else if (x <= 2.65e-98) {
		tmp = y * 3.13060547623;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-6.2d-122)) then
        tmp = x
    else if (x <= 2.65d-98) then
        tmp = y * 3.13060547623d0
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -6.2e-122) {
		tmp = x;
	} else if (x <= 2.65e-98) {
		tmp = y * 3.13060547623;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -6.2e-122:
		tmp = x
	elif x <= 2.65e-98:
		tmp = y * 3.13060547623
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -6.2e-122)
		tmp = x;
	elseif (x <= 2.65e-98)
		tmp = Float64(y * 3.13060547623);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -6.2e-122)
		tmp = x;
	elseif (x <= 2.65e-98)
		tmp = y * 3.13060547623;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -6.2e-122], x, If[LessEqual[x, 2.65e-98], N[(y * 3.13060547623), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -6.1999999999999997e-122 or 2.65000000000000015e-98 < x

   1. Initial program 59.3%

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

   3. Simplified 60.3%

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

   5. Taylor expanded in y around 0 62.5%

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

   if -6.1999999999999997e-122 < x < 2.65000000000000015e-98

   1. Initial program 63.6%

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

   3. Simplified 64.7%

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

   5. Taylor expanded in z around inf 37.4%

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

   6. Taylor expanded in x around 0 32.5%

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

   7. Taylor expanded in z around inf 33.5%

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

      1. *-commutative 33.5%

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

   9. Simplified 33.5%

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

Alternative 12: 44.7% accurate, 37.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 60.5%

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

3. Simplified 61.6%

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

5. Taylor expanded in y around 0 47.2%

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

Developer target: 98.5% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024111 
(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))))