Average Error: 29.8 → 0.7
Time: 40.5s
Precision: binary64
Cost: 52808
\[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
↓
\[\begin{array}{l} t_1 := a + \left(t \cdot -15.234687407 + -5864.8025282699045\right)\\ \mathbf{if}\;z \leq -1 \cdot 10^{+47}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, \mathsf{fma}\left(-36.52704169880642, \frac{y}{z}, x\right)\right) + \frac{\frac{y}{z}}{z} \cdot \left(\left(t + 457.9610022158428\right) + \frac{t_1}{z}\right)\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+17}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right)}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \left(3.13060547623 + \frac{-36.52704169880642}{z}\right) + \left(\left(\frac{457.9610022158428}{z \cdot z} + \frac{t}{z \cdot z}\right) + \frac{t_1}{{z}^{3}}\right), x\right)\\ \end{array} \]
(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))))
↓
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ a (+ (* t -15.234687407) -5864.8025282699045))))
   (if (<= z -1e+47)
     (+
      (fma 3.13060547623 y (fma -36.52704169880642 (/ y z) x))
      (* (/ (/ y z) z) (+ (+ t 457.9610022158428) (/ t_1 z))))
     (if (<= z 5.8e+17)
       (fma
        y
        (/
         (fma z (fma z (fma z (fma z 3.13060547623 11.1667541262) t) a) b)
         (fma
          z
          (fma z (fma z (+ z 15.234687407) 31.4690115749) 11.9400905721)
          0.607771387771))
        x)
       (fma
        y
        (+
         (+ 3.13060547623 (/ -36.52704169880642 z))
         (+
          (+ (/ 457.9610022158428 (* z z)) (/ t (* z z)))
          (/ t_1 (pow z 3.0))))
        x)))))
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));
}
↓
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a + ((t * -15.234687407) + -5864.8025282699045);
	double tmp;
	if (z <= -1e+47) {
		tmp = fma(3.13060547623, y, fma(-36.52704169880642, (y / z), x)) + (((y / z) / z) * ((t + 457.9610022158428) + (t_1 / z)));
	} else if (z <= 5.8e+17) {
		tmp = fma(y, (fma(z, fma(z, fma(z, fma(z, 3.13060547623, 11.1667541262), t), a), b) / fma(z, fma(z, fma(z, (z + 15.234687407), 31.4690115749), 11.9400905721), 0.607771387771)), x);
	} else {
		tmp = fma(y, ((3.13060547623 + (-36.52704169880642 / z)) + (((457.9610022158428 / (z * z)) + (t / (z * z))) + (t_1 / pow(z, 3.0)))), x);
	}
	return tmp;
}

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
↓
function code(x, y, z, t, a, b)
	t_1 = Float64(a + Float64(Float64(t * -15.234687407) + -5864.8025282699045))
	tmp = 0.0
	if (z <= -1e+47)
		tmp = Float64(fma(3.13060547623, y, fma(-36.52704169880642, Float64(y / z), x)) + Float64(Float64(Float64(y / z) / z) * Float64(Float64(t + 457.9610022158428) + Float64(t_1 / z))));
	elseif (z <= 5.8e+17)
		tmp = fma(y, Float64(fma(z, fma(z, fma(z, fma(z, 3.13060547623, 11.1667541262), t), a), b) / fma(z, fma(z, fma(z, Float64(z + 15.234687407), 31.4690115749), 11.9400905721), 0.607771387771)), x);
	else
		tmp = fma(y, Float64(Float64(3.13060547623 + Float64(-36.52704169880642 / z)) + Float64(Float64(Float64(457.9610022158428 / Float64(z * z)) + Float64(t / Float64(z * z))) + Float64(t_1 / (z ^ 3.0)))), x);
	end
	return tmp
end

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]
↓
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a + N[(N[(t * -15.234687407), $MachinePrecision] + -5864.8025282699045), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1e+47], N[(N[(3.13060547623 * y + N[(-36.52704169880642 * N[(y / z), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y / z), $MachinePrecision] / z), $MachinePrecision] * N[(N[(t + 457.9610022158428), $MachinePrecision] + N[(t$95$1 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.8e+17], N[(y * N[(N[(z * N[(z * N[(z * N[(z * 3.13060547623 + 11.1667541262), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision] + b), $MachinePrecision] / N[(z * N[(z * N[(z * N[(z + 15.234687407), $MachinePrecision] + 31.4690115749), $MachinePrecision] + 11.9400905721), $MachinePrecision] + 0.607771387771), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(y * N[(N[(3.13060547623 + N[(-36.52704169880642 / z), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(457.9610022158428 / N[(z * z), $MachinePrecision]), $MachinePrecision] + N[(t / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 / N[Power[z, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]]]

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}
↓
\begin{array}{l}
t_1 := a + \left(t \cdot -15.234687407 + -5864.8025282699045\right)\\
\mathbf{if}\;z \leq -1 \cdot 10^{+47}:\\
\;\;\;\;\mathsf{fma}\left(3.13060547623, y, \mathsf{fma}\left(-36.52704169880642, \frac{y}{z}, x\right)\right) + \frac{\frac{y}{z}}{z} \cdot \left(\left(t + 457.9610022158428\right) + \frac{t_1}{z}\right)\\

\mathbf{elif}\;z \leq 5.8 \cdot 10^{+17}:\\
\;\;\;\;\mathsf{fma}\left(y, \frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right)}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}, x\right)\\

\mathbf{else}:\\
\;\;\;\;\mathsf{fma}\left(y, \left(3.13060547623 + \frac{-36.52704169880642}{z}\right) + \left(\left(\frac{457.9610022158428}{z \cdot z} + \frac{t}{z \cdot z}\right) + \frac{t_1}{{z}^{3}}\right), x\right)\\


\end{array}

Error

Target

Original29.8
Target0.9
Herbie0.7
\[\begin{array}{l} \mathbf{if}\;z < -6.499344996252632 \cdot 10^{+53}:\\ \;\;\;\;x + \left(\left(3.13060547623 - \frac{36.527041698806414}{z}\right) + \frac{t}{z \cdot z}\right) \cdot \frac{y}{1}\\ \mathbf{elif}\;z < 7.066965436914287 \cdot 10^{+59}:\\ \;\;\;\;x + \frac{y}{\frac{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}{\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(3.13060547623 - \frac{36.527041698806414}{z}\right) + \frac{t}{z \cdot z}\right) \cdot \frac{y}{1}\\ \end{array} \]

Derivation

  1. Split input into 3 regimes

  2. if z < -1e47

    1. Initial program 60.5

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

    2. Simplified58.4

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right)}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}, x\right)} \]
      Proof
      (fma.f64 y (/.f64 (fma.f64 z (fma.f64 z (fma.f64 z (fma.f64 z 313060547623/100000000000 55833770631/5000000000) t) a) b) (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000)) x): 0 points increase in error, 0 points decrease in error
      (fma.f64 y (/.f64 (fma.f64 z (fma.f64 z (fma.f64 z (Rewrite<= fma-def_binary64 (+.f64 (*.f64 z 313060547623/100000000000) 55833770631/5000000000)) t) a) b) (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000)) x): 0 points increase in error, 0 points decrease in error
      (fma.f64 y (/.f64 (fma.f64 z (fma.f64 z (Rewrite<= fma-def_binary64 (+.f64 (*.f64 z (+.f64 (*.f64 z 313060547623/100000000000) 55833770631/5000000000)) t)) a) b) (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000)) x): 0 points increase in error, 0 points decrease in error
      (fma.f64 y (/.f64 (fma.f64 z (fma.f64 z (+.f64 (Rewrite<= *-commutative_binary64 (*.f64 (+.f64 (*.f64 z 313060547623/100000000000) 55833770631/5000000000) z)) t) a) b) (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000)) x): 0 points increase in error, 0 points decrease in error
      (fma.f64 y (/.f64 (fma.f64 z (Rewrite<= fma-def_binary64 (+.f64 (*.f64 z (+.f64 (*.f64 (+.f64 (*.f64 z 313060547623/100000000000) 55833770631/5000000000) z) t)) a)) b) (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000)) x): 0 points increase in error, 0 points decrease in error
      (fma.f64 y (/.f64 (fma.f64 z (+.f64 (Rewrite<= *-commutative_binary64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z 313060547623/100000000000) 55833770631/5000000000) z) t) z)) a) b) (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000)) x): 0 points increase in error, 0 points decrease in error
      (fma.f64 y (/.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 z (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z 313060547623/100000000000) 55833770631/5000000000) z) t) z) a)) b)) (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000)) x): 1 points increase in error, 0 points decrease in error
      (fma.f64 y (/.f64 (+.f64 (Rewrite<= *-commutative_binary64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z 313060547623/100000000000) 55833770631/5000000000) z) t) z) a) z)) b) (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000)) x): 0 points increase in error, 0 points decrease in error
      (fma.f64 y (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z 313060547623/100000000000) 55833770631/5000000000) z) t) z) a) z) b) (fma.f64 z (fma.f64 z (Rewrite<= fma-def_binary64 (+.f64 (*.f64 z (+.f64 z 15234687407/1000000000)) 314690115749/10000000000)) 119400905721/10000000000) 607771387771/1000000000000)) x): 0 points increase in error, 1 points decrease in error
      (fma.f64 y (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z 313060547623/100000000000) 55833770631/5000000000) z) t) z) a) z) b) (fma.f64 z (fma.f64 z (+.f64 (Rewrite<= *-commutative_binary64 (*.f64 (+.f64 z 15234687407/1000000000) z)) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000)) x): 0 points increase in error, 0 points decrease in error
      (fma.f64 y (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z 313060547623/100000000000) 55833770631/5000000000) z) t) z) a) z) b) (fma.f64 z (Rewrite<= fma-def_binary64 (+.f64 (*.f64 z (+.f64 (*.f64 (+.f64 z 15234687407/1000000000) z) 314690115749/10000000000)) 119400905721/10000000000)) 607771387771/1000000000000)) x): 0 points increase in error, 0 points decrease in error
      (fma.f64 y (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z 313060547623/100000000000) 55833770631/5000000000) z) t) z) a) z) b) (fma.f64 z (+.f64 (Rewrite<= *-commutative_binary64 (*.f64 (+.f64 (*.f64 (+.f64 z 15234687407/1000000000) z) 314690115749/10000000000) z)) 119400905721/10000000000) 607771387771/1000000000000)) x): 0 points increase in error, 0 points decrease in error
      (fma.f64 y (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z 313060547623/100000000000) 55833770631/5000000000) z) t) z) a) z) b) (Rewrite<= fma-def_binary64 (+.f64 (*.f64 z (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z 15234687407/1000000000) z) 314690115749/10000000000) z) 119400905721/10000000000)) 607771387771/1000000000000))) x): 0 points increase in error, 0 points decrease in error
      (fma.f64 y (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z 313060547623/100000000000) 55833770631/5000000000) z) t) z) a) z) b) (+.f64 (Rewrite<= *-commutative_binary64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z 15234687407/1000000000) z) 314690115749/10000000000) z) 119400905721/10000000000) z)) 607771387771/1000000000000)) x): 0 points increase in error, 0 points decrease in error
      (Rewrite<= fma-def_binary64 (+.f64 (*.f64 y (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z 313060547623/100000000000) 55833770631/5000000000) z) t) z) a) z) b) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z 15234687407/1000000000) z) 314690115749/10000000000) z) 119400905721/10000000000) z) 607771387771/1000000000000))) x)): 1 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite=> associate-*r/_binary64 (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z 313060547623/100000000000) 55833770631/5000000000) z) t) z) a) z) b)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z 15234687407/1000000000) z) 314690115749/10000000000) z) 119400905721/10000000000) z) 607771387771/1000000000000))) x): 18 points increase in error, 12 points decrease in error
      (Rewrite<= +-commutative_binary64 (+.f64 x (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z 313060547623/100000000000) 55833770631/5000000000) z) t) z) a) z) b)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z 15234687407/1000000000) z) 314690115749/10000000000) z) 119400905721/10000000000) z) 607771387771/1000000000000)))): 0 points increase in error, 0 points decrease in error

    3. Taylor expanded in z around inf 12.6

      \[\leadsto \color{blue}{-36.52704169880642 \cdot \frac{y}{z} + \left(\frac{y \cdot \left(\left(1112.0901850848957 + a\right) - 15.234687407 \cdot \left(457.9610022158428 + t\right)\right)}{{z}^{3}} + \left(3.13060547623 \cdot y + \left(\frac{y \cdot \left(457.9610022158428 + t\right)}{{z}^{2}} + x\right)\right)\right)} \]

    4. Simplified0.8

      \[\leadsto \color{blue}{\mathsf{fma}\left(3.13060547623, y, \mathsf{fma}\left(-36.52704169880642, \frac{y}{z}, x\right)\right) + \frac{\frac{y}{z}}{z} \cdot \left(\left(t + 457.9610022158428\right) + \frac{a + \left(t \cdot -15.234687407 + -5864.8025282699045\right)}{z}\right)} \]
      Proof
      (+.f64 (fma.f64 313060547623/100000000000 y (fma.f64 -3652704169880641883561/100000000000000000000 (/.f64 y z) x)) (*.f64 (/.f64 (/.f64 y z) z) (+.f64 (+.f64 t 45796100221584283915100827016327/100000000000000000000000000000) (/.f64 (+.f64 a (+.f64 (*.f64 t -15234687407/1000000000) -586480252826990429730394679450703430294089/100000000000000000000000000000000000000)) z)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (fma.f64 313060547623/100000000000 y (Rewrite<= fma-def_binary64 (+.f64 (*.f64 -3652704169880641883561/100000000000000000000 (/.f64 y z)) x))) (*.f64 (/.f64 (/.f64 y z) z) (+.f64 (+.f64 t 45796100221584283915100827016327/100000000000000000000000000000) (/.f64 (+.f64 a (+.f64 (*.f64 t -15234687407/1000000000) -586480252826990429730394679450703430294089/100000000000000000000000000000000000000)) z)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (fma.f64 313060547623/100000000000 y (Rewrite<= +-commutative_binary64 (+.f64 x (*.f64 -3652704169880641883561/100000000000000000000 (/.f64 y z))))) (*.f64 (/.f64 (/.f64 y z) z) (+.f64 (+.f64 t 45796100221584283915100827016327/100000000000000000000000000000) (/.f64 (+.f64 a (+.f64 (*.f64 t -15234687407/1000000000) -586480252826990429730394679450703430294089/100000000000000000000000000000000000000)) z)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 313060547623/100000000000 y) (+.f64 x (*.f64 -3652704169880641883561/100000000000000000000 (/.f64 y z))))) (*.f64 (/.f64 (/.f64 y z) z) (+.f64 (+.f64 t 45796100221584283915100827016327/100000000000000000000000000000) (/.f64 (+.f64 a (+.f64 (*.f64 t -15234687407/1000000000) -586480252826990429730394679450703430294089/100000000000000000000000000000000000000)) z)))): 2 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite<= associate-+l+_binary64 (+.f64 (+.f64 (*.f64 313060547623/100000000000 y) x) (*.f64 -3652704169880641883561/100000000000000000000 (/.f64 y z)))) (*.f64 (/.f64 (/.f64 y z) z) (+.f64 (+.f64 t 45796100221584283915100827016327/100000000000000000000000000000) (/.f64 (+.f64 a (+.f64 (*.f64 t -15234687407/1000000000) -586480252826990429730394679450703430294089/100000000000000000000000000000000000000)) z)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 -3652704169880641883561/100000000000000000000 (/.f64 y z)) (+.f64 (*.f64 313060547623/100000000000 y) x))) (*.f64 (/.f64 (/.f64 y z) z) (+.f64 (+.f64 t 45796100221584283915100827016327/100000000000000000000000000000) (/.f64 (+.f64 a (+.f64 (*.f64 t -15234687407/1000000000) -586480252826990429730394679450703430294089/100000000000000000000000000000000000000)) z)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (*.f64 -3652704169880641883561/100000000000000000000 (/.f64 y z)) (+.f64 (*.f64 313060547623/100000000000 y) x)) (*.f64 (Rewrite<= associate-/r*_binary64 (/.f64 y (*.f64 z z))) (+.f64 (+.f64 t 45796100221584283915100827016327/100000000000000000000000000000) (/.f64 (+.f64 a (+.f64 (*.f64 t -15234687407/1000000000) -586480252826990429730394679450703430294089/100000000000000000000000000000000000000)) z)))): 3 points increase in error, 3 points decrease in error
      (+.f64 (+.f64 (*.f64 -3652704169880641883561/100000000000000000000 (/.f64 y z)) (+.f64 (*.f64 313060547623/100000000000 y) x)) (*.f64 (/.f64 y (Rewrite<= unpow2_binary64 (pow.f64 z 2))) (+.f64 (+.f64 t 45796100221584283915100827016327/100000000000000000000000000000) (/.f64 (+.f64 a (+.f64 (*.f64 t -15234687407/1000000000) -586480252826990429730394679450703430294089/100000000000000000000000000000000000000)) z)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (*.f64 -3652704169880641883561/100000000000000000000 (/.f64 y z)) (+.f64 (*.f64 313060547623/100000000000 y) x)) (*.f64 (/.f64 y (pow.f64 z 2)) (+.f64 (Rewrite<= +-commutative_binary64 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t)) (/.f64 (+.f64 a (+.f64 (*.f64 t -15234687407/1000000000) -586480252826990429730394679450703430294089/100000000000000000000000000000000000000)) z)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (*.f64 -3652704169880641883561/100000000000000000000 (/.f64 y z)) (+.f64 (*.f64 313060547623/100000000000 y) x)) (*.f64 (/.f64 y (pow.f64 z 2)) (+.f64 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t) (/.f64 (+.f64 a (+.f64 (*.f64 t -15234687407/1000000000) (Rewrite<= metadata-eval (+.f64 -697689271335479999750499226480922330294089/100000000000000000000000000000000000000 1112090185084895700201045470302189/1000000000000000000000000000000)))) z)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (*.f64 -3652704169880641883561/100000000000000000000 (/.f64 y z)) (+.f64 (*.f64 313060547623/100000000000 y) x)) (*.f64 (/.f64 y (pow.f64 z 2)) (+.f64 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t) (/.f64 (+.f64 a (+.f64 (*.f64 t -15234687407/1000000000) (+.f64 (Rewrite<= metadata-eval (*.f64 45796100221584283915100827016327/100000000000000000000000000000 -15234687407/1000000000)) 1112090185084895700201045470302189/1000000000000000000000000000000))) z)))): 0 points increase in error, 5 points decrease in error
      (+.f64 (+.f64 (*.f64 -3652704169880641883561/100000000000000000000 (/.f64 y z)) (+.f64 (*.f64 313060547623/100000000000 y) x)) (*.f64 (/.f64 y (pow.f64 z 2)) (+.f64 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t) (/.f64 (+.f64 a (Rewrite<= associate-+l+_binary64 (+.f64 (+.f64 (*.f64 t -15234687407/1000000000) (*.f64 45796100221584283915100827016327/100000000000000000000000000000 -15234687407/1000000000)) 1112090185084895700201045470302189/1000000000000000000000000000000))) z)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (*.f64 -3652704169880641883561/100000000000000000000 (/.f64 y z)) (+.f64 (*.f64 313060547623/100000000000 y) x)) (*.f64 (/.f64 y (pow.f64 z 2)) (+.f64 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t) (/.f64 (+.f64 a (+.f64 (Rewrite<= distribute-rgt-in_binary64 (*.f64 -15234687407/1000000000 (+.f64 t 45796100221584283915100827016327/100000000000000000000000000000))) 1112090185084895700201045470302189/1000000000000000000000000000000)) z)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (*.f64 -3652704169880641883561/100000000000000000000 (/.f64 y z)) (+.f64 (*.f64 313060547623/100000000000 y) x)) (*.f64 (/.f64 y (pow.f64 z 2)) (+.f64 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t) (/.f64 (+.f64 a (+.f64 (*.f64 -15234687407/1000000000 (Rewrite<= +-commutative_binary64 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t))) 1112090185084895700201045470302189/1000000000000000000000000000000)) z)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (*.f64 -3652704169880641883561/100000000000000000000 (/.f64 y z)) (+.f64 (*.f64 313060547623/100000000000 y) x)) (*.f64 (/.f64 y (pow.f64 z 2)) (+.f64 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t) (/.f64 (Rewrite<= associate-+l+_binary64 (+.f64 (+.f64 a (*.f64 -15234687407/1000000000 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t))) 1112090185084895700201045470302189/1000000000000000000000000000000)) z)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (*.f64 -3652704169880641883561/100000000000000000000 (/.f64 y z)) (+.f64 (*.f64 313060547623/100000000000 y) x)) (*.f64 (/.f64 y (pow.f64 z 2)) (+.f64 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t) (/.f64 (+.f64 (+.f64 a (*.f64 (Rewrite<= metadata-eval (neg.f64 15234687407/1000000000)) (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t))) 1112090185084895700201045470302189/1000000000000000000000000000000) z)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (*.f64 -3652704169880641883561/100000000000000000000 (/.f64 y z)) (+.f64 (*.f64 313060547623/100000000000 y) x)) (*.f64 (/.f64 y (pow.f64 z 2)) (+.f64 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t) (/.f64 (+.f64 (Rewrite<= cancel-sign-sub-inv_binary64 (-.f64 a (*.f64 15234687407/1000000000 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t)))) 1112090185084895700201045470302189/1000000000000000000000000000000) z)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (*.f64 -3652704169880641883561/100000000000000000000 (/.f64 y z)) (+.f64 (*.f64 313060547623/100000000000 y) x)) (*.f64 (/.f64 y (pow.f64 z 2)) (+.f64 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t) (/.f64 (Rewrite<= +-commutative_binary64 (+.f64 1112090185084895700201045470302189/1000000000000000000000000000000 (-.f64 a (*.f64 15234687407/1000000000 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t))))) z)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (*.f64 -3652704169880641883561/100000000000000000000 (/.f64 y z)) (+.f64 (*.f64 313060547623/100000000000 y) x)) (*.f64 (/.f64 y (pow.f64 z 2)) (+.f64 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t) (/.f64 (Rewrite<= associate--l+_binary64 (-.f64 (+.f64 1112090185084895700201045470302189/1000000000000000000000000000000 a) (*.f64 15234687407/1000000000 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t)))) z)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (*.f64 -3652704169880641883561/100000000000000000000 (/.f64 y z)) (+.f64 (*.f64 313060547623/100000000000 y) x)) (*.f64 (/.f64 y (pow.f64 z 2)) (+.f64 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t) (/.f64 (Rewrite<= remove-double-neg_binary64 (neg.f64 (neg.f64 (-.f64 (+.f64 1112090185084895700201045470302189/1000000000000000000000000000000 a) (*.f64 15234687407/1000000000 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t)))))) z)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (*.f64 -3652704169880641883561/100000000000000000000 (/.f64 y z)) (+.f64 (*.f64 313060547623/100000000000 y) x)) (*.f64 (/.f64 y (pow.f64 z 2)) (+.f64 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t) (/.f64 (neg.f64 (neg.f64 (Rewrite=> cancel-sign-sub-inv_binary64 (+.f64 (+.f64 1112090185084895700201045470302189/1000000000000000000000000000000 a) (*.f64 (neg.f64 15234687407/1000000000) (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t)))))) z)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (*.f64 -3652704169880641883561/100000000000000000000 (/.f64 y z)) (+.f64 (*.f64 313060547623/100000000000 y) x)) (*.f64 (/.f64 y (pow.f64 z 2)) (+.f64 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t) (/.f64 (neg.f64 (neg.f64 (+.f64 (Rewrite=> +-commutative_binary64 (+.f64 a 1112090185084895700201045470302189/1000000000000000000000000000000)) (*.f64 (neg.f64 15234687407/1000000000) (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t))))) z)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (*.f64 -3652704169880641883561/100000000000000000000 (/.f64 y z)) (+.f64 (*.f64 313060547623/100000000000 y) x)) (*.f64 (/.f64 y (pow.f64 z 2)) (+.f64 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t) (/.f64 (neg.f64 (neg.f64 (+.f64 (+.f64 a 1112090185084895700201045470302189/1000000000000000000000000000000) (*.f64 (Rewrite=> metadata-eval -15234687407/1000000000) (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t))))) z)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (*.f64 -3652704169880641883561/100000000000000000000 (/.f64 y z)) (+.f64 (*.f64 313060547623/100000000000 y) x)) (*.f64 (/.f64 y (pow.f64 z 2)) (+.f64 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t) (/.f64 (neg.f64 (neg.f64 (Rewrite=> associate-+l+_binary64 (+.f64 a (+.f64 1112090185084895700201045470302189/1000000000000000000000000000000 (*.f64 -15234687407/1000000000 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t))))))) z)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (*.f64 -3652704169880641883561/100000000000000000000 (/.f64 y z)) (+.f64 (*.f64 313060547623/100000000000 y) x)) (*.f64 (/.f64 y (pow.f64 z 2)) (+.f64 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t) (/.f64 (neg.f64 (Rewrite<= distribute-neg-out_binary64 (+.f64 (neg.f64 a) (neg.f64 (+.f64 1112090185084895700201045470302189/1000000000000000000000000000000 (*.f64 -15234687407/1000000000 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t))))))) z)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (*.f64 -3652704169880641883561/100000000000000000000 (/.f64 y z)) (+.f64 (*.f64 313060547623/100000000000 y) x)) (*.f64 (/.f64 y (pow.f64 z 2)) (+.f64 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t) (/.f64 (neg.f64 (+.f64 (Rewrite<= mul-1-neg_binary64 (*.f64 -1 a)) (neg.f64 (+.f64 1112090185084895700201045470302189/1000000000000000000000000000000 (*.f64 -15234687407/1000000000 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t)))))) z)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (*.f64 -3652704169880641883561/100000000000000000000 (/.f64 y z)) (+.f64 (*.f64 313060547623/100000000000 y) x)) (*.f64 (/.f64 y (pow.f64 z 2)) (+.f64 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t) (/.f64 (neg.f64 (Rewrite<= sub-neg_binary64 (-.f64 (*.f64 -1 a) (+.f64 1112090185084895700201045470302189/1000000000000000000000000000000 (*.f64 -15234687407/1000000000 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t)))))) z)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (*.f64 -3652704169880641883561/100000000000000000000 (/.f64 y z)) (+.f64 (*.f64 313060547623/100000000000 y) x)) (*.f64 (/.f64 y (pow.f64 z 2)) (+.f64 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t) (Rewrite=> distribute-frac-neg_binary64 (neg.f64 (/.f64 (-.f64 (*.f64 -1 a) (+.f64 1112090185084895700201045470302189/1000000000000000000000000000000 (*.f64 -15234687407/1000000000 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t)))) z)))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (*.f64 -3652704169880641883561/100000000000000000000 (/.f64 y z)) (+.f64 (*.f64 313060547623/100000000000 y) x)) (*.f64 (/.f64 y (pow.f64 z 2)) (Rewrite<= sub-neg_binary64 (-.f64 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t) (/.f64 (-.f64 (*.f64 -1 a) (+.f64 1112090185084895700201045470302189/1000000000000000000000000000000 (*.f64 -15234687407/1000000000 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t)))) z))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (*.f64 -3652704169880641883561/100000000000000000000 (/.f64 y z)) (+.f64 (*.f64 313060547623/100000000000 y) x)) (Rewrite<= distribute-lft-out--_binary64 (-.f64 (*.f64 (/.f64 y (pow.f64 z 2)) (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t)) (*.f64 (/.f64 y (pow.f64 z 2)) (/.f64 (-.f64 (*.f64 -1 a) (+.f64 1112090185084895700201045470302189/1000000000000000000000000000000 (*.f64 -15234687407/1000000000 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t)))) z))))): 0 points increase in error, 1 points decrease in error
      (+.f64 (+.f64 (*.f64 -3652704169880641883561/100000000000000000000 (/.f64 y z)) (+.f64 (*.f64 313060547623/100000000000 y) x)) (-.f64 (*.f64 (/.f64 y (pow.f64 z 2)) (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t)) (Rewrite<= times-frac_binary64 (/.f64 (*.f64 y (-.f64 (*.f64 -1 a) (+.f64 1112090185084895700201045470302189/1000000000000000000000000000000 (*.f64 -15234687407/1000000000 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t))))) (*.f64 (pow.f64 z 2) z))))): 35 points increase in error, 4 points decrease in error
      (+.f64 (+.f64 (*.f64 -3652704169880641883561/100000000000000000000 (/.f64 y z)) (+.f64 (*.f64 313060547623/100000000000 y) x)) (-.f64 (*.f64 (/.f64 y (pow.f64 z 2)) (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t)) (/.f64 (Rewrite<= *-commutative_binary64 (*.f64 (-.f64 (*.f64 -1 a) (+.f64 1112090185084895700201045470302189/1000000000000000000000000000000 (*.f64 -15234687407/1000000000 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t)))) y)) (*.f64 (pow.f64 z 2) z)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (*.f64 -3652704169880641883561/100000000000000000000 (/.f64 y z)) (+.f64 (*.f64 313060547623/100000000000 y) x)) (-.f64 (*.f64 (/.f64 y (pow.f64 z 2)) (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t)) (/.f64 (*.f64 (-.f64 (*.f64 -1 a) (+.f64 1112090185084895700201045470302189/1000000000000000000000000000000 (*.f64 -15234687407/1000000000 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t)))) y) (*.f64 (Rewrite=> unpow2_binary64 (*.f64 z z)) z)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (*.f64 -3652704169880641883561/100000000000000000000 (/.f64 y z)) (+.f64 (*.f64 313060547623/100000000000 y) x)) (-.f64 (*.f64 (/.f64 y (pow.f64 z 2)) (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t)) (/.f64 (*.f64 (-.f64 (*.f64 -1 a) (+.f64 1112090185084895700201045470302189/1000000000000000000000000000000 (*.f64 -15234687407/1000000000 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t)))) y) (Rewrite<= unpow3_binary64 (pow.f64 z 3))))): 2 points increase in error, 2 points decrease in error
      (+.f64 (+.f64 (*.f64 -3652704169880641883561/100000000000000000000 (/.f64 y z)) (+.f64 (*.f64 313060547623/100000000000 y) x)) (-.f64 (Rewrite=> associate-*l/_binary64 (/.f64 (*.f64 y (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t)) (pow.f64 z 2))) (/.f64 (*.f64 (-.f64 (*.f64 -1 a) (+.f64 1112090185084895700201045470302189/1000000000000000000000000000000 (*.f64 -15234687407/1000000000 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t)))) y) (pow.f64 z 3)))): 0 points increase in error, 2 points decrease in error
      (+.f64 (+.f64 (*.f64 -3652704169880641883561/100000000000000000000 (/.f64 y z)) (+.f64 (*.f64 313060547623/100000000000 y) x)) (Rewrite<= unsub-neg_binary64 (+.f64 (/.f64 (*.f64 y (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t)) (pow.f64 z 2)) (neg.f64 (/.f64 (*.f64 (-.f64 (*.f64 -1 a) (+.f64 1112090185084895700201045470302189/1000000000000000000000000000000 (*.f64 -15234687407/1000000000 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t)))) y) (pow.f64 z 3)))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (*.f64 -3652704169880641883561/100000000000000000000 (/.f64 y z)) (+.f64 (*.f64 313060547623/100000000000 y) x)) (+.f64 (/.f64 (*.f64 y (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t)) (pow.f64 z 2)) (Rewrite=> distribute-neg-frac_binary64 (/.f64 (neg.f64 (*.f64 (-.f64 (*.f64 -1 a) (+.f64 1112090185084895700201045470302189/1000000000000000000000000000000 (*.f64 -15234687407/1000000000 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t)))) y)) (pow.f64 z 3))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (*.f64 -3652704169880641883561/100000000000000000000 (/.f64 y z)) (+.f64 (*.f64 313060547623/100000000000 y) x)) (+.f64 (/.f64 (*.f64 y (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t)) (pow.f64 z 2)) (/.f64 (Rewrite<= distribute-lft-neg-out_binary64 (*.f64 (neg.f64 (-.f64 (*.f64 -1 a) (+.f64 1112090185084895700201045470302189/1000000000000000000000000000000 (*.f64 -15234687407/1000000000 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t))))) y)) (pow.f64 z 3)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (*.f64 -3652704169880641883561/100000000000000000000 (/.f64 y z)) (+.f64 (*.f64 313060547623/100000000000 y) x)) (+.f64 (/.f64 (*.f64 y (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t)) (pow.f64 z 2)) (/.f64 (*.f64 (neg.f64 (Rewrite=> sub-neg_binary64 (+.f64 (*.f64 -1 a) (neg.f64 (+.f64 1112090185084895700201045470302189/1000000000000000000000000000000 (*.f64 -15234687407/1000000000 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t))))))) y) (pow.f64 z 3)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (*.f64 -3652704169880641883561/100000000000000000000 (/.f64 y z)) (+.f64 (*.f64 313060547623/100000000000 y) x)) (+.f64 (/.f64 (*.f64 y (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t)) (pow.f64 z 2)) (/.f64 (*.f64 (neg.f64 (+.f64 (Rewrite=> mul-1-neg_binary64 (neg.f64 a)) (neg.f64 (+.f64 1112090185084895700201045470302189/1000000000000000000000000000000 (*.f64 -15234687407/1000000000 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t)))))) y) (pow.f64 z 3)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (*.f64 -3652704169880641883561/100000000000000000000 (/.f64 y z)) (+.f64 (*.f64 313060547623/100000000000 y) x)) (+.f64 (/.f64 (*.f64 y (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t)) (pow.f64 z 2)) (/.f64 (*.f64 (neg.f64 (Rewrite=> distribute-neg-out_binary64 (neg.f64 (+.f64 a (+.f64 1112090185084895700201045470302189/1000000000000000000000000000000 (*.f64 -15234687407/1000000000 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t))))))) y) (pow.f64 z 3)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (*.f64 -3652704169880641883561/100000000000000000000 (/.f64 y z)) (+.f64 (*.f64 313060547623/100000000000 y) x)) (+.f64 (/.f64 (*.f64 y (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t)) (pow.f64 z 2)) (/.f64 (*.f64 (neg.f64 (neg.f64 (Rewrite<= associate-+l+_binary64 (+.f64 (+.f64 a 1112090185084895700201045470302189/1000000000000000000000000000000) (*.f64 -15234687407/1000000000 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t)))))) y) (pow.f64 z 3)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (*.f64 -3652704169880641883561/100000000000000000000 (/.f64 y z)) (+.f64 (*.f64 313060547623/100000000000 y) x)) (+.f64 (/.f64 (*.f64 y (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t)) (pow.f64 z 2)) (/.f64 (*.f64 (neg.f64 (neg.f64 (+.f64 (Rewrite<= +-commutative_binary64 (+.f64 1112090185084895700201045470302189/1000000000000000000000000000000 a)) (*.f64 -15234687407/1000000000 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t))))) y) (pow.f64 z 3)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (*.f64 -3652704169880641883561/100000000000000000000 (/.f64 y z)) (+.f64 (*.f64 313060547623/100000000000 y) x)) (+.f64 (/.f64 (*.f64 y (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t)) (pow.f64 z 2)) (/.f64 (*.f64 (neg.f64 (neg.f64 (+.f64 (+.f64 1112090185084895700201045470302189/1000000000000000000000000000000 a) (*.f64 (Rewrite<= metadata-eval (neg.f64 15234687407/1000000000)) (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t))))) y) (pow.f64 z 3)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (*.f64 -3652704169880641883561/100000000000000000000 (/.f64 y z)) (+.f64 (*.f64 313060547623/100000000000 y) x)) (+.f64 (/.f64 (*.f64 y (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t)) (pow.f64 z 2)) (/.f64 (*.f64 (neg.f64 (neg.f64 (Rewrite<= cancel-sign-sub-inv_binary64 (-.f64 (+.f64 1112090185084895700201045470302189/1000000000000000000000000000000 a) (*.f64 15234687407/1000000000 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t)))))) y) (pow.f64 z 3)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (*.f64 -3652704169880641883561/100000000000000000000 (/.f64 y z)) (+.f64 (*.f64 313060547623/100000000000 y) x)) (+.f64 (/.f64 (*.f64 y (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t)) (pow.f64 z 2)) (/.f64 (*.f64 (Rewrite=> remove-double-neg_binary64 (-.f64 (+.f64 1112090185084895700201045470302189/1000000000000000000000000000000 a) (*.f64 15234687407/1000000000 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t)))) y) (pow.f64 z 3)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (*.f64 -3652704169880641883561/100000000000000000000 (/.f64 y z)) (+.f64 (*.f64 313060547623/100000000000 y) x)) (+.f64 (/.f64 (*.f64 y (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t)) (pow.f64 z 2)) (/.f64 (Rewrite<= *-commutative_binary64 (*.f64 y (-.f64 (+.f64 1112090185084895700201045470302189/1000000000000000000000000000000 a) (*.f64 15234687407/1000000000 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t))))) (pow.f64 z 3)))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate-+l+_binary64 (+.f64 (+.f64 (+.f64 (*.f64 -3652704169880641883561/100000000000000000000 (/.f64 y z)) (+.f64 (*.f64 313060547623/100000000000 y) x)) (/.f64 (*.f64 y (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t)) (pow.f64 z 2))) (/.f64 (*.f64 y (-.f64 (+.f64 1112090185084895700201045470302189/1000000000000000000000000000000 a) (*.f64 15234687407/1000000000 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t)))) (pow.f64 z 3)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite=> associate-+l+_binary64 (+.f64 (*.f64 -3652704169880641883561/100000000000000000000 (/.f64 y z)) (+.f64 (+.f64 (*.f64 313060547623/100000000000 y) x) (/.f64 (*.f64 y (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t)) (pow.f64 z 2))))) (/.f64 (*.f64 y (-.f64 (+.f64 1112090185084895700201045470302189/1000000000000000000000000000000 a) (*.f64 15234687407/1000000000 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t)))) (pow.f64 z 3))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (*.f64 -3652704169880641883561/100000000000000000000 (/.f64 y z)) (Rewrite<= associate-+r+_binary64 (+.f64 (*.f64 313060547623/100000000000 y) (+.f64 x (/.f64 (*.f64 y (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t)) (pow.f64 z 2)))))) (/.f64 (*.f64 y (-.f64 (+.f64 1112090185084895700201045470302189/1000000000000000000000000000000 a) (*.f64 15234687407/1000000000 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t)))) (pow.f64 z 3))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (*.f64 -3652704169880641883561/100000000000000000000 (/.f64 y z)) (+.f64 (*.f64 313060547623/100000000000 y) (Rewrite<= +-commutative_binary64 (+.f64 (/.f64 (*.f64 y (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t)) (pow.f64 z 2)) x)))) (/.f64 (*.f64 y (-.f64 (+.f64 1112090185084895700201045470302189/1000000000000000000000000000000 a) (*.f64 15234687407/1000000000 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t)))) (pow.f64 z 3))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate-+r+_binary64 (+.f64 (*.f64 -3652704169880641883561/100000000000000000000 (/.f64 y z)) (+.f64 (+.f64 (*.f64 313060547623/100000000000 y) (+.f64 (/.f64 (*.f64 y (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t)) (pow.f64 z 2)) x)) (/.f64 (*.f64 y (-.f64 (+.f64 1112090185084895700201045470302189/1000000000000000000000000000000 a) (*.f64 15234687407/1000000000 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t)))) (pow.f64 z 3))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 -3652704169880641883561/100000000000000000000 (/.f64 y z)) (Rewrite<= +-commutative_binary64 (+.f64 (/.f64 (*.f64 y (-.f64 (+.f64 1112090185084895700201045470302189/1000000000000000000000000000000 a) (*.f64 15234687407/1000000000 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t)))) (pow.f64 z 3)) (+.f64 (*.f64 313060547623/100000000000 y) (+.f64 (/.f64 (*.f64 y (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t)) (pow.f64 z 2)) x))))): 0 points increase in error, 0 points decrease in error

    if -1e47 < z < 5.8e17

    1. Initial program 1.2

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

    2. Simplified0.6

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right)}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}, x\right)} \]
      Proof
      (fma.f64 y (/.f64 (fma.f64 z (fma.f64 z (fma.f64 z (fma.f64 z 313060547623/100000000000 55833770631/5000000000) t) a) b) (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000)) x): 0 points increase in error, 0 points decrease in error
      (fma.f64 y (/.f64 (fma.f64 z (fma.f64 z (fma.f64 z (Rewrite<= fma-def_binary64 (+.f64 (*.f64 z 313060547623/100000000000) 55833770631/5000000000)) t) a) b) (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000)) x): 0 points increase in error, 0 points decrease in error
      (fma.f64 y (/.f64 (fma.f64 z (fma.f64 z (Rewrite<= fma-def_binary64 (+.f64 (*.f64 z (+.f64 (*.f64 z 313060547623/100000000000) 55833770631/5000000000)) t)) a) b) (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000)) x): 0 points increase in error, 0 points decrease in error
      (fma.f64 y (/.f64 (fma.f64 z (fma.f64 z (+.f64 (Rewrite<= *-commutative_binary64 (*.f64 (+.f64 (*.f64 z 313060547623/100000000000) 55833770631/5000000000) z)) t) a) b) (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000)) x): 0 points increase in error, 0 points decrease in error
      (fma.f64 y (/.f64 (fma.f64 z (Rewrite<= fma-def_binary64 (+.f64 (*.f64 z (+.f64 (*.f64 (+.f64 (*.f64 z 313060547623/100000000000) 55833770631/5000000000) z) t)) a)) b) (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000)) x): 0 points increase in error, 0 points decrease in error
      (fma.f64 y (/.f64 (fma.f64 z (+.f64 (Rewrite<= *-commutative_binary64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z 313060547623/100000000000) 55833770631/5000000000) z) t) z)) a) b) (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000)) x): 0 points increase in error, 0 points decrease in error
      (fma.f64 y (/.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 z (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z 313060547623/100000000000) 55833770631/5000000000) z) t) z) a)) b)) (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000)) x): 1 points increase in error, 0 points decrease in error
      (fma.f64 y (/.f64 (+.f64 (Rewrite<= *-commutative_binary64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z 313060547623/100000000000) 55833770631/5000000000) z) t) z) a) z)) b) (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000)) x): 0 points increase in error, 0 points decrease in error
      (fma.f64 y (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z 313060547623/100000000000) 55833770631/5000000000) z) t) z) a) z) b) (fma.f64 z (fma.f64 z (Rewrite<= fma-def_binary64 (+.f64 (*.f64 z (+.f64 z 15234687407/1000000000)) 314690115749/10000000000)) 119400905721/10000000000) 607771387771/1000000000000)) x): 0 points increase in error, 1 points decrease in error
      (fma.f64 y (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z 313060547623/100000000000) 55833770631/5000000000) z) t) z) a) z) b) (fma.f64 z (fma.f64 z (+.f64 (Rewrite<= *-commutative_binary64 (*.f64 (+.f64 z 15234687407/1000000000) z)) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000)) x): 0 points increase in error, 0 points decrease in error
      (fma.f64 y (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z 313060547623/100000000000) 55833770631/5000000000) z) t) z) a) z) b) (fma.f64 z (Rewrite<= fma-def_binary64 (+.f64 (*.f64 z (+.f64 (*.f64 (+.f64 z 15234687407/1000000000) z) 314690115749/10000000000)) 119400905721/10000000000)) 607771387771/1000000000000)) x): 0 points increase in error, 0 points decrease in error
      (fma.f64 y (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z 313060547623/100000000000) 55833770631/5000000000) z) t) z) a) z) b) (fma.f64 z (+.f64 (Rewrite<= *-commutative_binary64 (*.f64 (+.f64 (*.f64 (+.f64 z 15234687407/1000000000) z) 314690115749/10000000000) z)) 119400905721/10000000000) 607771387771/1000000000000)) x): 0 points increase in error, 0 points decrease in error
      (fma.f64 y (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z 313060547623/100000000000) 55833770631/5000000000) z) t) z) a) z) b) (Rewrite<= fma-def_binary64 (+.f64 (*.f64 z (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z 15234687407/1000000000) z) 314690115749/10000000000) z) 119400905721/10000000000)) 607771387771/1000000000000))) x): 0 points increase in error, 0 points decrease in error
      (fma.f64 y (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z 313060547623/100000000000) 55833770631/5000000000) z) t) z) a) z) b) (+.f64 (Rewrite<= *-commutative_binary64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z 15234687407/1000000000) z) 314690115749/10000000000) z) 119400905721/10000000000) z)) 607771387771/1000000000000)) x): 0 points increase in error, 0 points decrease in error
      (Rewrite<= fma-def_binary64 (+.f64 (*.f64 y (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z 313060547623/100000000000) 55833770631/5000000000) z) t) z) a) z) b) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z 15234687407/1000000000) z) 314690115749/10000000000) z) 119400905721/10000000000) z) 607771387771/1000000000000))) x)): 1 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite=> associate-*r/_binary64 (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z 313060547623/100000000000) 55833770631/5000000000) z) t) z) a) z) b)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z 15234687407/1000000000) z) 314690115749/10000000000) z) 119400905721/10000000000) z) 607771387771/1000000000000))) x): 18 points increase in error, 12 points decrease in error
      (Rewrite<= +-commutative_binary64 (+.f64 x (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z 313060547623/100000000000) 55833770631/5000000000) z) t) z) a) z) b)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z 15234687407/1000000000) z) 314690115749/10000000000) z) 119400905721/10000000000) z) 607771387771/1000000000000)))): 0 points increase in error, 0 points decrease in error

    if 5.8e17 < z

    1. Initial program 57.7

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

    2. Simplified54.9

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right)}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}, x\right)} \]
      Proof
      (fma.f64 y (/.f64 (fma.f64 z (fma.f64 z (fma.f64 z (fma.f64 z 313060547623/100000000000 55833770631/5000000000) t) a) b) (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000)) x): 0 points increase in error, 0 points decrease in error
      (fma.f64 y (/.f64 (fma.f64 z (fma.f64 z (fma.f64 z (Rewrite<= fma-def_binary64 (+.f64 (*.f64 z 313060547623/100000000000) 55833770631/5000000000)) t) a) b) (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000)) x): 0 points increase in error, 0 points decrease in error
      (fma.f64 y (/.f64 (fma.f64 z (fma.f64 z (Rewrite<= fma-def_binary64 (+.f64 (*.f64 z (+.f64 (*.f64 z 313060547623/100000000000) 55833770631/5000000000)) t)) a) b) (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000)) x): 0 points increase in error, 0 points decrease in error
      (fma.f64 y (/.f64 (fma.f64 z (fma.f64 z (+.f64 (Rewrite<= *-commutative_binary64 (*.f64 (+.f64 (*.f64 z 313060547623/100000000000) 55833770631/5000000000) z)) t) a) b) (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000)) x): 0 points increase in error, 0 points decrease in error
      (fma.f64 y (/.f64 (fma.f64 z (Rewrite<= fma-def_binary64 (+.f64 (*.f64 z (+.f64 (*.f64 (+.f64 (*.f64 z 313060547623/100000000000) 55833770631/5000000000) z) t)) a)) b) (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000)) x): 0 points increase in error, 0 points decrease in error
      (fma.f64 y (/.f64 (fma.f64 z (+.f64 (Rewrite<= *-commutative_binary64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z 313060547623/100000000000) 55833770631/5000000000) z) t) z)) a) b) (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000)) x): 0 points increase in error, 0 points decrease in error
      (fma.f64 y (/.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 z (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z 313060547623/100000000000) 55833770631/5000000000) z) t) z) a)) b)) (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000)) x): 1 points increase in error, 0 points decrease in error
      (fma.f64 y (/.f64 (+.f64 (Rewrite<= *-commutative_binary64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z 313060547623/100000000000) 55833770631/5000000000) z) t) z) a) z)) b) (fma.f64 z (fma.f64 z (fma.f64 z (+.f64 z 15234687407/1000000000) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000)) x): 0 points increase in error, 0 points decrease in error
      (fma.f64 y (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z 313060547623/100000000000) 55833770631/5000000000) z) t) z) a) z) b) (fma.f64 z (fma.f64 z (Rewrite<= fma-def_binary64 (+.f64 (*.f64 z (+.f64 z 15234687407/1000000000)) 314690115749/10000000000)) 119400905721/10000000000) 607771387771/1000000000000)) x): 0 points increase in error, 1 points decrease in error
      (fma.f64 y (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z 313060547623/100000000000) 55833770631/5000000000) z) t) z) a) z) b) (fma.f64 z (fma.f64 z (+.f64 (Rewrite<= *-commutative_binary64 (*.f64 (+.f64 z 15234687407/1000000000) z)) 314690115749/10000000000) 119400905721/10000000000) 607771387771/1000000000000)) x): 0 points increase in error, 0 points decrease in error
      (fma.f64 y (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z 313060547623/100000000000) 55833770631/5000000000) z) t) z) a) z) b) (fma.f64 z (Rewrite<= fma-def_binary64 (+.f64 (*.f64 z (+.f64 (*.f64 (+.f64 z 15234687407/1000000000) z) 314690115749/10000000000)) 119400905721/10000000000)) 607771387771/1000000000000)) x): 0 points increase in error, 0 points decrease in error
      (fma.f64 y (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z 313060547623/100000000000) 55833770631/5000000000) z) t) z) a) z) b) (fma.f64 z (+.f64 (Rewrite<= *-commutative_binary64 (*.f64 (+.f64 (*.f64 (+.f64 z 15234687407/1000000000) z) 314690115749/10000000000) z)) 119400905721/10000000000) 607771387771/1000000000000)) x): 0 points increase in error, 0 points decrease in error
      (fma.f64 y (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z 313060547623/100000000000) 55833770631/5000000000) z) t) z) a) z) b) (Rewrite<= fma-def_binary64 (+.f64 (*.f64 z (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z 15234687407/1000000000) z) 314690115749/10000000000) z) 119400905721/10000000000)) 607771387771/1000000000000))) x): 0 points increase in error, 0 points decrease in error
      (fma.f64 y (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z 313060547623/100000000000) 55833770631/5000000000) z) t) z) a) z) b) (+.f64 (Rewrite<= *-commutative_binary64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z 15234687407/1000000000) z) 314690115749/10000000000) z) 119400905721/10000000000) z)) 607771387771/1000000000000)) x): 0 points increase in error, 0 points decrease in error
      (Rewrite<= fma-def_binary64 (+.f64 (*.f64 y (/.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z 313060547623/100000000000) 55833770631/5000000000) z) t) z) a) z) b) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z 15234687407/1000000000) z) 314690115749/10000000000) z) 119400905721/10000000000) z) 607771387771/1000000000000))) x)): 1 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite=> associate-*r/_binary64 (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z 313060547623/100000000000) 55833770631/5000000000) z) t) z) a) z) b)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z 15234687407/1000000000) z) 314690115749/10000000000) z) 119400905721/10000000000) z) 607771387771/1000000000000))) x): 18 points increase in error, 12 points decrease in error
      (Rewrite<= +-commutative_binary64 (+.f64 x (/.f64 (*.f64 y (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 z 313060547623/100000000000) 55833770631/5000000000) z) t) z) a) z) b)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 z 15234687407/1000000000) z) 314690115749/10000000000) z) 119400905721/10000000000) z) 607771387771/1000000000000)))): 0 points increase in error, 0 points decrease in error

    3. Taylor expanded in z around -inf 1.0

      \[\leadsto \mathsf{fma}\left(y, \color{blue}{\left(3.13060547623 + \left(457.9610022158428 \cdot \frac{1}{{z}^{2}} + \left(\frac{t}{{z}^{2}} + -1 \cdot \frac{-1 \cdot a - \left(1112.0901850848957 + -15.234687407 \cdot \left(457.9610022158428 + t\right)\right)}{{z}^{3}}\right)\right)\right) - 36.52704169880642 \cdot \frac{1}{z}}, x\right) \]

    4. Simplified1.0

      \[\leadsto \mathsf{fma}\left(y, \color{blue}{\left(3.13060547623 + \frac{-36.52704169880642}{z}\right) + \left(\left(\frac{457.9610022158428}{z \cdot z} + \frac{t}{z \cdot z}\right) + \frac{a + \left(t \cdot -15.234687407 + -5864.8025282699045\right)}{{z}^{3}}\right)}, x\right) \]
      Proof
      (+.f64 (+.f64 313060547623/100000000000 (/.f64 -3652704169880641883561/100000000000000000000 z)) (+.f64 (+.f64 (/.f64 45796100221584283915100827016327/100000000000000000000000000000 (*.f64 z z)) (/.f64 t (*.f64 z z))) (/.f64 (+.f64 a (+.f64 (*.f64 t -15234687407/1000000000) -586480252826990429730394679450703430294089/100000000000000000000000000000000000000)) (pow.f64 z 3)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 313060547623/100000000000 (/.f64 (Rewrite<= metadata-eval (neg.f64 3652704169880641883561/100000000000000000000)) z)) (+.f64 (+.f64 (/.f64 45796100221584283915100827016327/100000000000000000000000000000 (*.f64 z z)) (/.f64 t (*.f64 z z))) (/.f64 (+.f64 a (+.f64 (*.f64 t -15234687407/1000000000) -586480252826990429730394679450703430294089/100000000000000000000000000000000000000)) (pow.f64 z 3)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 313060547623/100000000000 (Rewrite<= distribute-neg-frac_binary64 (neg.f64 (/.f64 3652704169880641883561/100000000000000000000 z)))) (+.f64 (+.f64 (/.f64 45796100221584283915100827016327/100000000000000000000000000000 (*.f64 z z)) (/.f64 t (*.f64 z z))) (/.f64 (+.f64 a (+.f64 (*.f64 t -15234687407/1000000000) -586480252826990429730394679450703430294089/100000000000000000000000000000000000000)) (pow.f64 z 3)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 313060547623/100000000000 (neg.f64 (/.f64 (Rewrite<= metadata-eval (*.f64 3652704169880641883561/100000000000000000000 1)) z))) (+.f64 (+.f64 (/.f64 45796100221584283915100827016327/100000000000000000000000000000 (*.f64 z z)) (/.f64 t (*.f64 z z))) (/.f64 (+.f64 a (+.f64 (*.f64 t -15234687407/1000000000) -586480252826990429730394679450703430294089/100000000000000000000000000000000000000)) (pow.f64 z 3)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 313060547623/100000000000 (neg.f64 (Rewrite<= associate-*r/_binary64 (*.f64 3652704169880641883561/100000000000000000000 (/.f64 1 z))))) (+.f64 (+.f64 (/.f64 45796100221584283915100827016327/100000000000000000000000000000 (*.f64 z z)) (/.f64 t (*.f64 z z))) (/.f64 (+.f64 a (+.f64 (*.f64 t -15234687407/1000000000) -586480252826990429730394679450703430294089/100000000000000000000000000000000000000)) (pow.f64 z 3)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite<= sub-neg_binary64 (-.f64 313060547623/100000000000 (*.f64 3652704169880641883561/100000000000000000000 (/.f64 1 z)))) (+.f64 (+.f64 (/.f64 45796100221584283915100827016327/100000000000000000000000000000 (*.f64 z z)) (/.f64 t (*.f64 z z))) (/.f64 (+.f64 a (+.f64 (*.f64 t -15234687407/1000000000) -586480252826990429730394679450703430294089/100000000000000000000000000000000000000)) (pow.f64 z 3)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (-.f64 313060547623/100000000000 (*.f64 3652704169880641883561/100000000000000000000 (/.f64 1 z))) (+.f64 (+.f64 (/.f64 (Rewrite<= metadata-eval (*.f64 45796100221584283915100827016327/100000000000000000000000000000 1)) (*.f64 z z)) (/.f64 t (*.f64 z z))) (/.f64 (+.f64 a (+.f64 (*.f64 t -15234687407/1000000000) -586480252826990429730394679450703430294089/100000000000000000000000000000000000000)) (pow.f64 z 3)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (-.f64 313060547623/100000000000 (*.f64 3652704169880641883561/100000000000000000000 (/.f64 1 z))) (+.f64 (+.f64 (/.f64 (*.f64 45796100221584283915100827016327/100000000000000000000000000000 1) (Rewrite<= unpow2_binary64 (pow.f64 z 2))) (/.f64 t (*.f64 z z))) (/.f64 (+.f64 a (+.f64 (*.f64 t -15234687407/1000000000) -586480252826990429730394679450703430294089/100000000000000000000000000000000000000)) (pow.f64 z 3)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (-.f64 313060547623/100000000000 (*.f64 3652704169880641883561/100000000000000000000 (/.f64 1 z))) (+.f64 (+.f64 (Rewrite<= associate-*r/_binary64 (*.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 1 (pow.f64 z 2)))) (/.f64 t (*.f64 z z))) (/.f64 (+.f64 a (+.f64 (*.f64 t -15234687407/1000000000) -586480252826990429730394679450703430294089/100000000000000000000000000000000000000)) (pow.f64 z 3)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (-.f64 313060547623/100000000000 (*.f64 3652704169880641883561/100000000000000000000 (/.f64 1 z))) (+.f64 (+.f64 (*.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 1 (pow.f64 z 2))) (/.f64 t (Rewrite<= unpow2_binary64 (pow.f64 z 2)))) (/.f64 (+.f64 a (+.f64 (*.f64 t -15234687407/1000000000) -586480252826990429730394679450703430294089/100000000000000000000000000000000000000)) (pow.f64 z 3)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (-.f64 313060547623/100000000000 (*.f64 3652704169880641883561/100000000000000000000 (/.f64 1 z))) (+.f64 (+.f64 (*.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 1 (pow.f64 z 2))) (/.f64 t (pow.f64 z 2))) (/.f64 (+.f64 a (+.f64 (*.f64 t -15234687407/1000000000) (Rewrite<= metadata-eval (+.f64 -697689271335479999750499226480922330294089/100000000000000000000000000000000000000 1112090185084895700201045470302189/1000000000000000000000000000000)))) (pow.f64 z 3)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (-.f64 313060547623/100000000000 (*.f64 3652704169880641883561/100000000000000000000 (/.f64 1 z))) (+.f64 (+.f64 (*.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 1 (pow.f64 z 2))) (/.f64 t (pow.f64 z 2))) (/.f64 (+.f64 a (+.f64 (*.f64 t -15234687407/1000000000) (+.f64 (Rewrite<= metadata-eval (*.f64 45796100221584283915100827016327/100000000000000000000000000000 -15234687407/1000000000)) 1112090185084895700201045470302189/1000000000000000000000000000000))) (pow.f64 z 3)))): 1 points increase in error, 9 points decrease in error
      (+.f64 (-.f64 313060547623/100000000000 (*.f64 3652704169880641883561/100000000000000000000 (/.f64 1 z))) (+.f64 (+.f64 (*.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 1 (pow.f64 z 2))) (/.f64 t (pow.f64 z 2))) (/.f64 (+.f64 a (Rewrite<= associate-+l+_binary64 (+.f64 (+.f64 (*.f64 t -15234687407/1000000000) (*.f64 45796100221584283915100827016327/100000000000000000000000000000 -15234687407/1000000000)) 1112090185084895700201045470302189/1000000000000000000000000000000))) (pow.f64 z 3)))): 1 points increase in error, 0 points decrease in error
      (+.f64 (-.f64 313060547623/100000000000 (*.f64 3652704169880641883561/100000000000000000000 (/.f64 1 z))) (+.f64 (+.f64 (*.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 1 (pow.f64 z 2))) (/.f64 t (pow.f64 z 2))) (/.f64 (+.f64 a (+.f64 (Rewrite<= distribute-rgt-in_binary64 (*.f64 -15234687407/1000000000 (+.f64 t 45796100221584283915100827016327/100000000000000000000000000000))) 1112090185084895700201045470302189/1000000000000000000000000000000)) (pow.f64 z 3)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (-.f64 313060547623/100000000000 (*.f64 3652704169880641883561/100000000000000000000 (/.f64 1 z))) (+.f64 (+.f64 (*.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 1 (pow.f64 z 2))) (/.f64 t (pow.f64 z 2))) (/.f64 (+.f64 a (+.f64 (*.f64 -15234687407/1000000000 (Rewrite<= +-commutative_binary64 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t))) 1112090185084895700201045470302189/1000000000000000000000000000000)) (pow.f64 z 3)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (-.f64 313060547623/100000000000 (*.f64 3652704169880641883561/100000000000000000000 (/.f64 1 z))) (+.f64 (+.f64 (*.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 1 (pow.f64 z 2))) (/.f64 t (pow.f64 z 2))) (/.f64 (Rewrite<= associate-+l+_binary64 (+.f64 (+.f64 a (*.f64 -15234687407/1000000000 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t))) 1112090185084895700201045470302189/1000000000000000000000000000000)) (pow.f64 z 3)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (-.f64 313060547623/100000000000 (*.f64 3652704169880641883561/100000000000000000000 (/.f64 1 z))) (+.f64 (+.f64 (*.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 1 (pow.f64 z 2))) (/.f64 t (pow.f64 z 2))) (/.f64 (+.f64 (+.f64 a (*.f64 (Rewrite<= metadata-eval (neg.f64 15234687407/1000000000)) (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t))) 1112090185084895700201045470302189/1000000000000000000000000000000) (pow.f64 z 3)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (-.f64 313060547623/100000000000 (*.f64 3652704169880641883561/100000000000000000000 (/.f64 1 z))) (+.f64 (+.f64 (*.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 1 (pow.f64 z 2))) (/.f64 t (pow.f64 z 2))) (/.f64 (+.f64 (Rewrite<= cancel-sign-sub-inv_binary64 (-.f64 a (*.f64 15234687407/1000000000 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t)))) 1112090185084895700201045470302189/1000000000000000000000000000000) (pow.f64 z 3)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (-.f64 313060547623/100000000000 (*.f64 3652704169880641883561/100000000000000000000 (/.f64 1 z))) (+.f64 (+.f64 (*.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 1 (pow.f64 z 2))) (/.f64 t (pow.f64 z 2))) (/.f64 (Rewrite<= +-commutative_binary64 (+.f64 1112090185084895700201045470302189/1000000000000000000000000000000 (-.f64 a (*.f64 15234687407/1000000000 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t))))) (pow.f64 z 3)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (-.f64 313060547623/100000000000 (*.f64 3652704169880641883561/100000000000000000000 (/.f64 1 z))) (+.f64 (+.f64 (*.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 1 (pow.f64 z 2))) (/.f64 t (pow.f64 z 2))) (/.f64 (Rewrite<= associate--l+_binary64 (-.f64 (+.f64 1112090185084895700201045470302189/1000000000000000000000000000000 a) (*.f64 15234687407/1000000000 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t)))) (pow.f64 z 3)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (-.f64 313060547623/100000000000 (*.f64 3652704169880641883561/100000000000000000000 (/.f64 1 z))) (+.f64 (+.f64 (*.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 1 (pow.f64 z 2))) (/.f64 t (pow.f64 z 2))) (/.f64 (Rewrite<= remove-double-neg_binary64 (neg.f64 (neg.f64 (-.f64 (+.f64 1112090185084895700201045470302189/1000000000000000000000000000000 a) (*.f64 15234687407/1000000000 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t)))))) (pow.f64 z 3)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (-.f64 313060547623/100000000000 (*.f64 3652704169880641883561/100000000000000000000 (/.f64 1 z))) (+.f64 (+.f64 (*.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 1 (pow.f64 z 2))) (/.f64 t (pow.f64 z 2))) (/.f64 (neg.f64 (neg.f64 (Rewrite=> cancel-sign-sub-inv_binary64 (+.f64 (+.f64 1112090185084895700201045470302189/1000000000000000000000000000000 a) (*.f64 (neg.f64 15234687407/1000000000) (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t)))))) (pow.f64 z 3)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (-.f64 313060547623/100000000000 (*.f64 3652704169880641883561/100000000000000000000 (/.f64 1 z))) (+.f64 (+.f64 (*.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 1 (pow.f64 z 2))) (/.f64 t (pow.f64 z 2))) (/.f64 (neg.f64 (neg.f64 (+.f64 (Rewrite=> +-commutative_binary64 (+.f64 a 1112090185084895700201045470302189/1000000000000000000000000000000)) (*.f64 (neg.f64 15234687407/1000000000) (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t))))) (pow.f64 z 3)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (-.f64 313060547623/100000000000 (*.f64 3652704169880641883561/100000000000000000000 (/.f64 1 z))) (+.f64 (+.f64 (*.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 1 (pow.f64 z 2))) (/.f64 t (pow.f64 z 2))) (/.f64 (neg.f64 (neg.f64 (+.f64 (+.f64 a 1112090185084895700201045470302189/1000000000000000000000000000000) (*.f64 (Rewrite=> metadata-eval -15234687407/1000000000) (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t))))) (pow.f64 z 3)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (-.f64 313060547623/100000000000 (*.f64 3652704169880641883561/100000000000000000000 (/.f64 1 z))) (+.f64 (+.f64 (*.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 1 (pow.f64 z 2))) (/.f64 t (pow.f64 z 2))) (/.f64 (neg.f64 (neg.f64 (Rewrite=> associate-+l+_binary64 (+.f64 a (+.f64 1112090185084895700201045470302189/1000000000000000000000000000000 (*.f64 -15234687407/1000000000 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t))))))) (pow.f64 z 3)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (-.f64 313060547623/100000000000 (*.f64 3652704169880641883561/100000000000000000000 (/.f64 1 z))) (+.f64 (+.f64 (*.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 1 (pow.f64 z 2))) (/.f64 t (pow.f64 z 2))) (/.f64 (neg.f64 (Rewrite<= distribute-neg-out_binary64 (+.f64 (neg.f64 a) (neg.f64 (+.f64 1112090185084895700201045470302189/1000000000000000000000000000000 (*.f64 -15234687407/1000000000 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t))))))) (pow.f64 z 3)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (-.f64 313060547623/100000000000 (*.f64 3652704169880641883561/100000000000000000000 (/.f64 1 z))) (+.f64 (+.f64 (*.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 1 (pow.f64 z 2))) (/.f64 t (pow.f64 z 2))) (/.f64 (neg.f64 (+.f64 (Rewrite<= mul-1-neg_binary64 (*.f64 -1 a)) (neg.f64 (+.f64 1112090185084895700201045470302189/1000000000000000000000000000000 (*.f64 -15234687407/1000000000 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t)))))) (pow.f64 z 3)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (-.f64 313060547623/100000000000 (*.f64 3652704169880641883561/100000000000000000000 (/.f64 1 z))) (+.f64 (+.f64 (*.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 1 (pow.f64 z 2))) (/.f64 t (pow.f64 z 2))) (/.f64 (neg.f64 (Rewrite<= sub-neg_binary64 (-.f64 (*.f64 -1 a) (+.f64 1112090185084895700201045470302189/1000000000000000000000000000000 (*.f64 -15234687407/1000000000 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t)))))) (pow.f64 z 3)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (-.f64 313060547623/100000000000 (*.f64 3652704169880641883561/100000000000000000000 (/.f64 1 z))) (+.f64 (+.f64 (*.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 1 (pow.f64 z 2))) (/.f64 t (pow.f64 z 2))) (Rewrite<= distribute-neg-frac_binary64 (neg.f64 (/.f64 (-.f64 (*.f64 -1 a) (+.f64 1112090185084895700201045470302189/1000000000000000000000000000000 (*.f64 -15234687407/1000000000 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t)))) (pow.f64 z 3)))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (-.f64 313060547623/100000000000 (*.f64 3652704169880641883561/100000000000000000000 (/.f64 1 z))) (+.f64 (+.f64 (*.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 1 (pow.f64 z 2))) (/.f64 t (pow.f64 z 2))) (Rewrite<= mul-1-neg_binary64 (*.f64 -1 (/.f64 (-.f64 (*.f64 -1 a) (+.f64 1112090185084895700201045470302189/1000000000000000000000000000000 (*.f64 -15234687407/1000000000 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t)))) (pow.f64 z 3)))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (-.f64 313060547623/100000000000 (*.f64 3652704169880641883561/100000000000000000000 (/.f64 1 z))) (Rewrite<= associate-+r+_binary64 (+.f64 (*.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 1 (pow.f64 z 2))) (+.f64 (/.f64 t (pow.f64 z 2)) (*.f64 -1 (/.f64 (-.f64 (*.f64 -1 a) (+.f64 1112090185084895700201045470302189/1000000000000000000000000000000 (*.f64 -15234687407/1000000000 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t)))) (pow.f64 z 3))))))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= +-commutative_binary64 (+.f64 (+.f64 (*.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 1 (pow.f64 z 2))) (+.f64 (/.f64 t (pow.f64 z 2)) (*.f64 -1 (/.f64 (-.f64 (*.f64 -1 a) (+.f64 1112090185084895700201045470302189/1000000000000000000000000000000 (*.f64 -15234687407/1000000000 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t)))) (pow.f64 z 3))))) (-.f64 313060547623/100000000000 (*.f64 3652704169880641883561/100000000000000000000 (/.f64 1 z))))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate--l+_binary64 (-.f64 (+.f64 (+.f64 (*.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 1 (pow.f64 z 2))) (+.f64 (/.f64 t (pow.f64 z 2)) (*.f64 -1 (/.f64 (-.f64 (*.f64 -1 a) (+.f64 1112090185084895700201045470302189/1000000000000000000000000000000 (*.f64 -15234687407/1000000000 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t)))) (pow.f64 z 3))))) 313060547623/100000000000) (*.f64 3652704169880641883561/100000000000000000000 (/.f64 1 z)))): 0 points increase in error, 0 points decrease in error
      (-.f64 (Rewrite<= +-commutative_binary64 (+.f64 313060547623/100000000000 (+.f64 (*.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 1 (pow.f64 z 2))) (+.f64 (/.f64 t (pow.f64 z 2)) (*.f64 -1 (/.f64 (-.f64 (*.f64 -1 a) (+.f64 1112090185084895700201045470302189/1000000000000000000000000000000 (*.f64 -15234687407/1000000000 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t)))) (pow.f64 z 3))))))) (*.f64 3652704169880641883561/100000000000000000000 (/.f64 1 z))): 0 points increase in error, 0 points decrease in error
  3. Recombined 3 regimes into one program.

  4. Final simplification0.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+47}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, \mathsf{fma}\left(-36.52704169880642, \frac{y}{z}, x\right)\right) + \frac{\frac{y}{z}}{z} \cdot \left(\left(t + 457.9610022158428\right) + \frac{a + \left(t \cdot -15.234687407 + -5864.8025282699045\right)}{z}\right)\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+17}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right)}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \left(3.13060547623 + \frac{-36.52704169880642}{z}\right) + \left(\left(\frac{457.9610022158428}{z \cdot z} + \frac{t}{z \cdot z}\right) + \frac{a + \left(t \cdot -15.234687407 + -5864.8025282699045\right)}{{z}^{3}}\right), x\right)\\ \end{array} \]

Alternatives

Alternative 1
Error1.2
Cost19336
\[\begin{array}{l} t_1 := a + \left(t \cdot -15.234687407 + -5864.8025282699045\right)\\ t_2 := \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, \mathsf{fma}\left(-36.52704169880642, \frac{y}{z}, x\right)\right) + \frac{\frac{y}{z}}{z} \cdot \left(\left(t + 457.9610022158428\right) + \frac{t_1}{z}\right)\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+274}:\\ \;\;\;\;x + t_2\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \left(3.13060547623 + \frac{-36.52704169880642}{z}\right) + \left(\left(\frac{457.9610022158428}{z \cdot z} + \frac{t}{z \cdot z}\right) + \frac{t_1}{{z}^{3}}\right), x\right)\\ \end{array} \]
Alternative 2
Error1.2
Cost19144
\[\begin{array}{l} t_1 := \mathsf{fma}\left(3.13060547623, y, \mathsf{fma}\left(-36.52704169880642, \frac{y}{z}, x\right)\right) + \frac{\frac{y}{z}}{z} \cdot \left(\left(t + 457.9610022158428\right) + \frac{a + \left(t \cdot -15.234687407 + -5864.8025282699045\right)}{z}\right)\\ t_2 := \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+274}:\\ \;\;\;\;x + t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 3
Error1.6
Cost15876
\[\begin{array}{l} t_1 := \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)}\\ t_2 := 3.13060547623 + \frac{-36.52704169880642}{z}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\mathsf{fma}\left(y, t_2 + \frac{a}{{z}^{3}}, x\right)\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+274}:\\ \;\;\;\;x + t_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, t_2 - \frac{t \cdot \left(-1 + \frac{15.234687407}{z}\right)}{z \cdot z}, x\right)\\ \end{array} \]
Alternative 4
Error1.9
Cost12232
\[\begin{array}{l} t_1 := 0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)\\ t_2 := z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\right)\right)\\ t_3 := \frac{y \cdot \left(b + t_2\right)}{t_1}\\ \mathbf{if}\;t_3 \leq -\infty:\\ \;\;\;\;y \cdot \left(\frac{b}{t_1} + \frac{t_2}{t_1}\right)\\ \mathbf{elif}\;t_3 \leq 5 \cdot 10^{+274}:\\ \;\;\;\;x + t_3\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \left(3.13060547623 + \frac{-36.52704169880642}{z}\right) - \frac{t \cdot \left(-1 + \frac{15.234687407}{z}\right)}{z \cdot z}, x\right)\\ \end{array} \]
Alternative 5
Error2.8
Cost11208
\[\begin{array}{l} t_1 := 0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)\\ t_2 := z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\right)\right)\\ t_3 := \frac{y \cdot \left(b + t_2\right)}{t_1}\\ \mathbf{if}\;t_3 \leq -\infty:\\ \;\;\;\;y \cdot \left(\frac{b}{t_1} + \frac{t_2}{t_1}\right)\\ \mathbf{elif}\;t_3 \leq 5 \cdot 10^{+274}:\\ \;\;\;\;x + t_3\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623, x\right)\\ \end{array} \]
Alternative 6
Error2.7
Cost6984
\[\begin{array}{l} t_1 := 0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)\\ t_2 := \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\right)\right)\right)}{t_1}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;y \cdot \left(\frac{b}{t_1} + \left(3.13060547623 + \left(\frac{-36.52704169880642}{z} + \frac{t + 457.9610022158428}{z \cdot z}\right)\right)\right)\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+274}:\\ \;\;\;\;x + t_2\\ \mathbf{else}:\\ \;\;\;\;x + 3.13060547623 \cdot y\\ \end{array} \]
Alternative 7
Error2.8
Cost6984
\[\begin{array}{l} t_1 := 0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)\\ t_2 := z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\right)\right)\\ t_3 := \frac{y \cdot \left(b + t_2\right)}{t_1}\\ \mathbf{if}\;t_3 \leq -\infty:\\ \;\;\;\;y \cdot \left(\frac{b}{t_1} + \frac{t_2}{t_1}\right)\\ \mathbf{elif}\;t_3 \leq 5 \cdot 10^{+274}:\\ \;\;\;\;x + t_3\\ \mathbf{else}:\\ \;\;\;\;x + 3.13060547623 \cdot y\\ \end{array} \]
Alternative 8
Error5.2
Cost1992
\[\begin{array}{l} t_1 := x + 3.13060547623 \cdot y\\ \mathbf{if}\;z \leq -4500000:\\ \;\;\;\;t_1 + -36.52704169880642 \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+18}:\\ \;\;\;\;x + \frac{y \cdot b + a \cdot \left(z \cdot y\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 9
Error3.5
Cost1992
\[\begin{array}{l} t_1 := x + 3.13060547623 \cdot y\\ \mathbf{if}\;z \leq -5.2 \cdot 10^{-5}:\\ \;\;\;\;t_1 + -36.52704169880642 \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+18}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot \left(11.1667541262 + z \cdot 3.13060547623\right)\right)\right)\right)}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 10
Error5.6
Cost1480
\[\begin{array}{l} t_1 := \left(x + 3.13060547623 \cdot y\right) + -36.52704169880642 \cdot \frac{y}{z}\\ \mathbf{if}\;z \leq -4500000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-23}:\\ \;\;\;\;y \cdot \left(z \cdot \left(a \cdot 1.6453555072203998 - b \cdot 32.324150453290734\right)\right) + \left(x + \left(y \cdot b\right) \cdot 1.6453555072203998\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 11
Error18.8
Cost980
\[\begin{array}{l} t_1 := y \cdot \left(b \cdot 1.6453555072203998\right)\\ t_2 := x + 3.13060547623 \cdot y\\ \mathbf{if}\;z \leq -7.6 \cdot 10^{-114}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-236}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-215}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 9.7 \cdot 10^{-169}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-146}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]
Alternative 12
Error9.0
Cost836
\[\begin{array}{l} t_1 := x + 3.13060547623 \cdot y\\ \mathbf{if}\;z \leq -4500000:\\ \;\;\;\;t_1 + -36.52704169880642 \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+18}:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 13
Error28.5
Cost720
\[\begin{array}{l} \mathbf{if}\;x \leq -1.466024218386889 \cdot 10^{-63}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.6725719797941166 \cdot 10^{-237}:\\ \;\;\;\;3.13060547623 \cdot y\\ \mathbf{elif}\;x \leq 2.8138539659425858 \cdot 10^{-111}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.9328372914618022 \cdot 10^{-77}:\\ \;\;\;\;3.13060547623 \cdot y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
Alternative 14
Error9.0
Cost712
\[\begin{array}{l} t_1 := x + 3.13060547623 \cdot y\\ \mathbf{if}\;z \leq -4500000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+18}:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 15
Error32.0
Cost64
\[x \]

Error

Reproduce

herbie shell --seed 2022311 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, D"
  :precision binary64

  :herbie-target
  (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))))