Average Error: 29.4 → 0.8
Time: 48.0s
Precision: binary64
Cost: 21064
\[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771} \]
↓
\[\begin{array}{l} t_1 := 0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)\\ \mathbf{if}\;z \leq -2.1006979537140594 \cdot 10^{+42}:\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623 + \left(\frac{457.9610022158428}{z \cdot z} + \left(\frac{t}{z \cdot z} + \left(\frac{a - \left(5864.8025282699045 - t \cdot -15.234687407\right)}{{z}^{3}} + \frac{-36.52704169880642}{z}\right)\right)\right), x\right)\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+18}:\\ \;\;\;\;x + y \cdot \left(\frac{b}{t_1} + \frac{z \cdot \left(a - z \cdot \left(z \cdot \left(z \cdot -3.13060547623 + -11.1667541262\right) - t\right)\right)}{t_1}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, \mathsf{fma}\left(-36.52704169880642, \frac{y}{z}, x\right)\right) + \frac{\left(457.9610022158428 + t\right) + \frac{-5864.8025282699045 + \mathsf{fma}\left(t, -15.234687407, a\right)}{z}}{\frac{z}{\frac{y}{z}}}\\ \end{array} \]
(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
         (+
          0.607771387771
          (*
           z
           (+
            11.9400905721
            (* z (+ 31.4690115749 (* z (+ z 15.234687407)))))))))
   (if (<= z -2.1006979537140594e+42)
     (fma
      y
      (+
       3.13060547623
       (+
        (/ 457.9610022158428 (* z z))
        (+
         (/ t (* z z))
         (+
          (/ (- a (- 5864.8025282699045 (* t -15.234687407))) (pow z 3.0))
          (/ -36.52704169880642 z)))))
      x)
     (if (<= z 4e+18)
       (+
        x
        (*
         y
         (+
          (/ b t_1)
          (/
           (*
            z
            (- a (* z (- (* z (+ (* z -3.13060547623) -11.1667541262)) t))))
           t_1))))
       (+
        (fma 3.13060547623 y (fma -36.52704169880642 (/ y z) x))
        (/
         (+
          (+ 457.9610022158428 t)
          (/ (+ -5864.8025282699045 (fma t -15.234687407 a)) z))
         (/ z (/ y z))))))))
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 = 0.607771387771 + (z * (11.9400905721 + (z * (31.4690115749 + (z * (z + 15.234687407))))));
	double tmp;
	if (z <= -2.1006979537140594e+42) {
		tmp = fma(y, (3.13060547623 + ((457.9610022158428 / (z * z)) + ((t / (z * z)) + (((a - (5864.8025282699045 - (t * -15.234687407))) / pow(z, 3.0)) + (-36.52704169880642 / z))))), x);
	} else if (z <= 4e+18) {
		tmp = x + (y * ((b / t_1) + ((z * (a - (z * ((z * ((z * -3.13060547623) + -11.1667541262)) - t)))) / t_1)));
	} else {
		tmp = fma(3.13060547623, y, fma(-36.52704169880642, (y / z), x)) + (((457.9610022158428 + t) + ((-5864.8025282699045 + fma(t, -15.234687407, a)) / z)) / (z / (y / z)));
	}
	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(0.607771387771 + Float64(z * Float64(11.9400905721 + Float64(z * Float64(31.4690115749 + Float64(z * Float64(z + 15.234687407)))))))
	tmp = 0.0
	if (z <= -2.1006979537140594e+42)
		tmp = fma(y, Float64(3.13060547623 + Float64(Float64(457.9610022158428 / Float64(z * z)) + Float64(Float64(t / Float64(z * z)) + Float64(Float64(Float64(a - Float64(5864.8025282699045 - Float64(t * -15.234687407))) / (z ^ 3.0)) + Float64(-36.52704169880642 / z))))), x);
	elseif (z <= 4e+18)
		tmp = Float64(x + Float64(y * Float64(Float64(b / t_1) + Float64(Float64(z * Float64(a - Float64(z * Float64(Float64(z * Float64(Float64(z * -3.13060547623) + -11.1667541262)) - t)))) / t_1))));
	else
		tmp = Float64(fma(3.13060547623, y, fma(-36.52704169880642, Float64(y / z), x)) + Float64(Float64(Float64(457.9610022158428 + t) + Float64(Float64(-5864.8025282699045 + fma(t, -15.234687407, a)) / z)) / Float64(z / Float64(y / z))));
	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[(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]}, If[LessEqual[z, -2.1006979537140594e+42], N[(y * N[(3.13060547623 + N[(N[(457.9610022158428 / N[(z * z), $MachinePrecision]), $MachinePrecision] + N[(N[(t / N[(z * z), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(a - N[(5864.8025282699045 - N[(t * -15.234687407), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[Power[z, 3.0], $MachinePrecision]), $MachinePrecision] + N[(-36.52704169880642 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[z, 4e+18], N[(x + N[(y * N[(N[(b / t$95$1), $MachinePrecision] + N[(N[(z * N[(a - N[(z * N[(N[(z * N[(N[(z * -3.13060547623), $MachinePrecision] + -11.1667541262), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(3.13060547623 * y + N[(-36.52704169880642 * N[(y / z), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(457.9610022158428 + t), $MachinePrecision] + N[(N[(-5864.8025282699045 + N[(t * -15.234687407 + a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / N[(z / N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $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 := 0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)\\
\mathbf{if}\;z \leq -2.1006979537140594 \cdot 10^{+42}:\\
\;\;\;\;\mathsf{fma}\left(y, 3.13060547623 + \left(\frac{457.9610022158428}{z \cdot z} + \left(\frac{t}{z \cdot z} + \left(\frac{a - \left(5864.8025282699045 - t \cdot -15.234687407\right)}{{z}^{3}} + \frac{-36.52704169880642}{z}\right)\right)\right), x\right)\\

\mathbf{elif}\;z \leq 4 \cdot 10^{+18}:\\
\;\;\;\;x + y \cdot \left(\frac{b}{t_1} + \frac{z \cdot \left(a - z \cdot \left(z \cdot \left(z \cdot -3.13060547623 + -11.1667541262\right) - t\right)\right)}{t_1}\right)\\

\mathbf{else}:\\
\;\;\;\;\mathsf{fma}\left(3.13060547623, y, \mathsf{fma}\left(-36.52704169880642, \frac{y}{z}, x\right)\right) + \frac{\left(457.9610022158428 + t\right) + \frac{-5864.8025282699045 + \mathsf{fma}\left(t, -15.234687407, a\right)}{z}}{\frac{z}{\frac{y}{z}}}\\


\end{array}

Error

Target

Original29.4
Target1.0
Herbie0.8
\[\begin{array}{l} \mathbf{if}\;z < -6.499344996252632 \cdot 10^{+53}:\\ \;\;\;\;x + \left(\left(3.13060547623 - \frac{36.527041698806414}{z}\right) + \frac{t}{z \cdot z}\right) \cdot \frac{y}{1}\\ \mathbf{elif}\;z < 7.066965436914287 \cdot 10^{+59}:\\ \;\;\;\;x + \frac{y}{\frac{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}{\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(3.13060547623 - \frac{36.527041698806414}{z}\right) + \frac{t}{z \cdot z}\right) \cdot \frac{y}{1}\\ \end{array} \]

Derivation

  1. Split input into 3 regimes

  2. if z < -2.10069795371405939e42

    1. Initial program 60.2

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

    2. Simplified58.2

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right)}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}, x\right)} \]
      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): 1 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): 0 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, 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 (+.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)): 0 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): 22 points increase in error, 7 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 0.5

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

    4. Simplified0.5

      \[\leadsto \mathsf{fma}\left(y, \color{blue}{3.13060547623 + \left(\frac{457.9610022158428}{z \cdot z} + \left(\frac{t}{z \cdot z} + \left(\frac{a + \left(t \cdot -15.234687407 + -5864.8025282699045\right)}{{z}^{3}} + \frac{-36.52704169880642}{z}\right)\right)\right)}, x\right) \]
      Proof
      (+.f64 313060547623/100000000000 (+.f64 (/.f64 45796100221584283915100827016327/100000000000000000000000000000 (*.f64 z z)) (+.f64 (/.f64 t (*.f64 z z)) (+.f64 (/.f64 (+.f64 a (+.f64 (*.f64 t -15234687407/1000000000) -586480252826990429730394679450703430294089/100000000000000000000000000000000000000)) (pow.f64 z 3)) (/.f64 -3652704169880641883561/100000000000000000000 z))))): 0 points increase in error, 0 points decrease in error
      (+.f64 313060547623/100000000000 (+.f64 (/.f64 (Rewrite<= metadata-eval (*.f64 45796100221584283915100827016327/100000000000000000000000000000 1)) (*.f64 z z)) (+.f64 (/.f64 t (*.f64 z z)) (+.f64 (/.f64 (+.f64 a (+.f64 (*.f64 t -15234687407/1000000000) -586480252826990429730394679450703430294089/100000000000000000000000000000000000000)) (pow.f64 z 3)) (/.f64 -3652704169880641883561/100000000000000000000 z))))): 0 points increase in error, 0 points decrease in error
      (+.f64 313060547623/100000000000 (+.f64 (/.f64 (*.f64 45796100221584283915100827016327/100000000000000000000000000000 1) (Rewrite<= unpow2_binary64 (pow.f64 z 2))) (+.f64 (/.f64 t (*.f64 z z)) (+.f64 (/.f64 (+.f64 a (+.f64 (*.f64 t -15234687407/1000000000) -586480252826990429730394679450703430294089/100000000000000000000000000000000000000)) (pow.f64 z 3)) (/.f64 -3652704169880641883561/100000000000000000000 z))))): 0 points increase in error, 0 points decrease in error
      (+.f64 313060547623/100000000000 (+.f64 (Rewrite<= associate-*r/_binary64 (*.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 1 (pow.f64 z 2)))) (+.f64 (/.f64 t (*.f64 z z)) (+.f64 (/.f64 (+.f64 a (+.f64 (*.f64 t -15234687407/1000000000) -586480252826990429730394679450703430294089/100000000000000000000000000000000000000)) (pow.f64 z 3)) (/.f64 -3652704169880641883561/100000000000000000000 z))))): 0 points increase in error, 0 points decrease in error
      (+.f64 313060547623/100000000000 (+.f64 (*.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 1 (pow.f64 z 2))) (+.f64 (/.f64 t (Rewrite<= unpow2_binary64 (pow.f64 z 2))) (+.f64 (/.f64 (+.f64 a (+.f64 (*.f64 t -15234687407/1000000000) -586480252826990429730394679450703430294089/100000000000000000000000000000000000000)) (pow.f64 z 3)) (/.f64 -3652704169880641883561/100000000000000000000 z))))): 0 points increase in error, 0 points decrease in error
      (+.f64 313060547623/100000000000 (+.f64 (*.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 1 (pow.f64 z 2))) (+.f64 (/.f64 t (pow.f64 z 2)) (+.f64 (/.f64 (+.f64 a (+.f64 (*.f64 t -15234687407/1000000000) (Rewrite<= metadata-eval (+.f64 1112090185084895700201045470302189/1000000000000000000000000000000 -697689271335479999750499226480922330294089/100000000000000000000000000000000000000)))) (pow.f64 z 3)) (/.f64 -3652704169880641883561/100000000000000000000 z))))): 0 points increase in error, 0 points decrease in error
      (+.f64 313060547623/100000000000 (+.f64 (*.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 1 (pow.f64 z 2))) (+.f64 (/.f64 t (pow.f64 z 2)) (+.f64 (/.f64 (+.f64 a (+.f64 (*.f64 t -15234687407/1000000000) (+.f64 1112090185084895700201045470302189/1000000000000000000000000000000 (Rewrite<= metadata-eval (*.f64 45796100221584283915100827016327/100000000000000000000000000000 -15234687407/1000000000))))) (pow.f64 z 3)) (/.f64 -3652704169880641883561/100000000000000000000 z))))): 2 points increase in error, 7 points decrease in error
      (+.f64 313060547623/100000000000 (+.f64 (*.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 1 (pow.f64 z 2))) (+.f64 (/.f64 t (pow.f64 z 2)) (+.f64 (/.f64 (+.f64 a (Rewrite<= +-commutative_binary64 (+.f64 (+.f64 1112090185084895700201045470302189/1000000000000000000000000000000 (*.f64 45796100221584283915100827016327/100000000000000000000000000000 -15234687407/1000000000)) (*.f64 t -15234687407/1000000000)))) (pow.f64 z 3)) (/.f64 -3652704169880641883561/100000000000000000000 z))))): 0 points increase in error, 0 points decrease in error
      (+.f64 313060547623/100000000000 (+.f64 (*.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 1 (pow.f64 z 2))) (+.f64 (/.f64 t (pow.f64 z 2)) (+.f64 (/.f64 (+.f64 a (Rewrite<= associate-+r+_binary64 (+.f64 1112090185084895700201045470302189/1000000000000000000000000000000 (+.f64 (*.f64 45796100221584283915100827016327/100000000000000000000000000000 -15234687407/1000000000) (*.f64 t -15234687407/1000000000))))) (pow.f64 z 3)) (/.f64 -3652704169880641883561/100000000000000000000 z))))): 0 points increase in error, 0 points decrease in error
      (+.f64 313060547623/100000000000 (+.f64 (*.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 1 (pow.f64 z 2))) (+.f64 (/.f64 t (pow.f64 z 2)) (+.f64 (/.f64 (+.f64 a (+.f64 1112090185084895700201045470302189/1000000000000000000000000000000 (Rewrite<= distribute-rgt-in_binary64 (*.f64 -15234687407/1000000000 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t))))) (pow.f64 z 3)) (/.f64 -3652704169880641883561/100000000000000000000 z))))): 0 points increase in error, 0 points decrease in error
      (+.f64 313060547623/100000000000 (+.f64 (*.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 1 (pow.f64 z 2))) (+.f64 (/.f64 t (pow.f64 z 2)) (+.f64 (/.f64 (Rewrite<= associate-+l+_binary64 (+.f64 (+.f64 a 1112090185084895700201045470302189/1000000000000000000000000000000) (*.f64 -15234687407/1000000000 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t)))) (pow.f64 z 3)) (/.f64 -3652704169880641883561/100000000000000000000 z))))): 0 points increase in error, 0 points decrease in error
      (+.f64 313060547623/100000000000 (+.f64 (*.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 1 (pow.f64 z 2))) (+.f64 (/.f64 t (pow.f64 z 2)) (+.f64 (/.f64 (+.f64 (Rewrite<= +-commutative_binary64 (+.f64 1112090185084895700201045470302189/1000000000000000000000000000000 a)) (*.f64 -15234687407/1000000000 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t))) (pow.f64 z 3)) (/.f64 -3652704169880641883561/100000000000000000000 z))))): 0 points increase in error, 0 points decrease in error
      (+.f64 313060547623/100000000000 (+.f64 (*.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 1 (pow.f64 z 2))) (+.f64 (/.f64 t (pow.f64 z 2)) (+.f64 (/.f64 (+.f64 (+.f64 1112090185084895700201045470302189/1000000000000000000000000000000 a) (*.f64 (Rewrite<= metadata-eval (neg.f64 15234687407/1000000000)) (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t))) (pow.f64 z 3)) (/.f64 -3652704169880641883561/100000000000000000000 z))))): 0 points increase in error, 0 points decrease in error
      (+.f64 313060547623/100000000000 (+.f64 (*.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 1 (pow.f64 z 2))) (+.f64 (/.f64 t (pow.f64 z 2)) (+.f64 (/.f64 (Rewrite<= cancel-sign-sub-inv_binary64 (-.f64 (+.f64 1112090185084895700201045470302189/1000000000000000000000000000000 a) (*.f64 15234687407/1000000000 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t)))) (pow.f64 z 3)) (/.f64 -3652704169880641883561/100000000000000000000 z))))): 0 points increase in error, 0 points decrease in error
      (+.f64 313060547623/100000000000 (+.f64 (*.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 1 (pow.f64 z 2))) (+.f64 (/.f64 t (pow.f64 z 2)) (+.f64 (/.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)) (/.f64 -3652704169880641883561/100000000000000000000 z))))): 0 points increase in error, 0 points decrease in error
      (+.f64 313060547623/100000000000 (+.f64 (*.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 1 (pow.f64 z 2))) (+.f64 (/.f64 t (pow.f64 z 2)) (+.f64 (/.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)) (/.f64 -3652704169880641883561/100000000000000000000 z))))): 0 points increase in error, 0 points decrease in error
      (+.f64 313060547623/100000000000 (+.f64 (*.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 1 (pow.f64 z 2))) (+.f64 (/.f64 t (pow.f64 z 2)) (+.f64 (/.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)) (/.f64 -3652704169880641883561/100000000000000000000 z))))): 0 points increase in error, 0 points decrease in error
      (+.f64 313060547623/100000000000 (+.f64 (*.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 1 (pow.f64 z 2))) (+.f64 (/.f64 t (pow.f64 z 2)) (+.f64 (/.f64 (neg.f64 (neg.f64 (+.f64 (+.f64 a 1112090185084895700201045470302189/1000000000000000000000000000000) (*.f64 (Rewrite=> metadata-eval -15234687407/1000000000) (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t))))) (pow.f64 z 3)) (/.f64 -3652704169880641883561/100000000000000000000 z))))): 0 points increase in error, 0 points decrease in error
      (+.f64 313060547623/100000000000 (+.f64 (*.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 1 (pow.f64 z 2))) (+.f64 (/.f64 t (pow.f64 z 2)) (+.f64 (/.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)) (/.f64 -3652704169880641883561/100000000000000000000 z))))): 0 points increase in error, 0 points decrease in error
      (+.f64 313060547623/100000000000 (+.f64 (*.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 1 (pow.f64 z 2))) (+.f64 (/.f64 t (pow.f64 z 2)) (+.f64 (/.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)) (/.f64 -3652704169880641883561/100000000000000000000 z))))): 0 points increase in error, 0 points decrease in error
      (+.f64 313060547623/100000000000 (+.f64 (*.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 1 (pow.f64 z 2))) (+.f64 (/.f64 t (pow.f64 z 2)) (+.f64 (/.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)) (/.f64 -3652704169880641883561/100000000000000000000 z))))): 0 points increase in error, 0 points decrease in error
      (+.f64 313060547623/100000000000 (+.f64 (*.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 1 (pow.f64 z 2))) (+.f64 (/.f64 t (pow.f64 z 2)) (+.f64 (/.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)) (/.f64 -3652704169880641883561/100000000000000000000 z))))): 0 points increase in error, 0 points decrease in error
      (+.f64 313060547623/100000000000 (+.f64 (*.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 1 (pow.f64 z 2))) (+.f64 (/.f64 t (pow.f64 z 2)) (+.f64 (/.f64 (Rewrite<= mul-1-neg_binary64 (*.f64 -1 (-.f64 (*.f64 -1 a) (+.f64 1112090185084895700201045470302189/1000000000000000000000000000000 (*.f64 -15234687407/1000000000 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t)))))) (pow.f64 z 3)) (/.f64 -3652704169880641883561/100000000000000000000 z))))): 0 points increase in error, 0 points decrease in error
      (+.f64 313060547623/100000000000 (+.f64 (*.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 1 (pow.f64 z 2))) (+.f64 (/.f64 t (pow.f64 z 2)) (+.f64 (Rewrite<= associate-*r/_binary64 (*.f64 -1 (/.f64 (-.f64 (*.f64 -1 a) (+.f64 1112090185084895700201045470302189/1000000000000000000000000000000 (*.f64 -15234687407/1000000000 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t)))) (pow.f64 z 3)))) (/.f64 -3652704169880641883561/100000000000000000000 z))))): 0 points increase in error, 0 points decrease in error
      (+.f64 313060547623/100000000000 (+.f64 (*.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 1 (pow.f64 z 2))) (+.f64 (/.f64 t (pow.f64 z 2)) (+.f64 (*.f64 -1 (/.f64 (-.f64 (*.f64 -1 a) (+.f64 1112090185084895700201045470302189/1000000000000000000000000000000 (*.f64 -15234687407/1000000000 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t)))) (pow.f64 z 3))) (/.f64 (Rewrite<= metadata-eval (neg.f64 3652704169880641883561/100000000000000000000)) z))))): 0 points increase in error, 0 points decrease in error
      (+.f64 313060547623/100000000000 (+.f64 (*.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 1 (pow.f64 z 2))) (+.f64 (/.f64 t (pow.f64 z 2)) (+.f64 (*.f64 -1 (/.f64 (-.f64 (*.f64 -1 a) (+.f64 1112090185084895700201045470302189/1000000000000000000000000000000 (*.f64 -15234687407/1000000000 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t)))) (pow.f64 z 3))) (Rewrite<= distribute-neg-frac_binary64 (neg.f64 (/.f64 3652704169880641883561/100000000000000000000 z))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 313060547623/100000000000 (+.f64 (*.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 1 (pow.f64 z 2))) (+.f64 (/.f64 t (pow.f64 z 2)) (+.f64 (*.f64 -1 (/.f64 (-.f64 (*.f64 -1 a) (+.f64 1112090185084895700201045470302189/1000000000000000000000000000000 (*.f64 -15234687407/1000000000 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t)))) (pow.f64 z 3))) (neg.f64 (/.f64 (Rewrite<= metadata-eval (*.f64 3652704169880641883561/100000000000000000000 1)) z)))))): 0 points increase in error, 0 points decrease in error
      (+.f64 313060547623/100000000000 (+.f64 (*.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 1 (pow.f64 z 2))) (+.f64 (/.f64 t (pow.f64 z 2)) (+.f64 (*.f64 -1 (/.f64 (-.f64 (*.f64 -1 a) (+.f64 1112090185084895700201045470302189/1000000000000000000000000000000 (*.f64 -15234687407/1000000000 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t)))) (pow.f64 z 3))) (neg.f64 (Rewrite<= associate-*r/_binary64 (*.f64 3652704169880641883561/100000000000000000000 (/.f64 1 z)))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 313060547623/100000000000 (+.f64 (*.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 1 (pow.f64 z 2))) (+.f64 (/.f64 t (pow.f64 z 2)) (Rewrite<= sub-neg_binary64 (-.f64 (*.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
      (+.f64 313060547623/100000000000 (+.f64 (*.f64 45796100221584283915100827016327/100000000000000000000000000000 (/.f64 1 (pow.f64 z 2))) (Rewrite<= associate--l+_binary64 (-.f64 (+.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
      (+.f64 313060547623/100000000000 (Rewrite<= associate--l+_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 3652704169880641883561/100000000000000000000 (/.f64 1 z))))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate--l+_binary64 (-.f64 (+.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

    if -2.10069795371405939e42 < z < 4e18

    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. Simplified0.5

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right)}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}, x\right)} \]
      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): 1 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): 0 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, 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 (+.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)): 0 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): 22 points increase in error, 7 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 y around 0 0.5

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

    if 4e18 < z

    1. Initial program 57.5

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

    2. Simplified54.3

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right)}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}, x\right)} \]
      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): 1 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): 0 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, 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 (+.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)): 0 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): 22 points increase in error, 7 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 13.3

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

    4. Simplified1.5

      \[\leadsto \color{blue}{\mathsf{fma}\left(3.13060547623, y, \mathsf{fma}\left(-36.52704169880642, \frac{y}{z}, x\right)\right) + \frac{y}{z \cdot z} \cdot \left(\left(t + 457.9610022158428\right) - \frac{\left(5864.8025282699045 - t \cdot -15.234687407\right) - a}{z}\right)} \]
      Proof
      (+.f64 (fma.f64 313060547623/100000000000 y (fma.f64 -3652704169880641883561/100000000000000000000 (/.f64 y z) x)) (*.f64 (/.f64 y (*.f64 z z)) (-.f64 (+.f64 t 45796100221584283915100827016327/100000000000000000000000000000) (/.f64 (-.f64 (-.f64 586480252826990429730394679450703430294089/100000000000000000000000000000000000000 (*.f64 t -15234687407/1000000000)) a) 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 y (*.f64 z z)) (-.f64 (+.f64 t 45796100221584283915100827016327/100000000000000000000000000000) (/.f64 (-.f64 (-.f64 586480252826990429730394679450703430294089/100000000000000000000000000000000000000 (*.f64 t -15234687407/1000000000)) a) 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 y (*.f64 z z)) (-.f64 (+.f64 t 45796100221584283915100827016327/100000000000000000000000000000) (/.f64 (-.f64 (-.f64 586480252826990429730394679450703430294089/100000000000000000000000000000000000000 (*.f64 t -15234687407/1000000000)) a) 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 y (*.f64 z z)) (-.f64 (+.f64 t 45796100221584283915100827016327/100000000000000000000000000000) (/.f64 (-.f64 (-.f64 586480252826990429730394679450703430294089/100000000000000000000000000000000000000 (*.f64 t -15234687407/1000000000)) a) z)))): 0 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 y (*.f64 z z)) (-.f64 (+.f64 t 45796100221584283915100827016327/100000000000000000000000000000) (/.f64 (-.f64 (-.f64 586480252826990429730394679450703430294089/100000000000000000000000000000000000000 (*.f64 t -15234687407/1000000000)) a) 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 y (*.f64 z z)) (-.f64 (+.f64 t 45796100221584283915100827016327/100000000000000000000000000000) (/.f64 (-.f64 (-.f64 586480252826990429730394679450703430294089/100000000000000000000000000000000000000 (*.f64 t -15234687407/1000000000)) a) 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 (Rewrite<= unpow2_binary64 (pow.f64 z 2))) (-.f64 (+.f64 t 45796100221584283915100827016327/100000000000000000000000000000) (/.f64 (-.f64 (-.f64 586480252826990429730394679450703430294089/100000000000000000000000000000000000000 (*.f64 t -15234687407/1000000000)) a) 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 (-.f64 586480252826990429730394679450703430294089/100000000000000000000000000000000000000 (*.f64 t -15234687407/1000000000)) a) 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 (Rewrite<= metadata-eval (-.f64 0 -586480252826990429730394679450703430294089/100000000000000000000000000000000000000)) (*.f64 t -15234687407/1000000000)) a) 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 (-.f64 0 (Rewrite<= metadata-eval (+.f64 1112090185084895700201045470302189/1000000000000000000000000000000 -697689271335479999750499226480922330294089/100000000000000000000000000000000000000))) (*.f64 t -15234687407/1000000000)) a) 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 (-.f64 0 (+.f64 1112090185084895700201045470302189/1000000000000000000000000000000 (Rewrite<= metadata-eval (*.f64 45796100221584283915100827016327/100000000000000000000000000000 -15234687407/1000000000)))) (*.f64 t -15234687407/1000000000)) a) z)))): 0 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 y (pow.f64 z 2)) (-.f64 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t) (/.f64 (-.f64 (Rewrite<= associate--r+_binary64 (-.f64 0 (+.f64 (+.f64 1112090185084895700201045470302189/1000000000000000000000000000000 (*.f64 45796100221584283915100827016327/100000000000000000000000000000 -15234687407/1000000000)) (*.f64 t -15234687407/1000000000)))) a) 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 0 (Rewrite<= associate-+r+_binary64 (+.f64 1112090185084895700201045470302189/1000000000000000000000000000000 (+.f64 (*.f64 45796100221584283915100827016327/100000000000000000000000000000 -15234687407/1000000000) (*.f64 t -15234687407/1000000000))))) a) 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 0 (+.f64 1112090185084895700201045470302189/1000000000000000000000000000000 (Rewrite<= distribute-rgt-in_binary64 (*.f64 -15234687407/1000000000 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t))))) a) 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<= neg-sub0_binary64 (neg.f64 (+.f64 1112090185084895700201045470302189/1000000000000000000000000000000 (*.f64 -15234687407/1000000000 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t))))) a) 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<= unsub-neg_binary64 (+.f64 (neg.f64 (+.f64 1112090185084895700201045470302189/1000000000000000000000000000000 (*.f64 -15234687407/1000000000 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t)))) (neg.f64 a))) 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 (neg.f64 (+.f64 1112090185084895700201045470302189/1000000000000000000000000000000 (*.f64 -15234687407/1000000000 (+.f64 45796100221584283915100827016327/100000000000000000000000000000 t)))) (Rewrite<= mul-1-neg_binary64 (*.f64 -1 a))) 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 (*.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 (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)) (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))))): 1 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)) (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))))): 28 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, 6 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)))): 1 points increase in error, 0 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

    5. Applied egg-rr1.6

      \[\leadsto \mathsf{fma}\left(3.13060547623, y, \mathsf{fma}\left(-36.52704169880642, \frac{y}{z}, x\right)\right) + \color{blue}{\frac{\left(t + 457.9610022158428\right) - \frac{5864.8025282699045 - \mathsf{fma}\left(t, -15.234687407, a\right)}{z}}{\frac{z}{\frac{y}{z}}}} \]
  3. Recombined 3 regimes into one program.

  4. Final simplification0.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1006979537140594 \cdot 10^{+42}:\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623 + \left(\frac{457.9610022158428}{z \cdot z} + \left(\frac{t}{z \cdot z} + \left(\frac{a - \left(5864.8025282699045 - t \cdot -15.234687407\right)}{{z}^{3}} + \frac{-36.52704169880642}{z}\right)\right)\right), x\right)\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+18}:\\ \;\;\;\;x + y \cdot \left(\frac{b}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)} + \frac{z \cdot \left(a - z \cdot \left(z \cdot \left(z \cdot -3.13060547623 + -11.1667541262\right) - t\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(3.13060547623, y, \mathsf{fma}\left(-36.52704169880642, \frac{y}{z}, x\right)\right) + \frac{\left(457.9610022158428 + t\right) + \frac{-5864.8025282699045 + \mathsf{fma}\left(t, -15.234687407, a\right)}{z}}{\frac{z}{\frac{y}{z}}}\\ \end{array} \]

Alternatives

Alternative 1
Error0.7
Cost14984
\[\begin{array}{l} t_1 := \mathsf{fma}\left(y, 3.13060547623 + \left(\frac{457.9610022158428}{z \cdot z} + \left(\frac{t}{z \cdot z} + \left(\frac{a - \left(5864.8025282699045 - t \cdot -15.234687407\right)}{{z}^{3}} + \frac{-36.52704169880642}{z}\right)\right)\right), x\right)\\ t_2 := 0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)\\ \mathbf{if}\;z \leq -2.1006979537140594 \cdot 10^{+42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+18}:\\ \;\;\;\;x + y \cdot \left(\frac{b}{t_2} + \frac{z \cdot \left(a - z \cdot \left(z \cdot \left(z \cdot -3.13060547623 + -11.1667541262\right) - t\right)\right)}{t_2}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 2
Error0.9
Cost14792
\[\begin{array}{l} t_1 := 0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)\\ t_2 := \mathsf{fma}\left(3.13060547623, y, \mathsf{fma}\left(-36.52704169880642, \frac{y}{z}, x\right)\right) + \frac{y}{z \cdot z} \cdot \left(\left(457.9610022158428 + t\right) + \frac{a - \left(5864.8025282699045 - t \cdot -15.234687407\right)}{z}\right)\\ \mathbf{if}\;z \leq -2.1006979537140594 \cdot 10^{+42}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+18}:\\ \;\;\;\;x + y \cdot \left(\frac{b}{t_1} + \frac{z \cdot \left(a - z \cdot \left(z \cdot \left(z \cdot -3.13060547623 + -11.1667541262\right) - t\right)\right)}{t_1}\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]
Alternative 3
Error1.3
Cost7752
\[\begin{array}{l} t_1 := 0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)\\ \mathbf{if}\;z \leq -2.1006979537140594 \cdot 10^{+42}:\\ \;\;\;\;\mathsf{fma}\left(y, \left(3.13060547623 + \frac{-36.52704169880642}{z}\right) + \frac{457.9610022158428 + t}{z \cdot z}, x\right)\\ \mathbf{elif}\;z \leq 3.164869667069453 \cdot 10^{+57}:\\ \;\;\;\;x + y \cdot \left(\frac{b}{t_1} + \frac{z \cdot \left(a - z \cdot \left(z \cdot \left(z \cdot -3.13060547623 + -11.1667541262\right) - t\right)\right)}{t_1}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547623, x\right) + \frac{y}{z \cdot z} \cdot \left(457.9610022158428 - \frac{5864.8025282699045 - a}{z}\right)\\ \end{array} \]
Alternative 4
Error1.0
Cost7624
\[\begin{array}{l} t_1 := \mathsf{fma}\left(y, \left(3.13060547623 + \frac{-36.52704169880642}{z}\right) + \frac{457.9610022158428 + t}{z \cdot z}, x\right)\\ t_2 := 0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)\\ \mathbf{if}\;z \leq -2.1006979537140594 \cdot 10^{+42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.0830676597851144 \cdot 10^{+34}:\\ \;\;\;\;x + y \cdot \left(\frac{b}{t_2} + \frac{z \cdot \left(a - z \cdot \left(z \cdot \left(z \cdot -3.13060547623 + -11.1667541262\right) - t\right)\right)}{t_2}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 5
Error2.9
Cost6984
\[\begin{array}{l} t_1 := \frac{y \cdot \left(b + z \cdot \left(a - z \cdot \left(z \cdot \left(z \cdot -3.13060547623 + -11.1667541262\right) - t\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;x + \frac{y}{z} \cdot \left(-36.52704169880642 + \frac{457.9610022158428 - \frac{5864.8025282699045 - a}{z}}{z}\right)\\ \mathbf{elif}\;t_1 \leq 10^{+281}:\\ \;\;\;\;x + t_1\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \]
Alternative 6
Error2.8
Cost6984
\[\begin{array}{l} t_1 := 0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)\\ t_2 := z \cdot \left(a - z \cdot \left(z \cdot \left(z \cdot -3.13060547623 + -11.1667541262\right) - t\right)\right)\\ t_3 := \frac{y \cdot \left(b + t_2\right)}{t_1}\\ \mathbf{if}\;t_3 \leq -\infty:\\ \;\;\;\;y \cdot \left(\frac{b}{t_1} + \frac{t_2}{t_1}\right)\\ \mathbf{elif}\;t_3 \leq 10^{+281}:\\ \;\;\;\;x + t_3\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \]
Alternative 7
Error1.9
Cost3656
\[\begin{array}{l} t_1 := 0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)\\ t_2 := x + y \cdot 3.13060547623\\ \mathbf{if}\;z \leq -2.457301605674619 \cdot 10^{+60}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 3.164869667069453 \cdot 10^{+57}:\\ \;\;\;\;x + y \cdot \left(\frac{b}{t_1} + \frac{z \cdot \left(a - z \cdot \left(z \cdot \left(z \cdot -3.13060547623 + -11.1667541262\right) - t\right)\right)}{t_1}\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]
Alternative 8
Error3.5
Cost2376
\[\begin{array}{l} t_1 := x + y \cdot 3.13060547623\\ \mathbf{if}\;z \leq -0.45:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+18}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t + z \cdot 11.1667541262\right)\right)\right)}{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 9
Error5.5
Cost1480
\[\begin{array}{l} t_1 := \left(x + y \cdot 3.13060547623\right) + -36.52704169880642 \cdot \frac{y}{z}\\ \mathbf{if}\;z \leq -4.2 \cdot 10^{-13}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 0.0014:\\ \;\;\;\;y \cdot \left(z \cdot \left(a \cdot 1.6453555072203998 + b \cdot -32.324150453290734\right)\right) + \left(x + 1.6453555072203998 \cdot \left(y \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 10
Error5.5
Cost1352
\[\begin{array}{l} t_1 := \left(x + y \cdot 3.13060547623\right) + -36.52704169880642 \cdot \frac{y}{z}\\ \mathbf{if}\;z \leq -4.2 \cdot 10^{-13}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 0.0014:\\ \;\;\;\;x + y \cdot \left(z \cdot \left(a \cdot 1.6453555072203998 + b \cdot -32.324150453290734\right) + b \cdot 1.6453555072203998\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 11
Error5.5
Cost1224
\[\begin{array}{l} t_1 := \left(x + y \cdot 3.13060547623\right) + -36.52704169880642 \cdot \frac{y}{z}\\ \mathbf{if}\;z \leq -4.2 \cdot 10^{-13}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 0.0014:\\ \;\;\;\;x + \left(1.6453555072203998 \cdot \left(y \cdot b\right) + 1.6453555072203998 \cdot \left(y \cdot \left(z \cdot a\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 12
Error5.5
Cost1096
\[\begin{array}{l} t_1 := \left(x + y \cdot 3.13060547623\right) + -36.52704169880642 \cdot \frac{y}{z}\\ \mathbf{if}\;z \leq -4.2 \cdot 10^{-13}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 0.0014:\\ \;\;\;\;x + y \cdot \left(b \cdot 1.6453555072203998 + 1.6453555072203998 \cdot \left(z \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 13
Error8.9
Cost968
\[\begin{array}{l} t_1 := x + y \cdot 3.13060547623\\ \mathbf{if}\;z \leq -0.45:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 0.0014:\\ \;\;\;\;x + \frac{y \cdot b}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 14
Error9.2
Cost968
\[\begin{array}{l} t_1 := \left(x + y \cdot 3.13060547623\right) + -36.52704169880642 \cdot \frac{y}{z}\\ \mathbf{if}\;z \leq -1.05 \cdot 10^{-33}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 0.0014:\\ \;\;\;\;x + \frac{y \cdot b}{0.607771387771 + z \cdot 11.9400905721}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 15
Error28.0
Cost720
\[\begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+121}:\\ \;\;\;\;y \cdot 3.13060547623\\ \mathbf{elif}\;y \leq 5.66243733852232 \cdot 10^{+83}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+130}:\\ \;\;\;\;y \cdot 3.13060547623\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+189}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot 3.13060547623\\ \end{array} \]
Alternative 16
Error9.2
Cost712
\[\begin{array}{l} t_1 := x + y \cdot 3.13060547623\\ \mathbf{if}\;z \leq -1.05 \cdot 10^{-33}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 0.0014:\\ \;\;\;\;x + b \cdot \left(y \cdot 1.6453555072203998\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 17
Error9.2
Cost712
\[\begin{array}{l} t_1 := x + y \cdot 3.13060547623\\ \mathbf{if}\;z \leq -1.05 \cdot 10^{-33}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 0.0014:\\ \;\;\;\;x + 1.6453555072203998 \cdot \left(y \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 18
Error18.4
Cost584
\[\begin{array}{l} t_1 := x + y \cdot 3.13060547623\\ \mathbf{if}\;z \leq -9.8 \cdot 10^{-120}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-57}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 19
Error31.8
Cost64
\[x \]

Error

Reproduce

herbie shell --seed 2022294 
(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))))