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

Average Error: 29.6 → 1.0

Time: 1.1min

Precision: binary64

Cost: 11976

Math

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

↓

\[\begin{array}{l} t_1 := \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t - z \cdot \left(z \cdot -3.13060547623 + -11.1667541262\right)\right)\right)\right)}{0.607771387771 - z \cdot \left(z \cdot \left(z \cdot \left(-15.234687407 - z\right) + -31.4690115749\right) + -11.9400905721\right)}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;x + \left(\frac{y}{z} \cdot \left(11.1667541262 + \frac{t}{z}\right) + \mathsf{fma}\left(y, 3.13060547623, \frac{y}{z} \cdot \left(-47.69379582500642 + \frac{-98.5170599679272}{z}\right) - \frac{y}{z} \cdot \frac{-556.47806218377}{z}\right)\right)\\ \mathbf{elif}\;t_1 \leq 4 \cdot 10^{+300}:\\ \;\;\;\;x + t_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \left(3.13060547623 + \frac{t + 457.9610022158428}{z \cdot z}\right) + \frac{-36.52704169880642}{z}, x\right)\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (/
          (*
           y
           (+
            b
            (*
             z
             (+ a (* z (- t (* z (+ (* z -3.13060547623) -11.1667541262))))))))
          (-
           0.607771387771
           (*
            z
            (+
             (* z (+ (* z (- -15.234687407 z)) -31.4690115749))
             -11.9400905721))))))
   (if (<= t_1 (- INFINITY))
     (+
      x
      (+
       (* (/ y z) (+ 11.1667541262 (/ t z)))
       (fma
        y
        3.13060547623
        (-
         (* (/ y z) (+ -47.69379582500642 (/ -98.5170599679272 z)))
         (* (/ y z) (/ -556.47806218377 z))))))
     (if (<= t_1 4e+300)
       (+ x t_1)
       (fma
        y
        (+
         (+ 3.13060547623 (/ (+ t 457.9610022158428) (* z z)))
         (/ -36.52704169880642 z))
        x)))))

C

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

↓

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * (b + (z * (a + (z * (t - (z * ((z * -3.13060547623) + -11.1667541262)))))))) / (0.607771387771 - (z * ((z * ((z * (-15.234687407 - z)) + -31.4690115749)) + -11.9400905721)));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = x + (((y / z) * (11.1667541262 + (t / z))) + fma(y, 3.13060547623, (((y / z) * (-47.69379582500642 + (-98.5170599679272 / z))) - ((y / z) * (-556.47806218377 / z)))));
	} else if (t_1 <= 4e+300) {
		tmp = x + t_1;
	} else {
		tmp = fma(y, ((3.13060547623 + ((t + 457.9610022158428) / (z * z))) + (-36.52704169880642 / z)), x);
	}
	return tmp;
}

Julia

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

↓

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y * Float64(b + Float64(z * Float64(a + Float64(z * Float64(t - Float64(z * Float64(Float64(z * -3.13060547623) + -11.1667541262)))))))) / Float64(0.607771387771 - Float64(z * Float64(Float64(z * Float64(Float64(z * Float64(-15.234687407 - z)) + -31.4690115749)) + -11.9400905721))))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(x + Float64(Float64(Float64(y / z) * Float64(11.1667541262 + Float64(t / z))) + fma(y, 3.13060547623, Float64(Float64(Float64(y / z) * Float64(-47.69379582500642 + Float64(-98.5170599679272 / z))) - Float64(Float64(y / z) * Float64(-556.47806218377 / z))))));
	elseif (t_1 <= 4e+300)
		tmp = Float64(x + t_1);
	else
		tmp = fma(y, Float64(Float64(3.13060547623 + Float64(Float64(t + 457.9610022158428) / Float64(z * z))) + Float64(-36.52704169880642 / z)), x);
	end
	return tmp
end

Wolfram

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

↓

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y * N[(b + N[(z * N[(a + N[(z * N[(t - N[(z * N[(N[(z * -3.13060547623), $MachinePrecision] + -11.1667541262), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(0.607771387771 - N[(z * N[(N[(z * N[(N[(z * N[(-15.234687407 - z), $MachinePrecision]), $MachinePrecision] + -31.4690115749), $MachinePrecision]), $MachinePrecision] + -11.9400905721), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(x + N[(N[(N[(y / z), $MachinePrecision] * N[(11.1667541262 + N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * 3.13060547623 + N[(N[(N[(y / z), $MachinePrecision] * N[(-47.69379582500642 + N[(-98.5170599679272 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(y / z), $MachinePrecision] * N[(-556.47806218377 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 4e+300], N[(x + t$95$1), $MachinePrecision], N[(y * N[(N[(3.13060547623 + N[(N[(t + 457.9610022158428), $MachinePrecision] / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-36.52704169880642 / z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]]]

Target

Original	29.6
Target	1.1
Herbie	1.0

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

Derivation

1. Split input into 3 regimes

2. if (/.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)) < -inf.0

   1. Initial program 64.0

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

   2. Simplified 30.1

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right)}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}, x\right)} \]
      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): 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, 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): 1 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): 1 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): 19 points increase in error, 14 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 b around 0 63.9

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

   4. Taylor expanded in z around inf 25.1

      \[\leadsto \color{blue}{\left(\left(\frac{y \cdot t}{{z}^{2}} + \left(11.1667541262 \cdot \frac{y}{z} + 3.13060547623 \cdot y\right)\right) - \left(47.69379582500642 \cdot \frac{y}{z} + \left(98.5170599679272 \cdot \frac{y}{{z}^{2}} + 15.234687407 \cdot \frac{11.1667541262 \cdot y - 47.69379582500642 \cdot y}{{z}^{2}}\right)\right)\right)} + x \]

   5. Simplified 13.0

      \[\leadsto \color{blue}{\left(\frac{y}{z} \cdot \left(11.1667541262 + \frac{t}{z}\right) + \mathsf{fma}\left(y, 3.13060547623, \frac{y}{z} \cdot \frac{556.47806218377}{z} - \frac{y}{z} \cdot \left(47.69379582500642 + \frac{98.5170599679272}{z}\right)\right)\right)} + x \]
      Proof
      (+.f64 (*.f64 (/.f64 y z) (+.f64 55833770631/5000000000 (/.f64 t z))) (fma.f64 y 313060547623/100000000000 (-.f64 (*.f64 (/.f64 y z) (/.f64 55647806218377003596563527016327/100000000000000000000000000000 z)) (*.f64 (/.f64 y z) (+.f64 4769379582500641883561/100000000000000000000 (/.f64 98517059967927196814627/1000000000000000000000 z)))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite<= distribute-rgt-out_binary64 (+.f64 (*.f64 55833770631/5000000000 (/.f64 y z)) (*.f64 (/.f64 t z) (/.f64 y z)))) (fma.f64 y 313060547623/100000000000 (-.f64 (*.f64 (/.f64 y z) (/.f64 55647806218377003596563527016327/100000000000000000000000000000 z)) (*.f64 (/.f64 y z) (+.f64 4769379582500641883561/100000000000000000000 (/.f64 98517059967927196814627/1000000000000000000000 z)))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (*.f64 55833770631/5000000000 (/.f64 y z)) (Rewrite<= times-frac_binary64 (/.f64 (*.f64 t y) (*.f64 z z)))) (fma.f64 y 313060547623/100000000000 (-.f64 (*.f64 (/.f64 y z) (/.f64 55647806218377003596563527016327/100000000000000000000000000000 z)) (*.f64 (/.f64 y z) (+.f64 4769379582500641883561/100000000000000000000 (/.f64 98517059967927196814627/1000000000000000000000 z)))))): 36 points increase in error, 10 points decrease in error
      (+.f64 (+.f64 (*.f64 55833770631/5000000000 (/.f64 y z)) (/.f64 (Rewrite<= *-commutative_binary64 (*.f64 y t)) (*.f64 z z))) (fma.f64 y 313060547623/100000000000 (-.f64 (*.f64 (/.f64 y z) (/.f64 55647806218377003596563527016327/100000000000000000000000000000 z)) (*.f64 (/.f64 y z) (+.f64 4769379582500641883561/100000000000000000000 (/.f64 98517059967927196814627/1000000000000000000000 z)))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (*.f64 55833770631/5000000000 (/.f64 y z)) (/.f64 (*.f64 y t) (Rewrite<= unpow2_binary64 (pow.f64 z 2)))) (fma.f64 y 313060547623/100000000000 (-.f64 (*.f64 (/.f64 y z) (/.f64 55647806218377003596563527016327/100000000000000000000000000000 z)) (*.f64 (/.f64 y z) (+.f64 4769379582500641883561/100000000000000000000 (/.f64 98517059967927196814627/1000000000000000000000 z)))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite<= +-commutative_binary64 (+.f64 (/.f64 (*.f64 y t) (pow.f64 z 2)) (*.f64 55833770631/5000000000 (/.f64 y z)))) (fma.f64 y 313060547623/100000000000 (-.f64 (*.f64 (/.f64 y z) (/.f64 55647806218377003596563527016327/100000000000000000000000000000 z)) (*.f64 (/.f64 y z) (+.f64 4769379582500641883561/100000000000000000000 (/.f64 98517059967927196814627/1000000000000000000000 z)))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (/.f64 (*.f64 y t) (pow.f64 z 2)) (*.f64 55833770631/5000000000 (/.f64 y z))) (fma.f64 y 313060547623/100000000000 (-.f64 (*.f64 (/.f64 y z) (/.f64 (Rewrite<= metadata-eval (*.f64 -3652704169880641883561/100000000000000000000 -15234687407/1000000000)) z)) (*.f64 (/.f64 y z) (+.f64 4769379582500641883561/100000000000000000000 (/.f64 98517059967927196814627/1000000000000000000000 z)))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (/.f64 (*.f64 y t) (pow.f64 z 2)) (*.f64 55833770631/5000000000 (/.f64 y z))) (fma.f64 y 313060547623/100000000000 (-.f64 (*.f64 (/.f64 y z) (/.f64 (*.f64 (Rewrite<= metadata-eval (-.f64 55833770631/5000000000 4769379582500641883561/100000000000000000000)) -15234687407/1000000000) z)) (*.f64 (/.f64 y z) (+.f64 4769379582500641883561/100000000000000000000 (/.f64 98517059967927196814627/1000000000000000000000 z)))))): 11 points increase in error, 14 points decrease in error
      (+.f64 (+.f64 (/.f64 (*.f64 y t) (pow.f64 z 2)) (*.f64 55833770631/5000000000 (/.f64 y z))) (fma.f64 y 313060547623/100000000000 (-.f64 (Rewrite<= times-frac_binary64 (/.f64 (*.f64 y (*.f64 (-.f64 55833770631/5000000000 4769379582500641883561/100000000000000000000) -15234687407/1000000000)) (*.f64 z z))) (*.f64 (/.f64 y z) (+.f64 4769379582500641883561/100000000000000000000 (/.f64 98517059967927196814627/1000000000000000000000 z)))))): 6 points increase in error, 2 points decrease in error
      (+.f64 (+.f64 (/.f64 (*.f64 y t) (pow.f64 z 2)) (*.f64 55833770631/5000000000 (/.f64 y z))) (fma.f64 y 313060547623/100000000000 (-.f64 (/.f64 (*.f64 y (*.f64 (-.f64 55833770631/5000000000 4769379582500641883561/100000000000000000000) -15234687407/1000000000)) (Rewrite<= unpow2_binary64 (pow.f64 z 2))) (*.f64 (/.f64 y z) (+.f64 4769379582500641883561/100000000000000000000 (/.f64 98517059967927196814627/1000000000000000000000 z)))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (/.f64 (*.f64 y t) (pow.f64 z 2)) (*.f64 55833770631/5000000000 (/.f64 y z))) (fma.f64 y 313060547623/100000000000 (-.f64 (/.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 y (-.f64 55833770631/5000000000 4769379582500641883561/100000000000000000000)) -15234687407/1000000000)) (pow.f64 z 2)) (*.f64 (/.f64 y z) (+.f64 4769379582500641883561/100000000000000000000 (/.f64 98517059967927196814627/1000000000000000000000 z)))))): 3 points increase in error, 2 points decrease in error
      (+.f64 (+.f64 (/.f64 (*.f64 y t) (pow.f64 z 2)) (*.f64 55833770631/5000000000 (/.f64 y z))) (fma.f64 y 313060547623/100000000000 (-.f64 (/.f64 (*.f64 (Rewrite<= distribute-rgt-out--_binary64 (-.f64 (*.f64 55833770631/5000000000 y) (*.f64 4769379582500641883561/100000000000000000000 y))) -15234687407/1000000000) (pow.f64 z 2)) (*.f64 (/.f64 y z) (+.f64 4769379582500641883561/100000000000000000000 (/.f64 98517059967927196814627/1000000000000000000000 z)))))): 13 points increase in error, 7 points decrease in error
      (+.f64 (+.f64 (/.f64 (*.f64 y t) (pow.f64 z 2)) (*.f64 55833770631/5000000000 (/.f64 y z))) (fma.f64 y 313060547623/100000000000 (-.f64 (/.f64 (*.f64 (-.f64 (*.f64 55833770631/5000000000 y) (*.f64 4769379582500641883561/100000000000000000000 y)) (Rewrite<= metadata-eval (neg.f64 15234687407/1000000000))) (pow.f64 z 2)) (*.f64 (/.f64 y z) (+.f64 4769379582500641883561/100000000000000000000 (/.f64 98517059967927196814627/1000000000000000000000 z)))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (/.f64 (*.f64 y t) (pow.f64 z 2)) (*.f64 55833770631/5000000000 (/.f64 y z))) (fma.f64 y 313060547623/100000000000 (-.f64 (/.f64 (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 (-.f64 (*.f64 55833770631/5000000000 y) (*.f64 4769379582500641883561/100000000000000000000 y)) 15234687407/1000000000))) (pow.f64 z 2)) (*.f64 (/.f64 y z) (+.f64 4769379582500641883561/100000000000000000000 (/.f64 98517059967927196814627/1000000000000000000000 z)))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (/.f64 (*.f64 y t) (pow.f64 z 2)) (*.f64 55833770631/5000000000 (/.f64 y z))) (fma.f64 y 313060547623/100000000000 (-.f64 (/.f64 (neg.f64 (Rewrite<= *-commutative_binary64 (*.f64 15234687407/1000000000 (-.f64 (*.f64 55833770631/5000000000 y) (*.f64 4769379582500641883561/100000000000000000000 y))))) (pow.f64 z 2)) (*.f64 (/.f64 y z) (+.f64 4769379582500641883561/100000000000000000000 (/.f64 98517059967927196814627/1000000000000000000000 z)))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (/.f64 (*.f64 y t) (pow.f64 z 2)) (*.f64 55833770631/5000000000 (/.f64 y z))) (fma.f64 y 313060547623/100000000000 (-.f64 (Rewrite<= distribute-neg-frac_binary64 (neg.f64 (/.f64 (*.f64 15234687407/1000000000 (-.f64 (*.f64 55833770631/5000000000 y) (*.f64 4769379582500641883561/100000000000000000000 y))) (pow.f64 z 2)))) (*.f64 (/.f64 y z) (+.f64 4769379582500641883561/100000000000000000000 (/.f64 98517059967927196814627/1000000000000000000000 z)))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (/.f64 (*.f64 y t) (pow.f64 z 2)) (*.f64 55833770631/5000000000 (/.f64 y z))) (fma.f64 y 313060547623/100000000000 (-.f64 (neg.f64 (Rewrite<= associate-*r/_binary64 (*.f64 15234687407/1000000000 (/.f64 (-.f64 (*.f64 55833770631/5000000000 y) (*.f64 4769379582500641883561/100000000000000000000 y)) (pow.f64 z 2))))) (*.f64 (/.f64 y z) (+.f64 4769379582500641883561/100000000000000000000 (/.f64 98517059967927196814627/1000000000000000000000 z)))))): 4 points increase in error, 3 points decrease in error
      (+.f64 (+.f64 (/.f64 (*.f64 y t) (pow.f64 z 2)) (*.f64 55833770631/5000000000 (/.f64 y z))) (fma.f64 y 313060547623/100000000000 (-.f64 (Rewrite=> neg-sub0_binary64 (-.f64 0 (*.f64 15234687407/1000000000 (/.f64 (-.f64 (*.f64 55833770631/5000000000 y) (*.f64 4769379582500641883561/100000000000000000000 y)) (pow.f64 z 2))))) (*.f64 (/.f64 y z) (+.f64 4769379582500641883561/100000000000000000000 (/.f64 98517059967927196814627/1000000000000000000000 z)))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (/.f64 (*.f64 y t) (pow.f64 z 2)) (*.f64 55833770631/5000000000 (/.f64 y z))) (fma.f64 y 313060547623/100000000000 (-.f64 (-.f64 0 (*.f64 15234687407/1000000000 (/.f64 (-.f64 (*.f64 55833770631/5000000000 y) (*.f64 4769379582500641883561/100000000000000000000 y)) (pow.f64 z 2)))) (Rewrite<= distribute-rgt-out_binary64 (+.f64 (*.f64 4769379582500641883561/100000000000000000000 (/.f64 y z)) (*.f64 (/.f64 98517059967927196814627/1000000000000000000000 z) (/.f64 y z))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (/.f64 (*.f64 y t) (pow.f64 z 2)) (*.f64 55833770631/5000000000 (/.f64 y z))) (fma.f64 y 313060547623/100000000000 (-.f64 (-.f64 0 (*.f64 15234687407/1000000000 (/.f64 (-.f64 (*.f64 55833770631/5000000000 y) (*.f64 4769379582500641883561/100000000000000000000 y)) (pow.f64 z 2)))) (+.f64 (*.f64 4769379582500641883561/100000000000000000000 (/.f64 y z)) (Rewrite<= times-frac_binary64 (/.f64 (*.f64 98517059967927196814627/1000000000000000000000 y) (*.f64 z z))))))): 0 points increase in error, 2 points decrease in error
      (+.f64 (+.f64 (/.f64 (*.f64 y t) (pow.f64 z 2)) (*.f64 55833770631/5000000000 (/.f64 y z))) (fma.f64 y 313060547623/100000000000 (-.f64 (-.f64 0 (*.f64 15234687407/1000000000 (/.f64 (-.f64 (*.f64 55833770631/5000000000 y) (*.f64 4769379582500641883561/100000000000000000000 y)) (pow.f64 z 2)))) (+.f64 (*.f64 4769379582500641883561/100000000000000000000 (/.f64 y z)) (/.f64 (*.f64 98517059967927196814627/1000000000000000000000 y) (Rewrite<= unpow2_binary64 (pow.f64 z 2))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (/.f64 (*.f64 y t) (pow.f64 z 2)) (*.f64 55833770631/5000000000 (/.f64 y z))) (fma.f64 y 313060547623/100000000000 (-.f64 (-.f64 0 (*.f64 15234687407/1000000000 (/.f64 (-.f64 (*.f64 55833770631/5000000000 y) (*.f64 4769379582500641883561/100000000000000000000 y)) (pow.f64 z 2)))) (+.f64 (*.f64 4769379582500641883561/100000000000000000000 (/.f64 y z)) (Rewrite<= associate-*r/_binary64 (*.f64 98517059967927196814627/1000000000000000000000 (/.f64 y (pow.f64 z 2)))))))): 0 points increase in error, 1 points decrease in error
      (+.f64 (+.f64 (/.f64 (*.f64 y t) (pow.f64 z 2)) (*.f64 55833770631/5000000000 (/.f64 y z))) (fma.f64 y 313060547623/100000000000 (Rewrite<= associate--r+_binary64 (-.f64 0 (+.f64 (*.f64 15234687407/1000000000 (/.f64 (-.f64 (*.f64 55833770631/5000000000 y) (*.f64 4769379582500641883561/100000000000000000000 y)) (pow.f64 z 2))) (+.f64 (*.f64 4769379582500641883561/100000000000000000000 (/.f64 y z)) (*.f64 98517059967927196814627/1000000000000000000000 (/.f64 y (pow.f64 z 2))))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (/.f64 (*.f64 y t) (pow.f64 z 2)) (*.f64 55833770631/5000000000 (/.f64 y z))) (fma.f64 y 313060547623/100000000000 (-.f64 0 (Rewrite<= +-commutative_binary64 (+.f64 (+.f64 (*.f64 4769379582500641883561/100000000000000000000 (/.f64 y z)) (*.f64 98517059967927196814627/1000000000000000000000 (/.f64 y (pow.f64 z 2)))) (*.f64 15234687407/1000000000 (/.f64 (-.f64 (*.f64 55833770631/5000000000 y) (*.f64 4769379582500641883561/100000000000000000000 y)) (pow.f64 z 2)))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (/.f64 (*.f64 y t) (pow.f64 z 2)) (*.f64 55833770631/5000000000 (/.f64 y z))) (fma.f64 y 313060547623/100000000000 (-.f64 0 (Rewrite<= associate-+r+_binary64 (+.f64 (*.f64 4769379582500641883561/100000000000000000000 (/.f64 y z)) (+.f64 (*.f64 98517059967927196814627/1000000000000000000000 (/.f64 y (pow.f64 z 2))) (*.f64 15234687407/1000000000 (/.f64 (-.f64 (*.f64 55833770631/5000000000 y) (*.f64 4769379582500641883561/100000000000000000000 y)) (pow.f64 z 2))))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (/.f64 (*.f64 y t) (pow.f64 z 2)) (*.f64 55833770631/5000000000 (/.f64 y z))) (fma.f64 y 313060547623/100000000000 (Rewrite<= neg-sub0_binary64 (neg.f64 (+.f64 (*.f64 4769379582500641883561/100000000000000000000 (/.f64 y z)) (+.f64 (*.f64 98517059967927196814627/1000000000000000000000 (/.f64 y (pow.f64 z 2))) (*.f64 15234687407/1000000000 (/.f64 (-.f64 (*.f64 55833770631/5000000000 y) (*.f64 4769379582500641883561/100000000000000000000 y)) (pow.f64 z 2))))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (/.f64 (*.f64 y t) (pow.f64 z 2)) (*.f64 55833770631/5000000000 (/.f64 y z))) (Rewrite<= fma-neg_binary64 (-.f64 (*.f64 y 313060547623/100000000000) (+.f64 (*.f64 4769379582500641883561/100000000000000000000 (/.f64 y z)) (+.f64 (*.f64 98517059967927196814627/1000000000000000000000 (/.f64 y (pow.f64 z 2))) (*.f64 15234687407/1000000000 (/.f64 (-.f64 (*.f64 55833770631/5000000000 y) (*.f64 4769379582500641883561/100000000000000000000 y)) (pow.f64 z 2)))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (/.f64 (*.f64 y t) (pow.f64 z 2)) (*.f64 55833770631/5000000000 (/.f64 y z))) (-.f64 (Rewrite<= *-commutative_binary64 (*.f64 313060547623/100000000000 y)) (+.f64 (*.f64 4769379582500641883561/100000000000000000000 (/.f64 y z)) (+.f64 (*.f64 98517059967927196814627/1000000000000000000000 (/.f64 y (pow.f64 z 2))) (*.f64 15234687407/1000000000 (/.f64 (-.f64 (*.f64 55833770631/5000000000 y) (*.f64 4769379582500641883561/100000000000000000000 y)) (pow.f64 z 2))))))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate--l+_binary64 (-.f64 (+.f64 (+.f64 (/.f64 (*.f64 y t) (pow.f64 z 2)) (*.f64 55833770631/5000000000 (/.f64 y z))) (*.f64 313060547623/100000000000 y)) (+.f64 (*.f64 4769379582500641883561/100000000000000000000 (/.f64 y z)) (+.f64 (*.f64 98517059967927196814627/1000000000000000000000 (/.f64 y (pow.f64 z 2))) (*.f64 15234687407/1000000000 (/.f64 (-.f64 (*.f64 55833770631/5000000000 y) (*.f64 4769379582500641883561/100000000000000000000 y)) (pow.f64 z 2))))))): 0 points increase in error, 0 points decrease in error
      (-.f64 (Rewrite<= associate-+r+_binary64 (+.f64 (/.f64 (*.f64 y t) (pow.f64 z 2)) (+.f64 (*.f64 55833770631/5000000000 (/.f64 y z)) (*.f64 313060547623/100000000000 y)))) (+.f64 (*.f64 4769379582500641883561/100000000000000000000 (/.f64 y z)) (+.f64 (*.f64 98517059967927196814627/1000000000000000000000 (/.f64 y (pow.f64 z 2))) (*.f64 15234687407/1000000000 (/.f64 (-.f64 (*.f64 55833770631/5000000000 y) (*.f64 4769379582500641883561/100000000000000000000 y)) (pow.f64 z 2)))))): 0 points increase in error, 0 points decrease in error

   if -inf.0 < (/.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)) < 4.0000000000000002e300

   1. Initial program 0.2

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

   if 4.0000000000000002e300 < (/.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))

   1. Initial program 63.7

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

   2. Simplified 61.7

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right)}{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}, x\right)} \]
      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): 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, 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): 1 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): 1 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): 19 points increase in error, 14 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 b around 0 62.2

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

   4. Taylor expanded in z around -inf 1.2

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

   5. Simplified 1.2

      \[\leadsto \mathsf{fma}\left(y, \color{blue}{\left(3.13060547623 - \frac{-457.9610022158428 - t}{z \cdot z}\right) + \frac{-36.52704169880642}{z}}, x\right) \]
      Proof
      (+.f64 (-.f64 313060547623/100000000000 (/.f64 (-.f64 -45796100221584283915100827016327/100000000000000000000000000000 t) (*.f64 z z))) (/.f64 -3652704169880641883561/100000000000000000000 z)): 0 points increase in error, 0 points decrease in error
      (+.f64 (-.f64 313060547623/100000000000 (/.f64 (-.f64 (Rewrite<= metadata-eval (neg.f64 45796100221584283915100827016327/100000000000000000000000000000)) t) (*.f64 z z))) (/.f64 -3652704169880641883561/100000000000000000000 z)): 0 points increase in error, 0 points decrease in error
      (+.f64 (-.f64 313060547623/100000000000 (/.f64 (-.f64 (neg.f64 45796100221584283915100827016327/100000000000000000000000000000) t) (Rewrite<= unpow2_binary64 (pow.f64 z 2)))) (/.f64 -3652704169880641883561/100000000000000000000 z)): 0 points increase in error, 0 points decrease in error
      (+.f64 (-.f64 313060547623/100000000000 (/.f64 (Rewrite<= unsub-neg_binary64 (+.f64 (neg.f64 45796100221584283915100827016327/100000000000000000000000000000) (neg.f64 t))) (pow.f64 z 2))) (/.f64 -3652704169880641883561/100000000000000000000 z)): 0 points increase in error, 0 points decrease in error
      (+.f64 (-.f64 313060547623/100000000000 (/.f64 (+.f64 (neg.f64 45796100221584283915100827016327/100000000000000000000000000000) (Rewrite<= mul-1-neg_binary64 (*.f64 -1 t))) (pow.f64 z 2))) (/.f64 -3652704169880641883561/100000000000000000000 z)): 0 points increase in error, 0 points decrease in error
      (+.f64 (-.f64 313060547623/100000000000 (/.f64 (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 -1 t) (neg.f64 45796100221584283915100827016327/100000000000000000000000000000))) (pow.f64 z 2))) (/.f64 -3652704169880641883561/100000000000000000000 z)): 0 points increase in error, 0 points decrease in error
      (+.f64 (-.f64 313060547623/100000000000 (/.f64 (Rewrite<= sub-neg_binary64 (-.f64 (*.f64 -1 t) 45796100221584283915100827016327/100000000000000000000000000000)) (pow.f64 z 2))) (/.f64 -3652704169880641883561/100000000000000000000 z)): 0 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite<= unsub-neg_binary64 (+.f64 313060547623/100000000000 (neg.f64 (/.f64 (-.f64 (*.f64 -1 t) 45796100221584283915100827016327/100000000000000000000000000000) (pow.f64 z 2))))) (/.f64 -3652704169880641883561/100000000000000000000 z)): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 313060547623/100000000000 (Rewrite<= mul-1-neg_binary64 (*.f64 -1 (/.f64 (-.f64 (*.f64 -1 t) 45796100221584283915100827016327/100000000000000000000000000000) (pow.f64 z 2))))) (/.f64 -3652704169880641883561/100000000000000000000 z)): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 313060547623/100000000000 (*.f64 -1 (/.f64 (-.f64 (*.f64 -1 t) 45796100221584283915100827016327/100000000000000000000000000000) (pow.f64 z 2)))) (/.f64 (Rewrite<= metadata-eval (neg.f64 3652704169880641883561/100000000000000000000)) z)): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 313060547623/100000000000 (*.f64 -1 (/.f64 (-.f64 (*.f64 -1 t) 45796100221584283915100827016327/100000000000000000000000000000) (pow.f64 z 2)))) (Rewrite<= distribute-neg-frac_binary64 (neg.f64 (/.f64 3652704169880641883561/100000000000000000000 z)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 313060547623/100000000000 (*.f64 -1 (/.f64 (-.f64 (*.f64 -1 t) 45796100221584283915100827016327/100000000000000000000000000000) (pow.f64 z 2)))) (neg.f64 (/.f64 (Rewrite<= metadata-eval (*.f64 3652704169880641883561/100000000000000000000 1)) z))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 313060547623/100000000000 (*.f64 -1 (/.f64 (-.f64 (*.f64 -1 t) 45796100221584283915100827016327/100000000000000000000000000000) (pow.f64 z 2)))) (neg.f64 (Rewrite<= associate-*r/_binary64 (*.f64 3652704169880641883561/100000000000000000000 (/.f64 1 z))))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= sub-neg_binary64 (-.f64 (+.f64 313060547623/100000000000 (*.f64 -1 (/.f64 (-.f64 (*.f64 -1 t) 45796100221584283915100827016327/100000000000000000000000000000) (pow.f64 z 2)))) (*.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 simplification 1.0

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t - z \cdot \left(z \cdot -3.13060547623 + -11.1667541262\right)\right)\right)\right)}{0.607771387771 - z \cdot \left(z \cdot \left(z \cdot \left(-15.234687407 - z\right) + -31.4690115749\right) + -11.9400905721\right)} \leq -\infty:\\ \;\;\;\;x + \left(\frac{y}{z} \cdot \left(11.1667541262 + \frac{t}{z}\right) + \mathsf{fma}\left(y, 3.13060547623, \frac{y}{z} \cdot \left(-47.69379582500642 + \frac{-98.5170599679272}{z}\right) - \frac{y}{z} \cdot \frac{-556.47806218377}{z}\right)\right)\\ \mathbf{elif}\;\frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t - z \cdot \left(z \cdot -3.13060547623 + -11.1667541262\right)\right)\right)\right)}{0.607771387771 - z \cdot \left(z \cdot \left(z \cdot \left(-15.234687407 - z\right) + -31.4690115749\right) + -11.9400905721\right)} \leq 4 \cdot 10^{+300}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t - z \cdot \left(z \cdot -3.13060547623 + -11.1667541262\right)\right)\right)\right)}{0.607771387771 - z \cdot \left(z \cdot \left(z \cdot \left(-15.234687407 - z\right) + -31.4690115749\right) + -11.9400905721\right)}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \left(3.13060547623 + \frac{t + 457.9610022158428}{z \cdot z}\right) + \frac{-36.52704169880642}{z}, x\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	1.2
Cost	79176

\[\begin{array}{l} t_1 := \sqrt{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right), 0.607771387771\right)}\\ \mathbf{if}\;z \leq -350000000:\\ \;\;\;\;\mathsf{fma}\left(y, \left(3.13060547623 + \frac{t + 457.9610022158428}{z \cdot z}\right) + \frac{-36.52704169880642}{z}, x\right)\\ \mathbf{elif}\;z \leq 13000000000000:\\ \;\;\;\;x + \frac{\mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, \mathsf{fma}\left(z, 3.13060547623, 11.1667541262\right), t\right), a\right), b\right)}{t_1} \cdot \frac{y}{t_1}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \left(3.13060547623 + \frac{-36.52704169880642}{z}\right) + \left(\left(\frac{457.9610022158428}{z \cdot z} + \frac{t}{z \cdot z}\right) + \frac{a + \left(t \cdot -15.234687407 + -5864.8025282699045\right)}{{z}^{3}}\right), x\right)\\ \end{array} \]

Alternative 2
Error	1.2
Cost	22024

\[\begin{array}{l} \mathbf{if}\;z \leq -350000000:\\ \;\;\;\;\mathsf{fma}\left(y, \left(3.13060547623 + \frac{t + 457.9610022158428}{z \cdot z}\right) + \frac{-36.52704169880642}{z}, x\right)\\ \mathbf{elif}\;z \leq 13000000000000:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t - z \cdot \left(z \cdot -3.13060547623 + -11.1667541262\right)\right)\right)\right)}{0.607771387771 + \left(31.4690115749 \cdot {z}^{2} + \left({z}^{4} + \left(z \cdot 11.9400905721 + 15.234687407 \cdot {z}^{3}\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \left(3.13060547623 + \frac{-36.52704169880642}{z}\right) + \left(\left(\frac{457.9610022158428}{z \cdot z} + \frac{t}{z \cdot z}\right) + \frac{a + \left(t \cdot -15.234687407 + -5864.8025282699045\right)}{{z}^{3}}\right), x\right)\\ \end{array} \]

Alternative 3
Error	1.2
Cost	15176

\[\begin{array}{l} \mathbf{if}\;z \leq -350000000:\\ \;\;\;\;\mathsf{fma}\left(y, \left(3.13060547623 + \frac{t + 457.9610022158428}{z \cdot z}\right) + \frac{-36.52704169880642}{z}, x\right)\\ \mathbf{elif}\;z \leq 13000000000000:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t - z \cdot \left(z \cdot -3.13060547623 + -11.1667541262\right)\right)\right)\right)}{0.607771387771 + z \cdot \mathsf{fma}\left(z, \mathsf{fma}\left(z, z + 15.234687407, 31.4690115749\right), 11.9400905721\right)}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \left(3.13060547623 + \frac{-36.52704169880642}{z}\right) + \left(\left(\frac{457.9610022158428}{z \cdot z} + \frac{t}{z \cdot z}\right) + \frac{a + \left(t \cdot -15.234687407 + -5864.8025282699045\right)}{{z}^{3}}\right), x\right)\\ \end{array} \]

Alternative 4
Error	1.2
Cost	14984

\[\begin{array}{l} \mathbf{if}\;z \leq -350000000:\\ \;\;\;\;\mathsf{fma}\left(y, \left(3.13060547623 + \frac{t + 457.9610022158428}{z \cdot z}\right) + \frac{-36.52704169880642}{z}, x\right)\\ \mathbf{elif}\;z \leq 13000000000000:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t - z \cdot \left(z \cdot -3.13060547623 + -11.1667541262\right)\right)\right)\right)}{0.607771387771 - z \cdot \left(z \cdot \left(z \cdot \left(-15.234687407 - z\right) + -31.4690115749\right) + -11.9400905721\right)}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \left(3.13060547623 + \frac{-36.52704169880642}{z}\right) + \left(\left(\frac{457.9610022158428}{z \cdot z} + \frac{t}{z \cdot z}\right) + \frac{a + \left(t \cdot -15.234687407 + -5864.8025282699045\right)}{{z}^{3}}\right), x\right)\\ \end{array} \]

Alternative 5
Error	1.0
Cost	11976

\[\begin{array}{l} t_1 := \mathsf{fma}\left(y, \left(3.13060547623 + \frac{t + 457.9610022158428}{z \cdot z}\right) + \frac{-36.52704169880642}{z}, x\right)\\ t_2 := \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t - z \cdot \left(z \cdot -3.13060547623 + -11.1667541262\right)\right)\right)\right)}{0.607771387771 - z \cdot \left(z \cdot \left(z \cdot \left(-15.234687407 - z\right) + -31.4690115749\right) + -11.9400905721\right)}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 4 \cdot 10^{+300}:\\ \;\;\;\;x + t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	1.4
Cost	11272

\[\begin{array}{l} t_1 := 0.607771387771 - z \cdot \left(z \cdot \left(z \cdot \left(-15.234687407 - z\right) + -31.4690115749\right) + -11.9400905721\right)\\ \mathbf{if}\;z \leq -350000000:\\ \;\;\;\;\mathsf{fma}\left(y, \left(3.13060547623 + \frac{t + 457.9610022158428}{z \cdot z}\right) + \frac{-36.52704169880642}{z}, x\right)\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{+35}:\\ \;\;\;\;\frac{y \cdot \left(z \cdot a\right)}{t_1} + \left(x - y \cdot \left(\frac{{z}^{2} \cdot \left(z \cdot \left(z \cdot -3.13060547623 + -11.1667541262\right) - t\right)}{t_1} - \frac{b}{t_1}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{y}{z} \cdot \left(11.1667541262 + \frac{t}{z}\right) + \mathsf{fma}\left(y, 3.13060547623, \frac{y}{z} \cdot \left(-47.69379582500642 + \frac{-98.5170599679272}{z}\right) - \frac{y}{z} \cdot \frac{-556.47806218377}{z}\right)\right)\\ \end{array} \]

Alternative 7
Error	2.8
Cost	2632

\[\begin{array}{l} t_1 := x + y \cdot 3.13060547623\\ \mathbf{if}\;z \leq -350000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{+35}:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot \left(t - z \cdot \left(z \cdot -3.13060547623 + -11.1667541262\right)\right)\right)\right)}{0.607771387771 - z \cdot \left(z \cdot \left(z \cdot \left(-15.234687407 - z\right) + -31.4690115749\right) + -11.9400905721\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Error	3.6
Cost	2120

\[\begin{array}{l} \mathbf{if}\;z \leq -0.049:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 - \frac{y}{z} \cdot 36.52704169880642\right)\\ \mathbf{elif}\;z \leq 13000000000000:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot \left(a + z \cdot t\right)\right)}{0.607771387771 - z \cdot \left(z \cdot \left(z \cdot \left(-15.234687407 - z\right) + -31.4690115749\right) + -11.9400905721\right)}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \]

Alternative 9
Error	5.4
Cost	1992

\[\begin{array}{l} t_1 := x + y \cdot 3.13060547623\\ \mathbf{if}\;z \leq -4.81618081254796 \cdot 10^{+57}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 13000000000000:\\ \;\;\;\;x + \frac{y \cdot b + a \cdot \left(z \cdot y\right)}{0.607771387771 - z \cdot \left(z \cdot \left(z \cdot \left(-15.234687407 - z\right) + -31.4690115749\right) + -11.9400905721\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 10
Error	5.2
Cost	1864

\[\begin{array}{l} \mathbf{if}\;z \leq -0.049:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 - \frac{y}{z} \cdot 36.52704169880642\right)\\ \mathbf{elif}\;z \leq 13000000000000:\\ \;\;\;\;x + \frac{y \cdot \left(b + z \cdot a\right)}{0.607771387771 - z \cdot \left(z \cdot \left(z \cdot \left(-15.234687407 - z\right) + -31.4690115749\right) + -11.9400905721\right)}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \]

Alternative 11
Error	5.5
Cost	1480

\[\begin{array}{l} \mathbf{if}\;z \leq -0.049:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 - \frac{y}{z} \cdot 36.52704169880642\right)\\ \mathbf{elif}\;z \leq 130:\\ \;\;\;\;\left(x + \left(y \cdot b\right) \cdot 1.6453555072203998\right) - y \cdot \left(z \cdot \left(b \cdot 32.324150453290734 + a \cdot -1.6453555072203998\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \]

Alternative 12
Error	5.7
Cost	1224

\[\begin{array}{l} \mathbf{if}\;z \leq -0.049:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 - \frac{y}{z} \cdot 36.52704169880642\right)\\ \mathbf{elif}\;z \leq 130:\\ \;\;\;\;\left(x + \left(y \cdot b\right) \cdot 1.6453555072203998\right) + \left(a \cdot \left(z \cdot y\right)\right) \cdot 1.6453555072203998\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \]

Alternative 13
Error	21.4
Cost	976

\[\begin{array}{l} t_1 := x + y \cdot 3.13060547623\\ \mathbf{if}\;z \leq -1.7 \cdot 10^{-66}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-246}:\\ \;\;\;\;\left(y \cdot b\right) \cdot 1.6453555072203998\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-144}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-87}:\\ \;\;\;\;\left(y \cdot \left(z \cdot a\right)\right) \cdot 1.6453555072203998\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 14
Error	10.5
Cost	976

\[\begin{array}{l} t_1 := x + \frac{y}{\frac{0.607771387771}{b}}\\ t_2 := x + y \cdot 3.13060547623\\ \mathbf{if}\;z \leq -0.049:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-145}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.15 \cdot 10^{-86}:\\ \;\;\;\;\left(y \cdot \left(z \cdot a\right)\right) \cdot 1.6453555072203998\\ \mathbf{elif}\;z \leq 10^{-17}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 15
Error	10.5
Cost	976

\[\begin{array}{l} t_1 := x + \frac{y}{\frac{0.607771387771}{b}}\\ t_2 := x + y \cdot 3.13060547623\\ \mathbf{if}\;z \leq -0.049:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-145}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.15 \cdot 10^{-86}:\\ \;\;\;\;\left(a \cdot \left(z \cdot y\right)\right) \cdot 1.6453555072203998\\ \mathbf{elif}\;z \leq 10^{-17}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 16
Error	10.5
Cost	976

\[\begin{array}{l} t_1 := x + y \cdot 3.13060547623\\ \mathbf{if}\;z \leq -0.049:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-145}:\\ \;\;\;\;x - b \cdot \left(y \cdot -1.6453555072203998\right)\\ \mathbf{elif}\;z \leq 3.15 \cdot 10^{-86}:\\ \;\;\;\;\left(a \cdot \left(z \cdot y\right)\right) \cdot 1.6453555072203998\\ \mathbf{elif}\;z \leq 10^{-17}:\\ \;\;\;\;x + \frac{y}{\frac{0.607771387771}{b}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 17
Error	10.0
Cost	972

\[\begin{array}{l} t_1 := x + y \cdot 3.13060547623\\ \mathbf{if}\;z \leq -0.049:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-194}:\\ \;\;\;\;x - b \cdot \left(y \cdot -1.6453555072203998\right)\\ \mathbf{elif}\;z \leq 13000000000000:\\ \;\;\;\;x + y \cdot \left(z \cdot \left(a \cdot 1.6453555072203998\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 18
Error	10.0
Cost	972

\[\begin{array}{l} \mathbf{if}\;z \leq -0.049:\\ \;\;\;\;x + y \cdot \left(3.13060547623 - \frac{47.69379582500642}{z}\right)\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-194}:\\ \;\;\;\;x - b \cdot \left(y \cdot -1.6453555072203998\right)\\ \mathbf{elif}\;z \leq 13000000000000:\\ \;\;\;\;x + y \cdot \left(z \cdot \left(a \cdot 1.6453555072203998\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \]

Alternative 19
Error	10.1
Cost	972

\[\begin{array}{l} \mathbf{if}\;z \leq -0.049:\\ \;\;\;\;x + y \cdot \left(3.13060547623 - \frac{47.69379582500642}{z}\right)\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-194}:\\ \;\;\;\;x - b \cdot \left(y \cdot -1.6453555072203998\right)\\ \mathbf{elif}\;z \leq 13000000000000:\\ \;\;\;\;x + \left(a \cdot \left(z \cdot y\right)\right) \cdot 1.6453555072203998\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \]

Alternative 20
Error	10.1
Cost	972

\[\begin{array}{l} \mathbf{if}\;z \leq -0.049:\\ \;\;\;\;x + \left(y \cdot 3.13060547623 - \frac{y}{z} \cdot 36.52704169880642\right)\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-194}:\\ \;\;\;\;x - b \cdot \left(y \cdot -1.6453555072203998\right)\\ \mathbf{elif}\;z \leq 13000000000000:\\ \;\;\;\;x + \left(a \cdot \left(z \cdot y\right)\right) \cdot 1.6453555072203998\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot 3.13060547623\\ \end{array} \]

Alternative 21
Error	28.4
Cost	588

\[\begin{array}{l} \mathbf{if}\;x \leq -7.373137707127874 \cdot 10^{-160}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -1.5893847827083765 \cdot 10^{-239}:\\ \;\;\;\;\left(y \cdot b\right) \cdot 1.6453555072203998\\ \mathbf{elif}\;x \leq 1.4542237314197572 \cdot 10^{-133}:\\ \;\;\;\;y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 22
Error	21.3
Cost	584

\[\begin{array}{l} t_1 := x + y \cdot 3.13060547623\\ \mathbf{if}\;z \leq -1.7 \cdot 10^{-66}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{-186}:\\ \;\;\;\;\left(y \cdot b\right) \cdot 1.6453555072203998\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 23
Error	27.9
Cost	456

\[\begin{array}{l} \mathbf{if}\;x \leq -7.373137707127874 \cdot 10^{-160}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.4542237314197572 \cdot 10^{-133}:\\ \;\;\;\;y \cdot 3.13060547623\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 24
Error	31.6
Cost	64

\[x \]

Reproduce

herbie shell --seed 2022317 
(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))))