Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, I

Average Error: 3.7 → 1.4

Time: 46.3s

Precision: binary64

Cost: 33540

Math

\[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

↓

\[\begin{array}{l} t_1 := \sqrt{a + t}\\ t_2 := \left(c - b\right) \cdot \left(0.8333333333333334 + \left(a - \frac{0.6666666666666666}{t}\right)\right)\\ \mathbf{if}\;a \leq 3 \cdot 10^{+48}:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(y, {\left(e^{2}\right)}^{\left(\mathsf{fma}\left(z, \frac{t_1}{t}, t_2\right)\right)}, x\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(y, {\left(e^{2}\right)}^{\left(\mathsf{fma}\left(t_1, \frac{z}{t}, t_2\right)\right)}, x\right)}\\ \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (/
  x
  (+
   x
   (*
    y
    (exp
     (*
      2.0
      (-
       (/ (* z (sqrt (+ t a))) t)
       (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))))))))

↓

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (sqrt (+ a t)))
        (t_2
         (* (- c b) (+ 0.8333333333333334 (- a (/ 0.6666666666666666 t))))))
   (if (<= a 3e+48)
     (/ x (fma y (pow (exp 2.0) (fma z (/ t_1 t) t_2)) x))
     (/ x (fma y (pow (exp 2.0) (fma t_1 (/ z t) t_2)) x)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return x / (x + (y * exp((2.0 * (((z * sqrt((t + a))) / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0)))))))));
}

↓

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = sqrt((a + t));
	double t_2 = (c - b) * (0.8333333333333334 + (a - (0.6666666666666666 / t)));
	double tmp;
	if (a <= 3e+48) {
		tmp = x / fma(y, pow(exp(2.0), fma(z, (t_1 / t), t_2)), x);
	} else {
		tmp = x / fma(y, pow(exp(2.0), fma(t_1, (z / t), t_2)), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	return Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(Float64(z * sqrt(Float64(t + a))) / t) - Float64(Float64(b - c) * Float64(Float64(a + Float64(5.0 / 6.0)) - Float64(2.0 / Float64(t * 3.0))))))))))
end

↓

function code(x, y, z, t, a, b, c)
	t_1 = sqrt(Float64(a + t))
	t_2 = Float64(Float64(c - b) * Float64(0.8333333333333334 + Float64(a - Float64(0.6666666666666666 / t))))
	tmp = 0.0
	if (a <= 3e+48)
		tmp = Float64(x / fma(y, (exp(2.0) ^ fma(z, Float64(t_1 / t), t_2)), x));
	else
		tmp = Float64(x / fma(y, (exp(2.0) ^ fma(t_1, Float64(z / t), t_2)), x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(N[(z * N[Sqrt[N[(t + a), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision] - N[(N[(b - c), $MachinePrecision] * N[(N[(a + N[(5.0 / 6.0), $MachinePrecision]), $MachinePrecision] - N[(2.0 / N[(t * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[Sqrt[N[(a + t), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[(N[(c - b), $MachinePrecision] * N[(0.8333333333333334 + N[(a - N[(0.6666666666666666 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, 3e+48], N[(x / N[(y * N[Power[N[Exp[2.0], $MachinePrecision], N[(z * N[(t$95$1 / t), $MachinePrecision] + t$95$2), $MachinePrecision]], $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * N[Power[N[Exp[2.0], $MachinePrecision], N[(t$95$1 * N[(z / t), $MachinePrecision] + t$95$2), $MachinePrecision]], $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision]]]]

Target

Original	3.7
Target	3.1
Herbie	1.4

\[\begin{array}{l} \mathbf{if}\;t < -2.118326644891581 \cdot 10^{-50}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(a \cdot c + 0.8333333333333334 \cdot c\right) - a \cdot b\right)}}\\ \mathbf{elif}\;t < 5.196588770651547 \cdot 10^{-123}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{\left(z \cdot \sqrt{t + a}\right) \cdot \left(\left(3 \cdot t\right) \cdot \left(a - \frac{5}{6}\right)\right) - \left(\left(\frac{5}{6} + a\right) \cdot \left(3 \cdot t\right) - 2\right) \cdot \left(\left(a - \frac{5}{6}\right) \cdot \left(\left(b - c\right) \cdot t\right)\right)}{\left(\left(t \cdot t\right) \cdot 3\right) \cdot \left(a - \frac{5}{6}\right)}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\\ \end{array} \]

Derivation

1. Split input into 2 regimes

2. if a < 3e48

   1. Initial program 2.6

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Simplified 0.5

      \[\leadsto \color{blue}{\frac{x}{\mathsf{fma}\left(y, {\left(e^{2}\right)}^{\left(\mathsf{fma}\left(z, \frac{\sqrt{t + a}}{t}, \left(0.8333333333333334 + \left(a + \frac{-0.6666666666666666}{t}\right)\right) \cdot \left(c - b\right)\right)\right)}, x\right)}} \]
      Proof
      (/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 z (/.f64 (sqrt.f64 (+.f64 t a)) t) (*.f64 (+.f64 5/6 (+.f64 a (/.f64 -2/3 t))) (-.f64 c b)))) x)): 0 points increase in error, 0 points decrease in error
      (/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 z (/.f64 (sqrt.f64 (+.f64 t a)) t) (*.f64 (+.f64 (Rewrite<= metadata-eval (/.f64 5 6)) (+.f64 a (/.f64 -2/3 t))) (-.f64 c b)))) x)): 0 points increase in error, 0 points decrease in error
      (/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 z (/.f64 (sqrt.f64 (+.f64 t a)) t) (*.f64 (+.f64 (/.f64 5 6) (+.f64 a (/.f64 (Rewrite<= metadata-eval (neg.f64 2/3)) t))) (-.f64 c b)))) x)): 0 points increase in error, 0 points decrease in error
      (/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 z (/.f64 (sqrt.f64 (+.f64 t a)) t) (*.f64 (+.f64 (/.f64 5 6) (+.f64 a (/.f64 (neg.f64 (Rewrite<= metadata-eval (/.f64 2 3))) t))) (-.f64 c b)))) x)): 0 points increase in error, 0 points decrease in error
      (/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 z (/.f64 (sqrt.f64 (+.f64 t a)) t) (*.f64 (+.f64 (/.f64 5 6) (+.f64 a (Rewrite<= distribute-neg-frac_binary64 (neg.f64 (/.f64 (/.f64 2 3) t))))) (-.f64 c b)))) x)): 0 points increase in error, 0 points decrease in error
      (/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 z (/.f64 (sqrt.f64 (+.f64 t a)) t) (*.f64 (+.f64 (/.f64 5 6) (+.f64 a (neg.f64 (Rewrite<= associate-/r*_binary64 (/.f64 2 (*.f64 3 t)))))) (-.f64 c b)))) x)): 0 points increase in error, 0 points decrease in error
      (/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 z (/.f64 (sqrt.f64 (+.f64 t a)) t) (*.f64 (+.f64 (/.f64 5 6) (+.f64 a (neg.f64 (/.f64 2 (Rewrite<= *-commutative_binary64 (*.f64 t 3)))))) (-.f64 c b)))) x)): 0 points increase in error, 0 points decrease in error
      (/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 z (/.f64 (sqrt.f64 (+.f64 t a)) t) (*.f64 (+.f64 (/.f64 5 6) (Rewrite=> unsub-neg_binary64 (-.f64 a (/.f64 2 (*.f64 t 3))))) (-.f64 c b)))) x)): 0 points increase in error, 0 points decrease in error
      (/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 z (/.f64 (sqrt.f64 (+.f64 t a)) t) (*.f64 (Rewrite<= associate--l+_binary64 (-.f64 (+.f64 (/.f64 5 6) a) (/.f64 2 (*.f64 t 3)))) (-.f64 c b)))) x)): 0 points increase in error, 0 points decrease in error
      (/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 z (/.f64 (sqrt.f64 (+.f64 t a)) t) (*.f64 (-.f64 (Rewrite<= +-commutative_binary64 (+.f64 a (/.f64 5 6))) (/.f64 2 (*.f64 t 3))) (-.f64 c b)))) x)): 0 points increase in error, 0 points decrease in error
      (/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 z (/.f64 (sqrt.f64 (+.f64 t a)) t) (*.f64 (-.f64 (+.f64 a (/.f64 5 6)) (/.f64 2 (*.f64 t 3))) (Rewrite<= unsub-neg_binary64 (+.f64 c (neg.f64 b)))))) x)): 0 points increase in error, 0 points decrease in error
      (/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 z (/.f64 (sqrt.f64 (+.f64 t a)) t) (*.f64 (-.f64 (+.f64 a (/.f64 5 6)) (/.f64 2 (*.f64 t 3))) (Rewrite<= +-commutative_binary64 (+.f64 (neg.f64 b) c))))) x)): 0 points increase in error, 0 points decrease in error
      (/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 z (/.f64 (sqrt.f64 (+.f64 t a)) t) (*.f64 (-.f64 (+.f64 a (/.f64 5 6)) (/.f64 2 (*.f64 t 3))) (+.f64 (neg.f64 b) (Rewrite<= remove-double-neg_binary64 (neg.f64 (neg.f64 c))))))) x)): 0 points increase in error, 0 points decrease in error
      (/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 z (/.f64 (sqrt.f64 (+.f64 t a)) t) (*.f64 (-.f64 (+.f64 a (/.f64 5 6)) (/.f64 2 (*.f64 t 3))) (Rewrite<= distribute-neg-in_binary64 (neg.f64 (+.f64 b (neg.f64 c))))))) x)): 0 points increase in error, 0 points decrease in error
      (/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 z (/.f64 (sqrt.f64 (+.f64 t a)) t) (*.f64 (-.f64 (+.f64 a (/.f64 5 6)) (/.f64 2 (*.f64 t 3))) (neg.f64 (Rewrite<= sub-neg_binary64 (-.f64 b c)))))) x)): 0 points increase in error, 0 points decrease in error
      (/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 z (/.f64 (sqrt.f64 (+.f64 t a)) t) (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 (-.f64 (+.f64 a (/.f64 5 6)) (/.f64 2 (*.f64 t 3))) (-.f64 b c)))))) x)): 0 points increase in error, 0 points decrease in error
      (/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 z (/.f64 (sqrt.f64 (+.f64 t a)) t) (neg.f64 (Rewrite<= *-commutative_binary64 (*.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 5 6)) (/.f64 2 (*.f64 t 3)))))))) x)): 0 points increase in error, 0 points decrease in error
      (/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (Rewrite<= fma-neg_binary64 (-.f64 (*.f64 z (/.f64 (sqrt.f64 (+.f64 t a)) t)) (*.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 5 6)) (/.f64 2 (*.f64 t 3))))))) x)): 8 points increase in error, 0 points decrease in error
      (/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (-.f64 (Rewrite=> associate-*r/_binary64 (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)) (*.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 5 6)) (/.f64 2 (*.f64 t 3)))))) x)): 7 points increase in error, 5 points decrease in error
      (/.f64 x (fma.f64 y (Rewrite<= exp-prod_binary64 (exp.f64 (*.f64 2 (-.f64 (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t) (*.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 5 6)) (/.f64 2 (*.f64 t 3)))))))) x)): 0 points increase in error, 0 points decrease in error
      (/.f64 x (Rewrite<= fma-def_binary64 (+.f64 (*.f64 y (exp.f64 (*.f64 2 (-.f64 (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t) (*.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 5 6)) (/.f64 2 (*.f64 t 3)))))))) x))): 0 points increase in error, 0 points decrease in error
      (/.f64 x (Rewrite<= +-commutative_binary64 (+.f64 x (*.f64 y (exp.f64 (*.f64 2 (-.f64 (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t) (*.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 5 6)) (/.f64 2 (*.f64 t 3))))))))))): 0 points increase in error, 0 points decrease in error

   if 3e48 < a

   1. Initial program 5.7

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Simplified 2.8

      \[\leadsto \color{blue}{\frac{x}{\mathsf{fma}\left(y, {\left(e^{2}\right)}^{\left(\mathsf{fma}\left(\sqrt{t + a}, \frac{z}{t}, \left(0.8333333333333334 + \left(a - \frac{0.6666666666666666}{t}\right)\right) \cdot \left(c - b\right)\right)\right)}, x\right)}} \]
      Proof
      (/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 (sqrt.f64 (+.f64 t a)) (/.f64 z t) (*.f64 (+.f64 5/6 (-.f64 a (/.f64 2/3 t))) (-.f64 c b)))) x)): 0 points increase in error, 0 points decrease in error
      (/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 (sqrt.f64 (+.f64 t a)) (/.f64 z t) (*.f64 (+.f64 (Rewrite<= metadata-eval (/.f64 5 6)) (-.f64 a (/.f64 2/3 t))) (-.f64 c b)))) x)): 0 points increase in error, 0 points decrease in error
      (/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 (sqrt.f64 (+.f64 t a)) (/.f64 z t) (*.f64 (+.f64 (/.f64 5 6) (-.f64 a (/.f64 (Rewrite<= metadata-eval (/.f64 2 3)) t))) (-.f64 c b)))) x)): 0 points increase in error, 0 points decrease in error
      (/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 (sqrt.f64 (+.f64 t a)) (/.f64 z t) (*.f64 (+.f64 (/.f64 5 6) (-.f64 a (Rewrite<= associate-/r*_binary64 (/.f64 2 (*.f64 3 t))))) (-.f64 c b)))) x)): 0 points increase in error, 0 points decrease in error
      (/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 (sqrt.f64 (+.f64 t a)) (/.f64 z t) (*.f64 (+.f64 (/.f64 5 6) (-.f64 a (/.f64 2 (Rewrite<= *-commutative_binary64 (*.f64 t 3))))) (-.f64 c b)))) x)): 0 points increase in error, 0 points decrease in error
      (/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 (sqrt.f64 (+.f64 t a)) (/.f64 z t) (*.f64 (Rewrite<= associate--l+_binary64 (-.f64 (+.f64 (/.f64 5 6) a) (/.f64 2 (*.f64 t 3)))) (-.f64 c b)))) x)): 0 points increase in error, 0 points decrease in error
      (/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 (sqrt.f64 (+.f64 t a)) (/.f64 z t) (*.f64 (-.f64 (Rewrite<= +-commutative_binary64 (+.f64 a (/.f64 5 6))) (/.f64 2 (*.f64 t 3))) (-.f64 c b)))) x)): 0 points increase in error, 0 points decrease in error
      (/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 (sqrt.f64 (+.f64 t a)) (/.f64 z t) (*.f64 (-.f64 (+.f64 a (/.f64 5 6)) (/.f64 2 (*.f64 t 3))) (Rewrite<= unsub-neg_binary64 (+.f64 c (neg.f64 b)))))) x)): 0 points increase in error, 0 points decrease in error
      (/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 (sqrt.f64 (+.f64 t a)) (/.f64 z t) (*.f64 (-.f64 (+.f64 a (/.f64 5 6)) (/.f64 2 (*.f64 t 3))) (Rewrite<= +-commutative_binary64 (+.f64 (neg.f64 b) c))))) x)): 0 points increase in error, 0 points decrease in error
      (/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 (sqrt.f64 (+.f64 t a)) (/.f64 z t) (*.f64 (-.f64 (+.f64 a (/.f64 5 6)) (/.f64 2 (*.f64 t 3))) (+.f64 (neg.f64 b) (Rewrite<= remove-double-neg_binary64 (neg.f64 (neg.f64 c))))))) x)): 0 points increase in error, 0 points decrease in error
      (/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 (sqrt.f64 (+.f64 t a)) (/.f64 z t) (*.f64 (-.f64 (+.f64 a (/.f64 5 6)) (/.f64 2 (*.f64 t 3))) (Rewrite<= distribute-neg-in_binary64 (neg.f64 (+.f64 b (neg.f64 c))))))) x)): 0 points increase in error, 0 points decrease in error
      (/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 (sqrt.f64 (+.f64 t a)) (/.f64 z t) (*.f64 (-.f64 (+.f64 a (/.f64 5 6)) (/.f64 2 (*.f64 t 3))) (neg.f64 (Rewrite<= sub-neg_binary64 (-.f64 b c)))))) x)): 0 points increase in error, 0 points decrease in error
      (/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 (sqrt.f64 (+.f64 t a)) (/.f64 z t) (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 (-.f64 (+.f64 a (/.f64 5 6)) (/.f64 2 (*.f64 t 3))) (-.f64 b c)))))) x)): 0 points increase in error, 0 points decrease in error
      (/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (fma.f64 (sqrt.f64 (+.f64 t a)) (/.f64 z t) (neg.f64 (Rewrite<= *-commutative_binary64 (*.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 5 6)) (/.f64 2 (*.f64 t 3)))))))) x)): 0 points increase in error, 0 points decrease in error
      (/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (Rewrite<= fma-neg_binary64 (-.f64 (*.f64 (sqrt.f64 (+.f64 t a)) (/.f64 z t)) (*.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 5 6)) (/.f64 2 (*.f64 t 3))))))) x)): 3 points increase in error, 0 points decrease in error
      (/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (-.f64 (Rewrite<= *-commutative_binary64 (*.f64 (/.f64 z t) (sqrt.f64 (+.f64 t a)))) (*.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 5 6)) (/.f64 2 (*.f64 t 3)))))) x)): 0 points increase in error, 0 points decrease in error
      (/.f64 x (fma.f64 y (pow.f64 (exp.f64 2) (-.f64 (Rewrite=> associate-*l/_binary64 (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t)) (*.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 5 6)) (/.f64 2 (*.f64 t 3)))))) x)): 6 points increase in error, 5 points decrease in error
      (/.f64 x (fma.f64 y (Rewrite<= exp-prod_binary64 (exp.f64 (*.f64 2 (-.f64 (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t) (*.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 5 6)) (/.f64 2 (*.f64 t 3)))))))) x)): 0 points increase in error, 0 points decrease in error
      (/.f64 x (Rewrite<= fma-def_binary64 (+.f64 (*.f64 y (exp.f64 (*.f64 2 (-.f64 (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t) (*.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 5 6)) (/.f64 2 (*.f64 t 3)))))))) x))): 0 points increase in error, 0 points decrease in error
      (/.f64 x (Rewrite<= +-commutative_binary64 (+.f64 x (*.f64 y (exp.f64 (*.f64 2 (-.f64 (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t) (*.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 5 6)) (/.f64 2 (*.f64 t 3))))))))))): 0 points increase in error, 0 points decrease in error
3. Recombined 2 regimes into one program.

4. Final simplification 1.4

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 3 \cdot 10^{+48}:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(y, {\left(e^{2}\right)}^{\left(\mathsf{fma}\left(z, \frac{\sqrt{a + t}}{t}, \left(c - b\right) \cdot \left(0.8333333333333334 + \left(a - \frac{0.6666666666666666}{t}\right)\right)\right)\right)}, x\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(y, {\left(e^{2}\right)}^{\left(\mathsf{fma}\left(\sqrt{a + t}, \frac{z}{t}, \left(c - b\right) \cdot \left(0.8333333333333334 + \left(a - \frac{0.6666666666666666}{t}\right)\right)\right)\right)}, x\right)}\\ \end{array} \]

Alternatives

Alternative 1
Error	1.6
Cost	33672

\[\begin{array}{l} t_1 := \sqrt{a + t}\\ t_2 := \frac{x}{\mathsf{fma}\left(y, {\left(e^{2}\right)}^{\left(\mathsf{fma}\left(z, \frac{t_1}{t}, \left(c - b\right) \cdot \left(0.8333333333333334 + \left(a - \frac{0.6666666666666666}{t}\right)\right)\right)\right)}, x\right)}\\ \mathbf{if}\;z \leq -4 \cdot 10^{-102}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-125}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot t_1}{t} - \left(c - b\right) \cdot \left(\frac{2}{t \cdot 3} + \left(-0.8333333333333334 - a\right)\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 2
Error	2.0
Cost	22468

\[\begin{array}{l} t_1 := \frac{z \cdot \sqrt{a + t}}{t} - \left(c - b\right) \cdot \left(\frac{2}{t \cdot 3} + \left(-0.8333333333333334 - a\right)\right)\\ \mathbf{if}\;t_1 \leq \infty:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot t_1}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \left(\frac{0.6666666666666666}{t} + \left(-0.8333333333333334 - a\right)\right)\right)}}\\ \end{array} \]

Alternative 3
Error	8.3
Cost	14536

\[\begin{array}{l} t_1 := \frac{x}{x + y \cdot e^{2 \cdot \left(\left(c - b\right) \cdot \left(a + 0.8333333333333334\right)\right)}}\\ \mathbf{if}\;t \leq 8.4 \cdot 10^{-306}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+41}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(z \cdot \sqrt{\frac{1}{t}} + \left(c - b\right) \cdot \left(0.8333333333333334 - \frac{0.6666666666666666}{t}\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Error	12.6
Cost	14028

\[\begin{array}{l} t_1 := \frac{x}{x + y \cdot e^{2 \cdot \left(\left(c - b\right) \cdot \left(a + 0.8333333333333334\right)\right)}}\\ t_2 := \frac{x}{x + y \cdot e^{-2 \cdot \left(c \cdot \frac{0.6666666666666666}{t}\right)}}\\ \mathbf{if}\;t \leq -3.5 \cdot 10^{-301}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-234}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-182}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(z \cdot \sqrt{\frac{1}{t}}\right)}}\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-104}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-19}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \left(\frac{0.6666666666666666}{t} + \left(-0.8333333333333334 - a\right)\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Error	33.3
Cost	8820

\[\begin{array}{l} t_1 := \frac{x}{y \cdot e^{\left(c - b\right) \cdot 1.6666666666666667}}\\ t_2 := \frac{x}{y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{if}\;a \leq -1.32 \cdot 10^{+26}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{-110}:\\ \;\;\;\;\frac{x}{x + \frac{-1.3333333333333333 \cdot \left(y \cdot c\right)}{t}}\\ \mathbf{elif}\;a \leq -2.9 \cdot 10^{-157}:\\ \;\;\;\;\frac{x}{x + y \cdot \left(1 - 2 \cdot \left(b \cdot \left(\left(a + 0.8333333333333334\right) + 0.6666666666666666 \cdot \frac{-1}{t}\right)\right)\right)}\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-220}:\\ \;\;\;\;1\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{-174}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.08 \cdot 10^{-100}:\\ \;\;\;\;1\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{-53}:\\ \;\;\;\;\frac{x}{x + \left(y + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)\right)}\\ \mathbf{elif}\;a \leq 7 \cdot 10^{+103}:\\ \;\;\;\;1\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{+118}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 2.55 \cdot 10^{+147}:\\ \;\;\;\;1\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{+154}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2 \cdot 10^{+281}:\\ \;\;\;\;1\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{+303}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 6
Error	33.1
Cost	8032

\[\begin{array}{l} t_1 := \frac{x}{y \cdot e^{\left(c - b\right) \cdot 1.6666666666666667}}\\ \mathbf{if}\;z \leq -30000:\\ \;\;\;\;1\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-44}:\\ \;\;\;\;\frac{x}{x + \left(y + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)\right)}\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-297}:\\ \;\;\;\;1\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-260}:\\ \;\;\;\;\frac{x}{x - y \cdot \left(-1 + \left(a \cdot \left(c - b\right)\right) \cdot -2\right)}\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-240}:\\ \;\;\;\;1\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-156}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-139}:\\ \;\;\;\;1\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-130}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+107}:\\ \;\;\;\;\left(1 + \frac{x}{x + y}\right) + -1\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+181}:\\ \;\;\;\;\frac{x}{x + \frac{-1.3333333333333333 \cdot \left(y \cdot c\right)}{t}}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 7
Error	20.4
Cost	8024

\[\begin{array}{l} t_1 := \frac{x}{x + y \cdot e^{\left(c - b\right) \cdot 1.6666666666666667}}\\ t_2 := \frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{if}\;a \leq -27:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.95 \cdot 10^{-121}:\\ \;\;\;\;\frac{x}{x + \frac{-1.3333333333333333 \cdot \left(y \cdot c\right)}{t}}\\ \mathbf{elif}\;a \leq -6.5 \cdot 10^{-157}:\\ \;\;\;\;\frac{x}{x + y \cdot \left(1 - 2 \cdot \left(b \cdot \left(\left(a + 0.8333333333333334\right) + 0.6666666666666666 \cdot \frac{-1}{t}\right)\right)\right)}\\ \mathbf{elif}\;a \leq -5.4 \cdot 10^{-261}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{-227}:\\ \;\;\;\;1\\ \mathbf{elif}\;a \leq 10:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 8
Error	20.3
Cost	8024

\[\begin{array}{l} t_1 := \frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ t_2 := \frac{x}{x + y \cdot e^{\left(c - b\right) \cdot 1.6666666666666667}}\\ \mathbf{if}\;a \leq -27:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{-111}:\\ \;\;\;\;\frac{x}{x + \frac{-1.3333333333333333 \cdot \left(y \cdot c\right)}{t}}\\ \mathbf{elif}\;a \leq -6.5 \cdot 10^{-157}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \frac{0.6666666666666666}{t}\right)}}\\ \mathbf{elif}\;a \leq -5.6 \cdot 10^{-262}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-227}:\\ \;\;\;\;1\\ \mathbf{elif}\;a \leq 5000:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 9
Error	12.4
Cost	7884

\[\begin{array}{l} t_1 := \frac{x}{x + y \cdot e^{2 \cdot \left(\left(c - b\right) \cdot \left(a + 0.8333333333333334\right)\right)}}\\ \mathbf{if}\;t \leq -5.2 \cdot 10^{-302}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-104}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{-2 \cdot \left(c \cdot \frac{0.6666666666666666}{t}\right)}}\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-19}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \left(\frac{0.6666666666666666}{t} + \left(-0.8333333333333334 - a\right)\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 10
Error	18.2
Cost	7760

\[\begin{array}{l} t_1 := \frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{if}\;t \leq -2.25 \cdot 10^{-299}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-94}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{-2 \cdot \left(c \cdot \frac{0.6666666666666666}{t}\right)}}\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-22}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \frac{0.6666666666666666}{t}\right)}}\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{+174}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{\left(c - b\right) \cdot 1.6666666666666667}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 11
Error	13.2
Cost	7756

\[\begin{array}{l} t_1 := \frac{x}{x + y \cdot e^{2 \cdot \left(\left(c - b\right) \cdot \left(a + 0.8333333333333334\right)\right)}}\\ \mathbf{if}\;t \leq -1 \cdot 10^{-299}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-102}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{-2 \cdot \left(c \cdot \frac{0.6666666666666666}{t}\right)}}\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{-27}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \frac{0.6666666666666666}{t}\right)}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 12
Error	19.7
Cost	7368

\[\begin{array}{l} t_1 := \frac{x}{x + y \cdot e^{\left(c - b\right) \cdot 1.6666666666666667}}\\ \mathbf{if}\;t \leq -5 \cdot 10^{-310}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 10^{-15}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 13
Error	32.9
Cost	3036

\[\begin{array}{l} \mathbf{if}\;z \leq -9500:\\ \;\;\;\;1\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-46}:\\ \;\;\;\;\frac{x}{x + \left(y + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)\right)}\\ \mathbf{elif}\;z \leq -1.06 \cdot 10^{-296}:\\ \;\;\;\;1\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-261}:\\ \;\;\;\;\frac{x}{x - y \cdot \left(-1 + \left(a \cdot \left(c - b\right)\right) \cdot -2\right)}\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{-72}:\\ \;\;\;\;1\\ \mathbf{elif}\;z \leq 720000000000:\\ \;\;\;\;\frac{x}{x + y \cdot \left(1 - 2 \cdot \left(b \cdot \left(\left(a + 0.8333333333333334\right) + 0.6666666666666666 \cdot \frac{-1}{t}\right)\right)\right)}\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{+27}:\\ \;\;\;\;\frac{x}{x + \frac{\left(-4 \cdot \left(c \cdot c\right)\right) \cdot \left(\left(a \cdot y\right) \cdot \left(a \cdot y\right)\right)}{y + y \cdot \left(\left(a + \left(0.8333333333333334 - \frac{0.6666666666666666}{t}\right)\right) \cdot \left(c \cdot -2\right)\right)}}\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+101}:\\ \;\;\;\;\left(1 + \frac{x}{x + y}\right) + -1\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+188}:\\ \;\;\;\;\frac{x}{x + \frac{-1.3333333333333333 \cdot \left(y \cdot c\right)}{t}}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 14
Error	33.7
Cost	2548

\[\begin{array}{l} t_1 := \frac{x}{x + y}\\ t_2 := \frac{x}{x - y \cdot \left(-1 + \left(a \cdot \left(c - b\right)\right) \cdot -2\right)}\\ t_3 := \frac{x}{y \cdot y - x \cdot x} \cdot \left(y - x\right)\\ \mathbf{if}\;y \leq -9.5 \cdot 10^{+191}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{+158}:\\ \;\;\;\;\frac{x}{x + \left(y - \frac{y \cdot c}{t} \cdot 1.3333333333333333\right)}\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{+111}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -9.2 \cdot 10^{+46}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -2 \cdot 10^{+31}:\\ \;\;\;\;\frac{x}{x + \frac{-1.3333333333333333 \cdot \left(y \cdot c\right)}{t}}\\ \mathbf{elif}\;y \leq -46000:\\ \;\;\;\;\left(1 + t_1\right) + -1\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-165}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-266}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-213}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-152}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-124}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+136}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+169}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 15
Error	33.5
Cost	2548

\[\begin{array}{l} t_1 := \frac{x}{y \cdot y - x \cdot x} \cdot \left(y - x\right)\\ t_2 := \frac{x}{x + y}\\ t_3 := \frac{x}{x - y \cdot \left(-1 + \left(a \cdot \left(c - b\right)\right) \cdot -2\right)}\\ \mathbf{if}\;y \leq -5.2 \cdot 10^{+191}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{+164}:\\ \;\;\;\;\frac{x}{x + \left(y + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)\right)}\\ \mathbf{elif}\;y \leq -2.22 \cdot 10^{+111}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{+46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.12 \cdot 10^{+31}:\\ \;\;\;\;\frac{x}{x + \frac{-1.3333333333333333 \cdot \left(y \cdot c\right)}{t}}\\ \mathbf{elif}\;y \leq -200000:\\ \;\;\;\;\left(1 + t_2\right) + -1\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-169}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-273}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-213}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{-151}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{-125}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 2.45 \cdot 10^{+138}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+167}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 16
Error	33.3
Cost	2548

\[\begin{array}{l} t_1 := \frac{x}{y \cdot y - x \cdot x} \cdot \left(y - x\right)\\ t_2 := \frac{x}{x + y}\\ t_3 := \frac{x}{x - y \cdot \left(-1 + \left(a \cdot \left(c - b\right)\right) \cdot -2\right)}\\ \mathbf{if}\;y \leq -3.6 \cdot 10^{+191}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{+156}:\\ \;\;\;\;\frac{x}{x + \left(y + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)\right)}\\ \mathbf{elif}\;y \leq -9.4 \cdot 10^{+111}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -5.6 \cdot 10^{+47}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{+31}:\\ \;\;\;\;\frac{x}{x + \frac{-1.3333333333333333 \cdot \left(y \cdot c\right)}{t}}\\ \mathbf{elif}\;y \leq -100000000:\\ \;\;\;\;\left(1 + t_2\right) + -1\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{-164}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-265}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-205}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-154}:\\ \;\;\;\;\frac{x}{x + y \cdot \left(1 + 2 \cdot \left(c \cdot \left(0.8333333333333334 + \left(a - \frac{0.6666666666666666}{t}\right)\right)\right)\right)}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-124}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{+136}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2.45 \cdot 10^{+166}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 17
Error	32.9
Cost	2136

\[\begin{array}{l} t_1 := \frac{x}{x + y \cdot \left(1 - 2 \cdot \left(b \cdot \left(\left(a + 0.8333333333333334\right) + 0.6666666666666666 \cdot \frac{-1}{t}\right)\right)\right)}\\ \mathbf{if}\;x \leq -2.9 \cdot 10^{-131}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -1.78 \cdot 10^{-273}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-278}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{-263}:\\ \;\;\;\;-0.75 \cdot \frac{x \cdot t}{y \cdot c}\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-170}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 10^{-100}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{+169}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{+224}:\\ \;\;\;\;\frac{x}{x + \left(y + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x - y \cdot \left(-1 + 2 \cdot \left(c \cdot \frac{0.6666666666666666}{t}\right)\right)}\\ \end{array} \]

Alternative 18
Error	32.2
Cost	1888

\[\begin{array}{l} t_1 := \frac{x}{y \cdot y - x \cdot x} \cdot \left(y - x\right)\\ \mathbf{if}\;y \leq -2.3 \cdot 10^{+188}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{+163}:\\ \;\;\;\;0.5 \cdot \frac{\frac{\frac{x}{c}}{y}}{a}\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{+111}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -4 \cdot 10^{+47}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -9 \cdot 10^{+30}:\\ \;\;\;\;\frac{x}{x + \frac{-1.3333333333333333 \cdot \left(y \cdot c\right)}{t}}\\ \mathbf{elif}\;y \leq -5000:\\ \;\;\;\;\left(1 + \frac{x}{x + y}\right) + -1\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+139}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{+166}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 19
Error	32.0
Cost	1888

\[\begin{array}{l} t_1 := \frac{x}{y \cdot y - x \cdot x} \cdot \left(y - x\right)\\ \mathbf{if}\;y \leq -2.4 \cdot 10^{+191}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -9 \cdot 10^{+160}:\\ \;\;\;\;\frac{x}{x + \left(y - \frac{y \cdot c}{t} \cdot 1.3333333333333333\right)}\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{+112}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -5 \cdot 10^{+47}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2 \cdot 10^{+31}:\\ \;\;\;\;\frac{x}{x + \frac{-1.3333333333333333 \cdot \left(y \cdot c\right)}{t}}\\ \mathbf{elif}\;y \leq -640000:\\ \;\;\;\;\left(1 + \frac{x}{x + y}\right) + -1\\ \mathbf{elif}\;y \leq 1.42 \cdot 10^{+138}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2.45 \cdot 10^{+166}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 20
Error	31.3
Cost	1236

\[\begin{array}{l} t_1 := \left(1 + \frac{x}{x + y}\right) + -1\\ \mathbf{if}\;a \leq -2 \cdot 10^{-90}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-101}:\\ \;\;\;\;1\\ \mathbf{elif}\;a \leq 9.8 \cdot 10^{-52}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{+280}:\\ \;\;\;\;1\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{+305}:\\ \;\;\;\;0.5 \cdot \frac{x}{c \cdot \left(a \cdot y\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 21
Error	31.4
Cost	976

\[\begin{array}{l} t_1 := \left(1 + \frac{x}{y}\right) + -1\\ \mathbf{if}\;x \leq 8 \cdot 10^{-290}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.18 \cdot 10^{-262}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-170}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-123}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 22
Error	31.5
Cost	976

\[\begin{array}{l} \mathbf{if}\;x \leq 8 \cdot 10^{-277}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{-262}:\\ \;\;\;\;-0.75 \cdot \frac{x \cdot t}{y \cdot c}\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-170}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-123}:\\ \;\;\;\;\left(1 + \frac{x}{y}\right) + -1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 23
Error	31.4
Cost	584

\[\begin{array}{l} \mathbf{if}\;y \leq 6.2 \cdot 10^{+139}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2.45 \cdot 10^{+166}:\\ \;\;\;\;\frac{x}{x + y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 24
Error	31.6
Cost	456

\[\begin{array}{l} \mathbf{if}\;y \leq 6.2 \cdot 10^{+139}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+166}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 25
Error	31.2
Cost	64

\[1 \]

Reproduce

herbie shell --seed 2022329 
(FPCore (x y z t a b c)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, I"
  :precision binary64

  :herbie-target
  (if (< t -2.118326644891581e-50) (/ x (+ x (* y (exp (* 2.0 (- (+ (* a c) (* 0.8333333333333334 c)) (* a b))))))) (if (< t 5.196588770651547e-123) (/ x (+ x (* y (exp (* 2.0 (/ (- (* (* z (sqrt (+ t a))) (* (* 3.0 t) (- a (/ 5.0 6.0)))) (* (- (* (+ (/ 5.0 6.0) a) (* 3.0 t)) 2.0) (* (- a (/ 5.0 6.0)) (* (- b c) t)))) (* (* (* t t) 3.0) (- a (/ 5.0 6.0))))))))) (/ x (+ x (* y (exp (* 2.0 (- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))))))))))

  (/ x (+ x (* y (exp (* 2.0 (- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))))))))