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

Average Accuracy: 94.0% → 97.8%

Time: 43.4s

Precision: binary64

Cost: 33673

Math

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

↓

\[\begin{array}{l} t_1 := \sqrt{t + a}\\ \mathbf{if}\;z \leq -2 \cdot 10^{+62} \lor \neg \left(z \leq 5 \cdot 10^{-39}\right):\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(y, {\left(e^{2}\right)}^{\left(\mathsf{fma}\left(b - c, \frac{0.6666666666666666}{t} + \left(-0.8333333333333334 - a\right), z \cdot \frac{t_1}{t}\right)\right)}, x\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot t_1}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} + \left(-0.8333333333333334 - a\right)\right)\right)}}\\ \end{array} \]

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 (+ t a))))
   (if (or (<= z -2e+62) (not (<= z 5e-39)))
     (/
      x
      (fma
       y
       (pow
        (exp 2.0)
        (fma
         (- b c)
         (+ (/ 0.6666666666666666 t) (- -0.8333333333333334 a))
         (* z (/ t_1 t))))
       x))
     (/
      x
      (+
       x
       (*
        y
        (exp
         (*
          2.0
          (+
           (/ (* z t_1) t)
           (* (- b c) (+ (/ 2.0 (* t 3.0)) (- -0.8333333333333334 a))))))))))))

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((t + a));
	double tmp;
	if ((z <= -2e+62) || !(z <= 5e-39)) {
		tmp = x / fma(y, pow(exp(2.0), fma((b - c), ((0.6666666666666666 / t) + (-0.8333333333333334 - a)), (z * (t_1 / t)))), x);
	} else {
		tmp = x / (x + (y * exp((2.0 * (((z * t_1) / t) + ((b - c) * ((2.0 / (t * 3.0)) + (-0.8333333333333334 - a))))))));
	}
	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(t + a))
	tmp = 0.0
	if ((z <= -2e+62) || !(z <= 5e-39))
		tmp = Float64(x / fma(y, (exp(2.0) ^ fma(Float64(b - c), Float64(Float64(0.6666666666666666 / t) + Float64(-0.8333333333333334 - a)), Float64(z * Float64(t_1 / t)))), x));
	else
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(Float64(z * t_1) / t) + Float64(Float64(b - c) * Float64(Float64(2.0 / Float64(t * 3.0)) + Float64(-0.8333333333333334 - a)))))))));
	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[(t + a), $MachinePrecision]], $MachinePrecision]}, If[Or[LessEqual[z, -2e+62], N[Not[LessEqual[z, 5e-39]], $MachinePrecision]], N[(x / N[(y * N[Power[N[Exp[2.0], $MachinePrecision], N[(N[(b - c), $MachinePrecision] * N[(N[(0.6666666666666666 / t), $MachinePrecision] + N[(-0.8333333333333334 - a), $MachinePrecision]), $MachinePrecision] + N[(z * N[(t$95$1 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(N[(z * t$95$1), $MachinePrecision] / t), $MachinePrecision] + N[(N[(b - c), $MachinePrecision] * N[(N[(2.0 / N[(t * 3.0), $MachinePrecision]), $MachinePrecision] + N[(-0.8333333333333334 - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Target

Original	94.0%
Target	95.4%
Herbie	97.8%

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

Derivation

1. Split input into 2 regimes

2. if z < -2.00000000000000007e62 or 4.9999999999999998e-39 < z

   1. Initial program 87.9%

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

   2. Simplified 95.8%

      \[\leadsto \color{blue}{\frac{x}{\mathsf{fma}\left(y, {\left(e^{2}\right)}^{\left(\mathsf{fma}\left(b - c, \frac{0.6666666666666666}{t} - \left(a + 0.8333333333333334\right), z \cdot \frac{\sqrt{t + a}}{t}\right)\right)}, x\right)}} \]
      Proof

      [Start] 87.9	\[ \frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]
      +-commutative [=>] 87.9	\[ \frac{x}{\color{blue}{y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)} + x}} \]
      fma-def [=>] 87.9	\[ \frac{x}{\color{blue}{\mathsf{fma}\left(y, e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}, x\right)}} \]

   if -2.00000000000000007e62 < z < 4.9999999999999998e-39

   1. Initial program 99.5%

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

4. Final simplification 97.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+62} \lor \neg \left(z \leq 5 \cdot 10^{-39}\right):\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(y, {\left(e^{2}\right)}^{\left(\mathsf{fma}\left(b - c, \frac{0.6666666666666666}{t} + \left(-0.8333333333333334 - a\right), z \cdot \frac{\sqrt{t + a}}{t}\right)\right)}, x\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} + \left(-0.8333333333333334 - a\right)\right)\right)}}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	96.9%
Cost	22468

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

Alternative 2
Accuracy	74.5%
Cost	14800

\[\begin{array}{l} t_1 := \frac{x}{x + y \cdot e^{2 \cdot \left(\left(b - c\right) \cdot \left(-0.8333333333333334 - a\right)\right)}}\\ \mathbf{if}\;b - c \leq -1 \cdot 10^{+199}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b - c \leq -5 \cdot 10^{+154}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \left(\frac{0.6666666666666666}{t} + \left(-0.8333333333333334 - a\right)\right)\right)}}\\ \mathbf{elif}\;b - c \leq -40000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b - c \leq 4 \cdot 10^{+60}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\sqrt{t + a} \cdot \frac{z}{t}\right)}}\\ \mathbf{elif}\;b - c \leq 10^{+178}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(a + \left(0.8333333333333334 + \frac{-0.6666666666666666}{t}\right)\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Accuracy	80.7%
Cost	8140

\[\begin{array}{l} t_1 := \frac{x}{x + y \cdot e^{2 \cdot \frac{\left(c - b\right) \cdot \left(a \cdot a + -0.6944444444444444\right)}{a + -0.8333333333333334}}}\\ \mathbf{if}\;t \leq -5 \cdot 10^{-304}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-174}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(a + \left(0.8333333333333334 + \frac{-0.6666666666666666}{t}\right)\right)\right)}}\\ \mathbf{elif}\;t \leq 1.22 \cdot 10^{-23}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \left(\frac{0.6666666666666666}{t} + \left(-0.8333333333333334 - a\right)\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Accuracy	55.0%
Cost	8032

\[\begin{array}{l} t_1 := \frac{x}{x + y \cdot e^{b \cdot -1.6666666666666667}}\\ \mathbf{if}\;c \leq -4.8 \cdot 10^{+201}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -2 \cdot 10^{+141}:\\ \;\;\;\;\frac{x}{x + -1.3333333333333333 \cdot \frac{y}{\frac{t}{c}}}\\ \mathbf{elif}\;c \leq -5.4 \cdot 10^{+81}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -5.3 \cdot 10^{-92}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -2.45 \cdot 10^{-129}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 8 \cdot 10^{-212}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 2.5 \cdot 10^{-169}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 1.02 \cdot 10^{+137}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + \left(y + 2 \cdot \left(y \cdot \left(a \cdot \left(c - b\right)\right)\right)\right)}\\ \end{array} \]

Alternative 5
Accuracy	57.7%
Cost	8032

\[\begin{array}{l} t_1 := \frac{x}{x + y \cdot e^{b \cdot -1.6666666666666667}}\\ \mathbf{if}\;c \leq -4.8 \cdot 10^{+201}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -1.05 \cdot 10^{+143}:\\ \;\;\;\;\frac{x}{x + -1.3333333333333333 \cdot \frac{y}{\frac{t}{c}}}\\ \mathbf{elif}\;c \leq -7.2 \cdot 10^{+81}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -4.2 \cdot 10^{-92}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -4.4 \cdot 10^{-130}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 1.5 \cdot 10^{-211}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 8.5 \cdot 10^{-169}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 4.3 \cdot 10^{-38}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{c \cdot 1.6666666666666667}}\\ \end{array} \]

Alternative 6
Accuracy	78.7%
Cost	8016

\[\begin{array}{l} t_1 := \frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{if}\;t \leq -1.15 \cdot 10^{-304}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{-170}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \frac{-0.6666666666666666}{t}\right)}}\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-135}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.44 \cdot 10^{-21}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \left(\frac{0.6666666666666666}{t} + \left(-0.8333333333333334 - a\right)\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(b - c\right) \cdot \left(-0.8333333333333334 - a\right)\right)}}\\ \end{array} \]

Alternative 7
Accuracy	68.9%
Cost	7892

\[\begin{array}{l} t_1 := \frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{if}\;t \leq -8.4 \cdot 10^{-305}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.35 \cdot 10^{-173}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-97}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-60}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(0.6666666666666666 \cdot \frac{b}{t}\right)}}\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+222}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{\left(b - c\right) \cdot -1.6666666666666667}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Accuracy	80.5%
Cost	7884

\[\begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{-304}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-182}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(a + \left(0.8333333333333334 + \frac{-0.6666666666666666}{t}\right)\right)\right)}}\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-13}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \left(\frac{0.6666666666666666}{t} + \left(-0.8333333333333334 - a\right)\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(b - c\right) \cdot \left(-0.8333333333333334 - a\right)\right)}}\\ \end{array} \]

Alternative 9
Accuracy	70.1%
Cost	7761

\[\begin{array}{l} t_1 := \frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{if}\;t \leq -8.4 \cdot 10^{-305}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-170}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \frac{-0.6666666666666666}{t}\right)}}\\ \mathbf{elif}\;t \leq 2.35 \cdot 10^{-63} \lor \neg \left(t \leq 1.2 \cdot 10^{+225}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{\left(b - c\right) \cdot -1.6666666666666667}}\\ \end{array} \]

Alternative 10
Accuracy	67.7%
Cost	7760

\[\begin{array}{l} t_1 := \frac{x}{x + y \cdot e^{\left(b - c\right) \cdot -1.6666666666666667}}\\ \mathbf{if}\;t \leq -8.4 \cdot 10^{-305}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-168}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-101}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{b \cdot -1.6666666666666667}}\\ \mathbf{elif}\;t \leq 6.1 \cdot 10^{-61}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(0.6666666666666666 \cdot \frac{b}{t}\right)}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 11
Accuracy	76.4%
Cost	7756

\[\begin{array}{l} t_1 := \frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{if}\;t \leq -1.8 \cdot 10^{-304}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-172}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \frac{-0.6666666666666666}{t}\right)}}\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-63}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(b - c\right) \cdot \left(-0.8333333333333334 - a\right)\right)}}\\ \end{array} \]

Alternative 12
Accuracy	66.2%
Cost	7632

\[\begin{array}{l} t_1 := \frac{x}{x + y \cdot e^{\left(b - c\right) \cdot -1.6666666666666667}}\\ \mathbf{if}\;t \leq -8.4 \cdot 10^{-305}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-168}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-96}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{b \cdot -1.6666666666666667}}\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+32}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{c \cdot 1.6666666666666667}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 13
Accuracy	56.4%
Cost	6980

\[\begin{array}{l} \mathbf{if}\;b \leq -150:\\ \;\;\;\;\frac{x}{y \cdot e^{b \cdot -1.6666666666666667}}\\ \mathbf{elif}\;b \leq -6.5 \cdot 10^{-274}:\\ \;\;\;\;1\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{-267} \lor \neg \left(b \leq 2.1 \cdot 10^{-146}\right) \land b \leq 4.2 \cdot 10^{-48}:\\ \;\;\;\;\frac{x}{x + y \cdot \left(1 + -1.3333333333333333 \cdot \frac{c}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 14
Accuracy	50.6%
Cost	2000

\[\begin{array}{l} \mathbf{if}\;c \leq -5.2 \cdot 10^{+201}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -2.2 \cdot 10^{+144}:\\ \;\;\;\;\frac{x}{x + -1.3333333333333333 \cdot \frac{y}{\frac{t}{c}}}\\ \mathbf{elif}\;c \leq -2.2 \cdot 10^{+49}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -1.65 \cdot 10^{-47}:\\ \;\;\;\;\frac{x}{y + \left(x + 2 \cdot \frac{\left(y \cdot a\right) \cdot \left(c \cdot c - b \cdot b\right)}{b + c}\right)}\\ \mathbf{elif}\;c \leq 1.75 \cdot 10^{+137}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + \left(y + 2 \cdot \left(y \cdot \left(a \cdot \left(c - b\right)\right)\right)\right)}\\ \end{array} \]

Alternative 15
Accuracy	45.9%
Cost	1894

\[\begin{array}{l} \mathbf{if}\;a \leq -2.5 \cdot 10^{+63}:\\ \;\;\;\;\frac{x}{x + -1.3333333333333333 \cdot \frac{y}{\frac{t}{c}}}\\ \mathbf{elif}\;a \leq -3.7 \cdot 10^{-282}:\\ \;\;\;\;\frac{x}{x + \left(y - 1.6666666666666667 \cdot \left(y \cdot b\right)\right)}\\ \mathbf{elif}\;a \leq -3.6 \cdot 10^{-282}:\\ \;\;\;\;-0.75 \cdot \left(\frac{t}{c} \cdot \frac{x}{y}\right)\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{+64}:\\ \;\;\;\;1\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{+107} \lor \neg \left(a \leq 6.8 \cdot 10^{+137}\right) \land \left(a \leq 1.7 \cdot 10^{+185} \lor \neg \left(a \leq 8.8 \cdot 10^{+253}\right) \land a \leq 2.9 \cdot 10^{+300}\right):\\ \;\;\;\;0.5 \cdot \frac{x}{y \cdot \left(a \cdot \left(c - b\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 16
Accuracy	45.9%
Cost	1892

\[\begin{array}{l} t_1 := \frac{x}{y - y \cdot \left(\left(b - c\right) \cdot \left(2 \cdot a\right)\right)}\\ \mathbf{if}\;a \leq -1.8 \cdot 10^{+51}:\\ \;\;\;\;\frac{x}{x + -1.3333333333333333 \cdot \frac{y}{\frac{t}{c}}}\\ \mathbf{elif}\;a \leq -3.7 \cdot 10^{-282}:\\ \;\;\;\;\frac{x}{x + \left(y - 1.6666666666666667 \cdot \left(y \cdot b\right)\right)}\\ \mathbf{elif}\;a \leq -3.6 \cdot 10^{-282}:\\ \;\;\;\;-0.75 \cdot \left(\frac{t}{c} \cdot \frac{x}{y}\right)\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{+64}:\\ \;\;\;\;1\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{+108}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{+137}:\\ \;\;\;\;1\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{+184}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{+253}:\\ \;\;\;\;1\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+300}:\\ \;\;\;\;0.5 \cdot \frac{x}{y \cdot \left(a \cdot \left(c - b\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 17
Accuracy	45.5%
Cost	1630

\[\begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{-282}:\\ \;\;\;\;\frac{x}{x + -1.3333333333333333 \cdot \frac{y}{\frac{t}{c}}}\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{+64}:\\ \;\;\;\;1\\ \mathbf{elif}\;a \leq 4 \cdot 10^{+108} \lor \neg \left(a \leq 7.6 \cdot 10^{+137}\right) \land \left(a \leq 3.05 \cdot 10^{+184} \lor \neg \left(a \leq 2.7 \cdot 10^{+253}\right) \land a \leq 6.2 \cdot 10^{+299}\right):\\ \;\;\;\;0.5 \cdot \frac{x}{y \cdot \left(a \cdot \left(c - b\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 18
Accuracy	50.3%
Cost	1621

\[\begin{array}{l} \mathbf{if}\;c \leq -4.8 \cdot 10^{+201}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -1.8 \cdot 10^{+141}:\\ \;\;\;\;\frac{x}{x + -1.3333333333333333 \cdot \frac{y}{\frac{t}{c}}}\\ \mathbf{elif}\;c \leq -2.5 \cdot 10^{+49}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -1.75 \cdot 10^{-47} \lor \neg \left(c \leq 2.2 \cdot 10^{+137}\right):\\ \;\;\;\;\frac{x}{x + \left(y + 2 \cdot \left(y \cdot \left(a \cdot \left(c - b\right)\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 19
Accuracy	50.0%
Cost	1620

\[\begin{array}{l} \mathbf{if}\;c \leq -5.2 \cdot 10^{+201}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -5.5 \cdot 10^{+144}:\\ \;\;\;\;\frac{x}{x + -1.3333333333333333 \cdot \frac{y}{\frac{t}{c}}}\\ \mathbf{elif}\;c \leq -2.7 \cdot 10^{+81}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -1.75 \cdot 10^{-47}:\\ \;\;\;\;\frac{x}{y + \left(x + -2 \cdot \left(a \cdot \left(y \cdot \left(b - c\right)\right)\right)\right)}\\ \mathbf{elif}\;c \leq 1.52 \cdot 10^{+137}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + \left(y + 2 \cdot \left(y \cdot \left(a \cdot \left(c - b\right)\right)\right)\right)}\\ \end{array} \]

Alternative 20
Accuracy	48.0%
Cost	1498

\[\begin{array}{l} \mathbf{if}\;a \leq 9 \cdot 10^{+64}:\\ \;\;\;\;1\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{+107} \lor \neg \left(a \leq 6.2 \cdot 10^{+137}\right) \land \left(a \leq 6.5 \cdot 10^{+184} \lor \neg \left(a \leq 8.2 \cdot 10^{+253}\right) \land a \leq 9.2 \cdot 10^{+299}\right):\\ \;\;\;\;0.5 \cdot \frac{x}{y \cdot \left(a \cdot \left(c - b\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 21
Accuracy	50.2%
Cost	840

\[\begin{array}{l} \mathbf{if}\;x \leq 5 \cdot 10^{-281}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-225}:\\ \;\;\;\;-0.75 \cdot \left(\frac{t}{c} \cdot \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 22
Accuracy	50.0%
Cost	840

\[\begin{array}{l} \mathbf{if}\;x \leq 7.6 \cdot 10^{-276}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 5.4 \cdot 10^{-212}:\\ \;\;\;\;-0.75 \cdot \frac{x \cdot t}{y \cdot c}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 23
Accuracy	51.2%
Cost	708

\[\begin{array}{l} \mathbf{if}\;c \leq 2.2 \cdot 10^{+137}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x}{c \cdot \left(y \cdot a\right)}\\ \end{array} \]

Alternative 24
Accuracy	51.9%
Cost	708

\[\begin{array}{l} \mathbf{if}\;c \leq 10^{+137}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 0.5}{a \cdot \left(y \cdot c\right)}\\ \end{array} \]

Alternative 25
Accuracy	50.5%
Cost	456

\[\begin{array}{l} \mathbf{if}\;y \leq 1.2 \cdot 10^{+180}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+218}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 26
Accuracy	51.1%
Cost	64

\[1 \]

Reproduce

herbie shell --seed 2023140 
(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)))))))))))