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

Average Accuracy: 93.6% → 97.1%

Time: 39.7s

Precision: binary64

Cost: 33408

Math

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

↓

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

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
 (/
  x
  (fma
   y
   (pow
    (exp 2.0)
    (fma
     (- b c)
     (+ (/ 0.6666666666666666 t) (- -0.8333333333333334 a))
     (* (sqrt (+ t a)) (/ z t))))
   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) {
	return x / fma(y, pow(exp(2.0), fma((b - c), ((0.6666666666666666 / t) + (-0.8333333333333334 - a)), (sqrt((t + a)) * (z / t)))), x);
}

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)
	return Float64(x / fma(y, (exp(2.0) ^ fma(Float64(b - c), Float64(Float64(0.6666666666666666 / t) + Float64(-0.8333333333333334 - a)), Float64(sqrt(Float64(t + a)) * Float64(z / t)))), x))
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_] := 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[(N[Sqrt[N[(t + a), $MachinePrecision]], $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision]

Target

Original	93.6%
Target	95.2%
Herbie	97.1%

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

Derivation

1. Initial program 93.6%

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

2. Simplified 97.1%

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

   [Start] 93.6	\[ \frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]
   +-commutative [=>] 93.6	\[ \frac{x}{\color{blue}{y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)} + x}} \]
   fma-def [=>] 93.6	\[ \frac{x}{\color{blue}{\mathsf{fma}\left(y, e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}, x\right)}} \]

3. Final simplification 97.1%

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

Alternatives

Alternative 1
Accuracy	97.1%
Cost	41220

\[\begin{array}{l} t_1 := \sqrt{t + a}\\ \mathbf{if}\;\frac{t_1 \cdot z}{t} - \left(c - b\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + 0.8333333333333334\right)\right) \leq \infty:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(y, {\left(e^{2}\right)}^{\left(\mathsf{fma}\left(t_1, \frac{z}{t}, \left(b - c\right) \cdot \left(\left(\frac{0.6666666666666666}{t} + -0.8333333333333334\right) - a\right)\right)\right)}, x\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 2
Accuracy	96.8%
Cost	28804

\[\begin{array}{l} t_1 := \frac{2}{t \cdot 3} - \left(a + 0.8333333333333334\right)\\ t_2 := \sqrt{t + a}\\ \mathbf{if}\;\frac{t_2 \cdot z}{t} - \left(c - b\right) \cdot t_1 \leq \infty:\\ \;\;\;\;\frac{x}{x + y \cdot {\left(e^{2}\right)}^{\left(\frac{z}{\frac{t}{t_2}} + \left(b - c\right) \cdot t_1\right)}}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 3
Accuracy	96.4%
Cost	22468

\[\begin{array}{l} t_1 := \frac{\sqrt{t + a} \cdot z}{t} - \left(c - b\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + 0.8333333333333334\right)\right)\\ \mathbf{if}\;t_1 \leq \infty:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot t_1}}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 4
Accuracy	56.6%
Cost	8688

\[\begin{array}{l} t_1 := \frac{x}{x + y \cdot e^{2 \cdot \left(-0.6666666666666666 \cdot \frac{c}{t}\right)}}\\ t_2 := \frac{x}{x + y \cdot e^{\left(c - b\right) \cdot 1.6666666666666667}}\\ \mathbf{if}\;x \leq -5 \cdot 10^{+286}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -3 \cdot 10^{+82}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -3.7 \cdot 10^{+22}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -8.6 \cdot 10^{-93}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2.25 \cdot 10^{-122}:\\ \;\;\;\;\frac{x}{x + \frac{-1.3333333333333333}{\frac{t}{y \cdot c}}}\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-304}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-293}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-182}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-66}:\\ \;\;\;\;\left(1 + \frac{x}{x + y}\right) + -1\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-12}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 63000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+213}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 5
Accuracy	56.6%
Cost	8424

\[\begin{array}{l} t_1 := \frac{x}{x + y \cdot e^{\left(c - b\right) \cdot 1.6666666666666667}}\\ \mathbf{if}\;x \leq -4 \cdot 10^{+280}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -3.7 \cdot 10^{+185}:\\ \;\;\;\;\frac{x}{y \cdot y - x \cdot x} \cdot \left(y - x\right)\\ \mathbf{elif}\;x \leq -4.6 \cdot 10^{+82}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-305}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-293}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-183}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-67}:\\ \;\;\;\;\left(1 + \frac{x}{x + y}\right) + -1\\ \mathbf{elif}\;x \leq 4 \cdot 10^{-9}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 19000000:\\ \;\;\;\;\frac{x}{y \cdot e^{\frac{c}{t} \cdot -1.3333333333333333}}\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+214}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 6
Accuracy	46.0%
Cost	8292

\[\begin{array}{l} t_1 := \frac{x}{y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ t_2 := \left(1 + \frac{x}{x + y}\right) + -1\\ \mathbf{if}\;y \leq -3.1 \cdot 10^{+154}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{+36}:\\ \;\;\;\;\frac{x}{x + \frac{-1.3333333333333333}{\frac{t}{y \cdot c}}}\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{+18}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-54}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-97}:\\ \;\;\;\;\frac{x}{x - y \cdot \left(-1 - \frac{c}{t} \cdot -1.3333333333333333\right)}\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-108}:\\ \;\;\;\;\frac{x}{y \cdot e^{\left(c - b\right) \cdot 1.6666666666666667}}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-196}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-92}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-9}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.15 \cdot 10^{+149}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 10^{+216}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+252}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\left(1 + \frac{x}{y}\right) + -1\\ \end{array} \]

Alternative 7
Accuracy	81.0%
Cost	8280

\[\begin{array}{l} t_1 := \frac{x}{x + y \cdot e^{2 \cdot \left(\left(a + 0.8333333333333334\right) \cdot \left(c - b\right)\right)}}\\ t_2 := \frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(a - \left(\frac{0.6666666666666666}{t} - 0.8333333333333334\right)\right)\right)}}\\ \mathbf{if}\;t \leq -2 \cdot 10^{-287}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.75 \cdot 10^{-303}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{b}{\frac{t}{0.6666666666666666}}}}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-303}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-92}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-42}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \left(\frac{0.6666666666666666}{t} - \left(a + 0.8333333333333334\right)\right)\right)}}\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{-6}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Accuracy	68.2%
Cost	8156

\[\begin{array}{l} t_1 := \frac{x}{x + y \cdot e^{\left(c - b\right) \cdot 1.6666666666666667}}\\ t_2 := \frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{if}\;t \leq -2.1 \cdot 10^{-294}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-200}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 10^{-17}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(-0.6666666666666666 \cdot \frac{c}{t}\right)}}\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{+54}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 6.7 \cdot 10^{+230}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{+282}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{+297}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 9
Accuracy	69.2%
Cost	8156

\[\begin{array}{l} t_1 := \frac{x}{x + y \cdot e^{\left(c - b\right) \cdot 1.6666666666666667}}\\ t_2 := \frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{if}\;t \leq -4 \cdot 10^{-287}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-303}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{b}{\frac{t}{0.6666666666666666}}}}\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-17}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(-0.6666666666666666 \cdot \frac{c}{t}\right)}}\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{+54}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+229}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{+282}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{+297}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 10
Accuracy	79.9%
Cost	8020

\[\begin{array}{l} t_1 := \frac{x}{x + y \cdot e^{2 \cdot \left(-0.6666666666666666 \cdot \frac{c}{t}\right)}}\\ t_2 := \frac{x}{x + y \cdot e^{2 \cdot \left(\left(a + 0.8333333333333334\right) \cdot \left(c - b\right)\right)}}\\ t_3 := \frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \left(\frac{0.6666666666666666}{t} - \left(a + 0.8333333333333334\right)\right)\right)}}\\ \mathbf{if}\;t \leq -7.5 \cdot 10^{-288}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-203}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-93}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-26}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{-17}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 11
Accuracy	51.3%
Cost	7900

\[\begin{array}{l} t_1 := \left(1 + \frac{x}{x + y}\right) + -1\\ t_2 := \frac{x}{y \cdot e^{\frac{c}{t} \cdot -1.3333333333333333}}\\ \mathbf{if}\;z \leq -1.6 \cdot 10^{+71}:\\ \;\;\;\;1\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-66}:\\ \;\;\;\;\frac{x}{x - y \cdot \left(-1 + \left(2 \cdot c\right) \cdot \left(\left(\frac{0.6666666666666666}{t} - a\right) - 0.8333333333333334\right)\right)}\\ \mathbf{elif}\;z \leq -2.25 \cdot 10^{-135}:\\ \;\;\;\;1\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-143}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-291}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-233}:\\ \;\;\;\;1\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-230}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-147}:\\ \;\;\;\;\frac{x}{x + y \cdot \left(1 + a \cdot \left(2 \cdot \left(c - b\right)\right)\right)}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+175}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 12
Accuracy	78.4%
Cost	7888

\[\begin{array}{l} t_1 := \frac{x}{x + y \cdot e^{2 \cdot \left(\left(a + 0.8333333333333334\right) \cdot \left(c - b\right)\right)}}\\ \mathbf{if}\;t \leq -5 \cdot 10^{-287}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.75 \cdot 10^{-303}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{b}{\frac{t}{0.6666666666666666}}}}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-302}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 10^{-17}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(-0.6666666666666666 \cdot \frac{c}{t}\right)}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 13
Accuracy	52.4%
Cost	7240

\[\begin{array}{l} t_1 := \left(1 + \frac{x}{x + y}\right) + -1\\ \mathbf{if}\;b \leq -2.2 \cdot 10^{+168}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -2.5 \cdot 10^{+35}:\\ \;\;\;\;\frac{x}{y \cdot e^{\left(c - b\right) \cdot 1.6666666666666667}}\\ \mathbf{elif}\;b \leq -3.4 \cdot 10^{-105}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -1.4 \cdot 10^{-218}:\\ \;\;\;\;1\\ \mathbf{elif}\;b \leq -6.4 \cdot 10^{-288} \lor \neg \left(b \leq 9.2 \cdot 10^{-57}\right) \land b \leq 1.95 \cdot 10^{+46}:\\ \;\;\;\;\frac{x}{y \cdot y - x \cdot x} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 14
Accuracy	46.4%
Cost	2008

\[\begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+158}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{+36}:\\ \;\;\;\;\frac{x}{x + \frac{-1.3333333333333333}{\frac{t}{y \cdot c}}}\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{+18}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-87}:\\ \;\;\;\;\frac{x}{y \cdot y - x \cdot x} \cdot \left(y - x\right)\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{-150}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-9}:\\ \;\;\;\;\frac{x}{x - y \cdot \left(-1 + \left(2 \cdot c\right) \cdot \left(\left(\frac{0.6666666666666666}{t} - a\right) - 0.8333333333333334\right)\right)}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+150}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2.55 \cdot 10^{+216}:\\ \;\;\;\;\left(1 + \frac{x}{x + y}\right) + -1\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+252}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\left(1 + \frac{x}{y}\right) + -1\\ \end{array} \]

Alternative 15
Accuracy	51.7%
Cost	1493

\[\begin{array}{l} \mathbf{if}\;b \leq -1.1 \cdot 10^{-103}:\\ \;\;\;\;\left(1 + \frac{x}{x + y}\right) + -1\\ \mathbf{elif}\;b \leq -4.1 \cdot 10^{-219}:\\ \;\;\;\;1\\ \mathbf{elif}\;b \leq -2.6 \cdot 10^{-290} \lor \neg \left(b \leq 9 \cdot 10^{-57}\right) \land b \leq 7.4 \cdot 10^{+45}:\\ \;\;\;\;\frac{x}{y \cdot y - x \cdot x} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 16
Accuracy	49.1%
Cost	1372

\[\begin{array}{l} t_1 := \left(1 + \frac{x}{x + y}\right) + -1\\ \mathbf{if}\;y \leq -7.2 \cdot 10^{+154}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -9 \cdot 10^{+36}:\\ \;\;\;\;\frac{x}{x + \frac{-1.3333333333333333}{\frac{t}{y \cdot c}}}\\ \mathbf{elif}\;y \leq -102000000000:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-108}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 10^{+149}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{+215}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+247}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\left(1 + \frac{x}{y}\right) + -1\\ \end{array} \]

Alternative 17
Accuracy	48.5%
Cost	977

\[\begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{-99}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{-304} \lor \neg \left(x \leq 3.5 \cdot 10^{-152}\right) \land x \leq 3.8 \cdot 10^{-75}:\\ \;\;\;\;\left(1 + \frac{x}{y}\right) + -1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 18
Accuracy	50.9%
Cost	973

\[\begin{array}{l} \mathbf{if}\;a \leq 1.65 \cdot 10^{-199} \lor \neg \left(a \leq 1.65 \cdot 10^{-43}\right) \land a \leq 3 \cdot 10^{+151}:\\ \;\;\;\;\left(1 + \frac{x}{x + y}\right) + -1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 19
Accuracy	50.8%
Cost	584

\[\begin{array}{l} \mathbf{if}\;t \leq 1.4 \cdot 10^{+150}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+180}:\\ \;\;\;\;\frac{x}{x + y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 20
Accuracy	49.8%
Cost	456

\[\begin{array}{l} \mathbf{if}\;t \leq 6 \cdot 10^{+152}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+180}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 21
Accuracy	51.0%
Cost	64

\[1 \]

Reproduce

herbie shell --seed 2023151 
(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)))))))))))