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

Average Accuracy: 94.1% → 97.4%

Time: 39.4s

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	94.1%
Target	95.5%
Herbie	97.4%

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

Derivation

1. Initial program 94.1%

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

2. Simplified 97.4%

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

   [Start] 94.1	\[ \frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]
   +-commutative [=>] 94.1	\[ \frac{x}{\color{blue}{y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)} + x}} \]
   fma-def [=>] 94.1	\[ \frac{x}{\color{blue}{\mathsf{fma}\left(y, e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}, x\right)}} \]

3. Final simplification 97.4%

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

Alternatives

Alternative 1
Accuracy	97.2%
Cost	41220

\[\begin{array}{l} t_1 := \sqrt{t + a}\\ \mathbf{if}\;\frac{t_1 \cdot z}{t} + \left(b - c\right) \cdot \left(\left(-0.8333333333333334 - a\right) - \frac{-2}{t \cdot 3}\right) \leq \infty:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(y, {\left(e^{2}\right)}^{\left(\mathsf{fma}\left(t_1, \frac{z}{t}, \left(b - c\right) \cdot \left(\left(-0.8333333333333334 - \frac{-0.6666666666666666}{t}\right) - a\right)\right)\right)}, x\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(a + \frac{0.6944444444444444 + \frac{-0.4444444444444444}{t \cdot t}}{\frac{0.6666666666666666}{t} + 0.8333333333333334}\right)\right)}}\\ \end{array} \]

Alternative 2
Accuracy	96.7%
Cost	22468

\[\begin{array}{l} t_1 := \frac{\sqrt{t + a} \cdot z}{t} + \left(b - c\right) \cdot \left(\left(-0.8333333333333334 - a\right) - \frac{-2}{t \cdot 3}\right)\\ \mathbf{if}\;t_1 \leq \infty:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot t_1}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(a + \frac{0.6944444444444444 + \frac{-0.4444444444444444}{t \cdot t}}{\frac{0.6666666666666666}{t} + 0.8333333333333334}\right)\right)}}\\ \end{array} \]

Alternative 3
Accuracy	78.4%
Cost	14816

\[\begin{array}{l} t_1 := \frac{x}{x + y \cdot e^{2 \cdot \left(\sqrt{t + a} \cdot \frac{z}{t}\right)}}\\ \mathbf{if}\;t \leq -1.58 \cdot 10^{-245}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-231}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(a + \frac{0.6944444444444444 + \frac{-0.4444444444444444}{t \cdot t}}{\frac{0.6666666666666666}{t} + 0.8333333333333334}\right)\right)}}\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-140}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-106}:\\ \;\;\;\;1 + \left(\frac{x}{x + y} + -1\right)\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-75}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-48}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{b}{\frac{t}{0.6666666666666666}}}}\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-24}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(-0.6666666666666666 \cdot \frac{c}{t}\right)}}\\ \mathbf{elif}\;t \leq 0.085:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(b - c\right) \cdot \left(-0.8333333333333334 - a\right)\right)}}\\ \end{array} \]

Alternative 4
Accuracy	78.5%
Cost	14292

\[\begin{array}{l} t_1 := \frac{x}{x + y \cdot e^{2 \cdot \frac{b}{\frac{t}{0.6666666666666666}}}}\\ \mathbf{if}\;t \leq -5.6 \cdot 10^{-244}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-251}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(a + \frac{0.6944444444444444 + \frac{-0.4444444444444444}{t \cdot t}}{\frac{0.6666666666666666}{t} + 0.8333333333333334}\right)\right)}}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-139}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-105}:\\ \;\;\;\;1 + \left(\frac{x}{x + y} + -1\right)\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-64}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(z \cdot \sqrt{\frac{1}{t}}\right)}}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-47}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 0.4:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(-0.6666666666666666 \cdot \frac{c}{t}\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(b - c\right) \cdot \left(-0.8333333333333334 - a\right)\right)}}\\ \end{array} \]

Alternative 5
Accuracy	78.0%
Cost	8284

\[\begin{array}{l} t_1 := \frac{x}{x + y \cdot e^{2 \cdot \frac{b}{\frac{t}{0.6666666666666666}}}}\\ t_2 := \frac{x}{x + y \cdot e^{2 \cdot \left(-0.6666666666666666 \cdot \frac{c}{t}\right)}}\\ \mathbf{if}\;t \leq -8.2 \cdot 10^{-156}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-251}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{-139}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{-98}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-77}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \left(\frac{0.6666666666666666}{t} + \left(-0.8333333333333334 - a\right)\right)\right)}}\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-48}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 0.15:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(b - c\right) \cdot \left(-0.8333333333333334 - a\right)\right)}}\\ \end{array} \]

Alternative 6
Accuracy	78.3%
Cost	8264

\[\begin{array}{l} \mathbf{if}\;t \leq -2.35 \cdot 10^{-244}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-249}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(a + \frac{0.6944444444444444 + \frac{-0.4444444444444444}{t \cdot t}}{\frac{0.6666666666666666}{t} + 0.8333333333333334}\right)\right)}}\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{-48}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{b}{\frac{t}{0.6666666666666666}}}}\\ \mathbf{elif}\;t \leq 0.24:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(-0.6666666666666666 \cdot \frac{c}{t}\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(b - c\right) \cdot \left(-0.8333333333333334 - a\right)\right)}}\\ \end{array} \]

Alternative 7
Accuracy	68.6%
Cost	8024

\[\begin{array}{l} t_1 := \frac{x}{x + y \cdot e^{2 \cdot \left(-0.6666666666666666 \cdot \frac{c}{t}\right)}}\\ \mathbf{if}\;t \leq -1.1 \cdot 10^{-196}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{-2 \cdot \left(b \cdot a\right)}}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-231}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-198}:\\ \;\;\;\;1 + \left(\frac{x}{x + y} + -1\right)\\ \mathbf{elif}\;t \leq 7.6 \cdot 10^{-94}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-47}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 0.22:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{\left(b - c\right) \cdot -1.6666666666666667}}\\ \end{array} \]

Alternative 8
Accuracy	71.6%
Cost	8024

\[\begin{array}{l} t_1 := \frac{x}{x + y \cdot e^{2 \cdot \left(-0.6666666666666666 \cdot \frac{c}{t}\right)}}\\ \mathbf{if}\;t \leq -7.5 \cdot 10^{-156}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-231}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{-196}:\\ \;\;\;\;1 + \left(\frac{x}{x + y} + -1\right)\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-98}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 6.4 \cdot 10^{-49}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 0.72:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{\left(b - c\right) \cdot -1.6666666666666667}}\\ \end{array} \]

Alternative 9
Accuracy	77.6%
Cost	8020

\[\begin{array}{l} t_1 := \frac{x}{x + y \cdot e^{2 \cdot \left(-0.6666666666666666 \cdot \frac{c}{t}\right)}}\\ \mathbf{if}\;t \leq -8.8 \cdot 10^{-156}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{elif}\;t \leq 10^{-251}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-48}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{b}{\frac{t}{0.6666666666666666}}}}\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-13}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 0.45:\\ \;\;\;\;1 + \left(\frac{x}{x + y} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(b - c\right) \cdot \left(-0.8333333333333334 - a\right)\right)}}\\ \end{array} \]

Alternative 10
Accuracy	56.7%
Cost	7901

\[\begin{array}{l} t_1 := \frac{x}{x + y \cdot e^{b \cdot -1.6666666666666667}}\\ \mathbf{if}\;c \leq -1.75 \cdot 10^{-106}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -6.2 \cdot 10^{-277}:\\ \;\;\;\;\left(1 + \frac{x}{x + y}\right) + -1\\ \mathbf{elif}\;c \leq 7 \cdot 10^{-167}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 150000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.15 \cdot 10^{+37}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 3.1 \cdot 10^{+48} \lor \neg \left(c \leq 2.2 \cdot 10^{+124}\right):\\ \;\;\;\;\frac{x}{y \cdot e^{\left(b - c\right) \cdot -1.6666666666666667}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 11
Accuracy	71.8%
Cost	7764

\[\begin{array}{l} t_1 := \frac{x}{x + y \cdot e^{2 \cdot \left(-0.6666666666666666 \cdot \frac{c}{t}\right)}}\\ \mathbf{if}\;t \leq -1.45 \cdot 10^{-154}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-248}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-49}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{b}{\frac{t}{0.6666666666666666}}}}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-13}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 0.8:\\ \;\;\;\;1 + \left(\frac{x}{x + y} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{\left(b - c\right) \cdot -1.6666666666666667}}\\ \end{array} \]

Alternative 12
Accuracy	69.0%
Cost	7632

\[\begin{array}{l} t_1 := \frac{x}{x + y \cdot e^{\left(b - c\right) \cdot -1.6666666666666667}}\\ \mathbf{if}\;t \leq -5.6 \cdot 10^{-285}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-281}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-98}:\\ \;\;\;\;1 + \left(\frac{x}{x + y} + -1\right)\\ \mathbf{elif}\;t \leq 0.122:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 13
Accuracy	51.6%
Cost	7240

\[\begin{array}{l} t_1 := \left(1 + \frac{x}{x + y}\right) + -1\\ \mathbf{if}\;z \leq -3.8 \cdot 10^{+77}:\\ \;\;\;\;1\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{+58}:\\ \;\;\;\;\frac{x}{y \cdot e^{\left(b - c\right) \cdot -1.6666666666666667}}\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-113}:\\ \;\;\;\;1\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-138}:\\ \;\;\;\;\frac{x}{y + \left(2 \cdot a\right) \cdot \left(y \cdot \left(c - b\right)\right)}\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-185}:\\ \;\;\;\;1\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-295}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+102}:\\ \;\;\;\;1\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{+177}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+250}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(x + y\right) \cdot \left(x + y\right)} \cdot \left(y - x\right)\\ \end{array} \]

Alternative 14
Accuracy	54.1%
Cost	2269

\[\begin{array}{l} t_1 := \frac{x}{x + y}\\ t_2 := 1 + \left(t_1 + -1\right)\\ \mathbf{if}\;c \leq -2 \cdot 10^{-106}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -8 \cdot 10^{-277}:\\ \;\;\;\;\left(1 + t_1\right) + -1\\ \mathbf{elif}\;c \leq 1.1 \cdot 10^{-169}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 10^{-123}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 1.55 \cdot 10^{+74}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 7.8 \cdot 10^{+202} \lor \neg \left(c \leq 1.6 \cdot 10^{+246}\right):\\ \;\;\;\;\frac{x}{x + y \cdot \left(1 + 2 \cdot \left(c \cdot a + \left(c \cdot c\right) \cdot \left(a \cdot a\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 15
Accuracy	52.1%
Cost	1756

\[\begin{array}{l} t_1 := \left(1 + \frac{x}{x + y}\right) + -1\\ \mathbf{if}\;z \leq -4.2 \cdot 10^{-113}:\\ \;\;\;\;1\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-138}:\\ \;\;\;\;\frac{x}{y + \left(2 \cdot a\right) \cdot \left(y \cdot \left(c - b\right)\right)}\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-185}:\\ \;\;\;\;1\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-294}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+101}:\\ \;\;\;\;1\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+177}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+247}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(x + y\right) \cdot \left(x + y\right)} \cdot \left(y - x\right)\\ \end{array} \]

Alternative 16
Accuracy	53.0%
Cost	1624

\[\begin{array}{l} t_1 := \frac{x}{x + y}\\ t_2 := 1 + \left(t_1 + -1\right)\\ \mathbf{if}\;c \leq -4.7 \cdot 10^{-108}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -6.2 \cdot 10^{-277}:\\ \;\;\;\;\left(1 + t_1\right) + -1\\ \mathbf{elif}\;c \leq 1.8 \cdot 10^{-171}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 2 \cdot 10^{-123}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 10^{+163}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 2.1 \cdot 10^{+246}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(1 + a \cdot \left(2 \cdot \left(c - b\right)\right)\right)}\\ \end{array} \]

Alternative 17
Accuracy	52.5%
Cost	1492

\[\begin{array}{l} t_1 := \left(1 + \frac{x}{x + y}\right) + -1\\ \mathbf{if}\;z \leq -1.7 \cdot 10^{-185}:\\ \;\;\;\;1\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-295}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+104}:\\ \;\;\;\;1\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+177}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.08 \cdot 10^{+247}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(x + y\right) \cdot \left(x + y\right)} \cdot \left(y - x\right)\\ \end{array} \]

Alternative 18
Accuracy	53.1%
Cost	1238

\[\begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{-185}:\\ \;\;\;\;1\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-295} \lor \neg \left(z \leq 4 \cdot 10^{+106} \lor \neg \left(z \leq 4 \cdot 10^{+177}\right) \land z \leq 2 \cdot 10^{+244}\right):\\ \;\;\;\;1 + \left(\frac{x}{x + y} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 19
Accuracy	53.1%
Cost	1236

\[\begin{array}{l} t_1 := \frac{x}{x + y}\\ t_2 := \left(1 + t_1\right) + -1\\ \mathbf{if}\;z \leq -2.45 \cdot 10^{-185}:\\ \;\;\;\;1\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-295}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+102}:\\ \;\;\;\;1\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{+177}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+247}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;1 + \left(t_1 + -1\right)\\ \end{array} \]

Alternative 20
Accuracy	52.0%
Cost	708

\[\begin{array}{l} \mathbf{if}\;y \leq 5 \cdot 10^{+187}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{x}{y \cdot y}\\ \end{array} \]

Alternative 21
Accuracy	52.2%
Cost	64

\[1 \]

Reproduce

herbie shell --seed 2023136 
(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)))))))))))