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

?

Percentage Accurate: 94.6% → 95.8%
Time: 25.8s
Precision: binary64
Cost: 33540

?

\[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]
↓
\[\begin{array}{l} \mathbf{if}\;t \leq 1.18 \cdot 10^{-197}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{z \cdot \sqrt{a} + -0.6666666666666666 \cdot \left(c - b\right)}{t}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(y, {\left(e^{2}\right)}^{\left(\mathsf{fma}\left(\sqrt{t + a}, \frac{z}{t}, \left(c - b\right) \cdot \left(a - \left(\frac{0.6666666666666666}{t} + -0.8333333333333334\right)\right)\right)\right)}, x\right)}\\ \end{array} \]
(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
 (if (<= t 1.18e-197)
   (/
    x
    (+
     x
     (*
      y
      (exp (* 2.0 (/ (+ (* z (sqrt a)) (* -0.6666666666666666 (- c b))) t))))))
   (/
    x
    (fma
     y
     (pow
      (exp 2.0)
      (fma
       (sqrt (+ t a))
       (/ z t)
       (* (- c b) (- a (+ (/ 0.6666666666666666 t) -0.8333333333333334)))))
     x))))
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 tmp;
	if (t <= 1.18e-197) {
		tmp = x / (x + (y * exp((2.0 * (((z * sqrt(a)) + (-0.6666666666666666 * (c - b))) / t)))));
	} else {
		tmp = x / fma(y, pow(exp(2.0), fma(sqrt((t + a)), (z / t), ((c - b) * (a - ((0.6666666666666666 / t) + -0.8333333333333334))))), x);
	}
	return tmp;
}

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)
	tmp = 0.0
	if (t <= 1.18e-197)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(Float64(z * sqrt(a)) + Float64(-0.6666666666666666 * Float64(c - b))) / t))))));
	else
		tmp = Float64(x / fma(y, (exp(2.0) ^ fma(sqrt(Float64(t + a)), Float64(z / t), Float64(Float64(c - b) * Float64(a - Float64(Float64(0.6666666666666666 / t) + -0.8333333333333334))))), x));
	end
	return tmp
end

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_] := If[LessEqual[t, 1.18e-197], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(N[(z * N[Sqrt[a], $MachinePrecision]), $MachinePrecision] + N[(-0.6666666666666666 * N[(c - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * N[Power[N[Exp[2.0], $MachinePrecision], N[(N[Sqrt[N[(t + a), $MachinePrecision]], $MachinePrecision] * N[(z / t), $MachinePrecision] + N[(N[(c - b), $MachinePrecision] * N[(a - N[(N[(0.6666666666666666 / t), $MachinePrecision] + -0.8333333333333334), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision]]

\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}
\mathbf{if}\;t \leq 1.18 \cdot 10^{-197}:\\
\;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{z \cdot \sqrt{a} + -0.6666666666666666 \cdot \left(c - b\right)}{t}}}\\

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


\end{array}

Local Percentage Accuracy vs ?

The average percentage accuracy by input value. Horizontal axis shows value of an input variable; the variable is choosen in the title. Vertical axis is accuracy; higher is better. Red represent the original program, while blue represents Herbie's suggestion. These can be toggled with buttons below the plot. The line is an average while dots represent individual samples.

Herbie found 24 alternatives:

AlternativeAccuracySpeedup

Accuracy vs Speed

The accuracy (vertical axis) and speed (horizontal axis) of each alternatives. Up and to the right is better. The red square shows the initial program, and each blue circle shows an alternative.The line shows the best available speed-accuracy tradeoffs.

Bogosity?

Bogosity

Target

Original94.6%
Target95.2%
Herbie95.8%
\[\begin{array}{l} \mathbf{if}\;t < -2.118326644891581 \cdot 10^{-50}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(a \cdot c + 0.8333333333333334 \cdot c\right) - a \cdot b\right)}}\\ \mathbf{elif}\;t < 5.196588770651547 \cdot 10^{-123}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{\left(z \cdot \sqrt{t + a}\right) \cdot \left(\left(3 \cdot t\right) \cdot \left(a - \frac{5}{6}\right)\right) - \left(\left(\frac{5}{6} + a\right) \cdot \left(3 \cdot t\right) - 2\right) \cdot \left(\left(a - \frac{5}{6}\right) \cdot \left(\left(b - c\right) \cdot t\right)\right)}{\left(\left(t \cdot t\right) \cdot 3\right) \cdot \left(a - \frac{5}{6}\right)}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\\ \end{array} \]

Derivation?

  1. Split input into 2 regimes

  2. if t < 1.17999999999999995e-197

    1. Initial program 87.6%

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

    2. Taylor expanded in t around 0 94.5%

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

    if 1.17999999999999995e-197 < t

    1. Initial program 96.4%

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

    2. Simplified100.0%

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

      [Start]96.4%

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

      +-commutative [=>]96.4%

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

      fma-def [=>]96.4%

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

  4. Final simplification98.1%

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 1.18 \cdot 10^{-197}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{z \cdot \sqrt{a} + -0.6666666666666666 \cdot \left(c - b\right)}{t}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(y, {\left(e^{2}\right)}^{\left(\mathsf{fma}\left(\sqrt{t + a}, \frac{z}{t}, \left(c - b\right) \cdot \left(a - \left(\frac{0.6666666666666666}{t} + -0.8333333333333334\right)\right)\right)\right)}, x\right)}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy95.8%
Cost33540
\[\begin{array}{l} \mathbf{if}\;t \leq 1.18 \cdot 10^{-197}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{z \cdot \sqrt{a} + -0.6666666666666666 \cdot \left(c - b\right)}{t}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(y, {\left(e^{2}\right)}^{\left(\mathsf{fma}\left(\sqrt{t + a}, \frac{z}{t}, \left(c - b\right) \cdot \left(a - \left(\frac{0.6666666666666666}{t} + -0.8333333333333334\right)\right)\right)\right)}, x\right)}\\ \end{array} \]
Alternative 2
Accuracy97.3%
Cost33408
\[\frac{x}{\mathsf{fma}\left(y, {\left(e^{2}\right)}^{\left(\mathsf{fma}\left(b - c, \frac{0.6666666666666666}{t} + \left(-0.8333333333333334 - a\right), \sqrt{t + a} \cdot \frac{z}{t}\right)\right)}, x\right)} \]
Alternative 3
Accuracy97.6%
Cost22468
\[\begin{array}{l} t_1 := \frac{\sqrt{t + a} \cdot z}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + 0.8333333333333334\right)\right)\\ \mathbf{if}\;t_1 \leq \infty:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot t_1}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{z \cdot \sqrt{a} + -0.6666666666666666 \cdot \left(c - b\right)}{t}}}\\ \end{array} \]
Alternative 4
Accuracy95.7%
Cost21124
\[\begin{array}{l} \mathbf{if}\;t \leq 1.1 \cdot 10^{-197}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{z \cdot \sqrt{a} + -0.6666666666666666 \cdot \left(c - b\right)}{t}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot {\left(e^{2}\right)}^{\left(\frac{z}{\frac{t}{\sqrt{t + a}}} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + 0.8333333333333334\right)\right)\right)}}\\ \end{array} \]
Alternative 5
Accuracy89.1%
Cost14536
\[\begin{array}{l} \mathbf{if}\;t \leq 1.18 \cdot 10^{-197}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{z \cdot \sqrt{a} + -0.6666666666666666 \cdot \left(c - b\right)}{t}}}\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+108}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(z \cdot \sqrt{\frac{1}{t}} + \left(b - c\right) \cdot \left(\frac{0.6666666666666666}{t} - 0.8333333333333334\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(c - b\right) \cdot \left(a - -0.8333333333333334\right)\right)}}\\ \end{array} \]
Alternative 6
Accuracy85.3%
Cost14148
\[\begin{array}{l} \mathbf{if}\;t \leq 4.5 \cdot 10^{-260}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{z \cdot \sqrt{a} + -0.6666666666666666 \cdot \left(c - b\right)}{t}}}\\ \mathbf{elif}\;t \leq 0.000235:\\ \;\;\;\;\frac{x}{x + y \cdot e^{1.3333333333333333 \cdot \frac{b - c}{t}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(c - b\right) \cdot \left(a - -0.8333333333333334\right)\right)}}\\ \end{array} \]
Alternative 7
Accuracy81.2%
Cost13896
\[\begin{array}{l} \mathbf{if}\;t \leq -1.22 \cdot 10^{-105}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{elif}\;t \leq 10^{-299}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z}{t} \cdot \sqrt{a}\right)}}\\ \mathbf{elif}\;t \leq 0.008:\\ \;\;\;\;\frac{x}{x + y \cdot e^{1.3333333333333333 \cdot \frac{b - c}{t}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(c - b\right) \cdot \left(a - -0.8333333333333334\right)\right)}}\\ \end{array} \]
Alternative 8
Accuracy81.1%
Cost8136
\[\begin{array}{l} \mathbf{if}\;t \leq -1.85 \cdot 10^{-116}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-304}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \frac{\frac{0.4444444444444444}{t \cdot t}}{\frac{0.6666666666666666}{t} + \left(a + 0.8333333333333334\right)}\right)}}\\ \mathbf{elif}\;t \leq 0.034:\\ \;\;\;\;\frac{x}{x + y \cdot e^{1.3333333333333333 \cdot \frac{b - c}{t}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(c - b\right) \cdot \left(a - -0.8333333333333334\right)\right)}}\\ \end{array} \]
Alternative 9
Accuracy82.1%
Cost8008
\[\begin{array}{l} t_1 := \frac{x}{x + y \cdot e^{2 \cdot \left(\left(c - b\right) \cdot \left(a - -0.8333333333333334\right)\right)}}\\ \mathbf{if}\;t \leq -4.4 \cdot 10^{-287}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{-290}:\\ \;\;\;\;\frac{x}{x + \left(y - 2 \cdot \frac{y \cdot \left(\left(b - c\right) \cdot -0.6666666666666666 - z \cdot \sqrt{a}\right)}{t}\right)}\\ \mathbf{elif}\;t \leq 0.75:\\ \;\;\;\;\frac{x}{x + y \cdot e^{1.3333333333333333 \cdot \frac{b - c}{t}}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 10
Accuracy58.0%
Cost7632
\[\begin{array}{l} \mathbf{if}\;c \leq -6.2 \cdot 10^{+151}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -9.5 \cdot 10^{+91}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{-2 \cdot \left(b \cdot a\right)}}\\ \mathbf{elif}\;c \leq -2.25 \cdot 10^{-115}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 9 \cdot 10^{-59}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{b \cdot -1.6666666666666667}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{a \cdot \left(2 \cdot c\right)}}\\ \end{array} \]
Alternative 11
Accuracy71.4%
Cost7632
\[\begin{array}{l} t_1 := \frac{x}{x + y \cdot e^{-1.3333333333333333 \cdot \frac{c}{t}}}\\ t_2 := \frac{x}{x + y \cdot e^{\left(b - c\right) \cdot -1.6666666666666667}}\\ \mathbf{if}\;t \leq -1.85 \cdot 10^{-301}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{-67}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-33}:\\ \;\;\;\;\frac{x}{x - \left(2 \cdot \left(a \cdot \left(y \cdot \left(b - c\right)\right)\right) - y\right)}\\ \mathbf{elif}\;t \leq 1.38 \cdot 10^{-5}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]
Alternative 12
Accuracy67.5%
Cost7500
\[\begin{array}{l} t_1 := \frac{x}{x + y \cdot e^{\left(b - c\right) \cdot -1.6666666666666667}}\\ \mathbf{if}\;t \leq -1.85 \cdot 10^{-301}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-60}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+28}:\\ \;\;\;\;\frac{x}{x - y \cdot \left(-1 + 2 \cdot \left(b \cdot \left(\left(a + 0.8333333333333334\right) + 0.6666666666666666 \cdot \frac{-1}{t}\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 13
Accuracy82.0%
Cost7492
\[\begin{array}{l} \mathbf{if}\;t \leq 5 \cdot 10^{-7}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{1.3333333333333333 \cdot \frac{b - c}{t}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(c - b\right) \cdot \left(a - -0.8333333333333334\right)\right)}}\\ \end{array} \]
Alternative 14
Accuracy56.5%
Cost7372
\[\begin{array}{l} t_1 := \frac{x}{x + y \cdot e^{b \cdot -1.6666666666666667}}\\ \mathbf{if}\;t \leq -3.6 \cdot 10^{-301}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-60}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+28}:\\ \;\;\;\;\frac{x}{x - y \cdot \left(-1 + 2 \cdot \left(b \cdot \left(\left(a + 0.8333333333333334\right) + 0.6666666666666666 \cdot \frac{-1}{t}\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 15
Accuracy58.6%
Cost7368
\[\begin{array}{l} \mathbf{if}\;c \leq -1.2 \cdot 10^{-114}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 5.6 \cdot 10^{-58}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{b \cdot -1.6666666666666667}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{a \cdot \left(2 \cdot c\right)}}\\ \end{array} \]
Alternative 16
Accuracy76.2%
Cost7364
\[\begin{array}{l} \mathbf{if}\;t \leq 1.35 \cdot 10^{-5}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{1.3333333333333333 \cdot \frac{b - c}{t}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{\left(b - c\right) \cdot -1.6666666666666667}}\\ \end{array} \]
Alternative 17
Accuracy49.4%
Cost1608
\[\begin{array}{l} \mathbf{if}\;c \leq -3.1 \cdot 10^{-206}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 4.7 \cdot 10^{+123}:\\ \;\;\;\;\frac{x}{x - y \cdot \left(-1 + 2 \cdot \left(b \cdot \left(\left(a + 0.8333333333333334\right) + 0.6666666666666666 \cdot \frac{-1}{t}\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
Alternative 18
Accuracy48.3%
Cost1096
\[\begin{array}{l} \mathbf{if}\;c \leq -4.7 \cdot 10^{-210}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 10^{+147}:\\ \;\;\;\;\frac{x}{x + y \cdot \left(-2 \cdot \left(b \cdot a\right) + 1\right)}\\ \mathbf{elif}\;c \leq 7.5 \cdot 10^{+277}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x}{c \cdot \left(y \cdot a\right)}\\ \end{array} \]
Alternative 19
Accuracy50.4%
Cost1092
\[\begin{array}{l} \mathbf{if}\;c \leq -2.65 \cdot 10^{-213}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x - \left(2 \cdot \left(a \cdot \left(y \cdot \left(b - c\right)\right)\right) - y\right)}\\ \end{array} \]
Alternative 20
Accuracy51.3%
Cost964
\[\begin{array}{l} \mathbf{if}\;y \leq -3.25 \cdot 10^{+146}:\\ \;\;\;\;\frac{x}{x + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
Alternative 21
Accuracy50.9%
Cost964
\[\begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{+146}:\\ \;\;\;\;\frac{x}{x + \left(y + -1.3333333333333333 \cdot \frac{c}{\frac{t}{y}}\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
Alternative 22
Accuracy52.0%
Cost836
\[\begin{array}{l} \mathbf{if}\;b \leq -1.8 \cdot 10^{+113}:\\ \;\;\;\;0.5 \cdot \frac{x}{y \cdot \left(a \cdot \left(c - b\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
Alternative 23
Accuracy50.7%
Cost836
\[\begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{+146}:\\ \;\;\;\;\frac{x}{x + -1.3333333333333333 \cdot \frac{c}{\frac{t}{y}}}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
Alternative 24
Accuracy51.6%
Cost64
\[1 \]

Reproduce?

herbie shell --seed 2023165 
(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)))))))))))