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

Average Error: 6.39% → 3.21%

Time: 40.3s

Precision: binary64

Cost: 33408

Math

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

↓

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

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))
     (* z (/ (sqrt (+ t a)) 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)), (z * (sqrt((t + a)) / 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(z * Float64(sqrt(Float64(t + a)) / 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[(z * N[(N[Sqrt[N[(t + a), $MachinePrecision]], $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision]

Target

Original	6.39%
Target	4.77%
Herbie	3.21%

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

Derivation

1. Initial program 6.39

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

2. Simplified 3.21

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

   [Start] 6.39	\[ \frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]
   +-commutative [=>] 6.39	\[ \frac{x}{\color{blue}{y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)} + x}} \]
   fma-def [=>] 6.39	\[ \frac{x}{\color{blue}{\mathsf{fma}\left(y, e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}, x\right)}} \]

3. Final simplification 3.21

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

Alternatives

Alternative 1
Error	3.1%
Cost	28804

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

Alternative 2
Error	3.49%
Cost	22468

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

Alternative 3
Error	25.31%
Cost	14420

\[\begin{array}{l} t_1 := \frac{x}{x + y \cdot e^{-2 \cdot \left(b \cdot \left(\left(a + 0.8333333333333334\right) + \frac{-0.6666666666666666}{t}\right)\right)}}\\ t_2 := \frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(a + \left(0.8333333333333334 + \frac{-0.6666666666666666}{t}\right)\right)\right)}}\\ \mathbf{if}\;a \leq -6 \cdot 10^{-107}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(b - c\right) \cdot \left(-0.8333333333333334 - a\right)\right)}}\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{-225}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-146}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-124}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{-69}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\sqrt{t + a} \cdot \frac{z}{t}\right)}}\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{+35}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \end{array} \]

Alternative 4
Error	33.91%
Cost	7761

\[\begin{array}{l} t_1 := \frac{x}{x + y \cdot e^{2 \cdot \left(\left(b - c\right) \cdot -0.8333333333333334\right)}}\\ \mathbf{if}\;t \leq -7.8 \cdot 10^{-249}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.52 \cdot 10^{-73}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{+219} \lor \neg \left(t \leq 5.5 \cdot 10^{+289}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot a\right)}}\\ \end{array} \]

Alternative 5
Error	19.81%
Cost	7753

\[\begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{-257} \lor \neg \left(t \leq 4.2 \cdot 10^{-10}\right):\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(b - c\right) \cdot \left(-0.8333333333333334 - a\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{-2 \cdot \left(b \cdot \left(\left(a + 0.8333333333333334\right) + \frac{-0.6666666666666666}{t}\right)\right)}}\\ \end{array} \]

Alternative 6
Error	19.9%
Cost	7753

\[\begin{array}{l} \mathbf{if}\;c \leq -1.86 \cdot 10^{+17} \lor \neg \left(c \leq 3.3 \cdot 10^{+40}\right):\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(a + \left(0.8333333333333334 + \frac{-0.6666666666666666}{t}\right)\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{-2 \cdot \left(b \cdot \left(\left(a + 0.8333333333333334\right) + \frac{-0.6666666666666666}{t}\right)\right)}}\\ \end{array} \]

Alternative 7
Error	29.98%
Cost	7628

\[\begin{array}{l} t_1 := \frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{if}\;a \leq -0.85:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{-135}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(b - c\right) \cdot -0.8333333333333334\right)}}\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{-71}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Error	28.99%
Cost	7628

\[\begin{array}{l} t_1 := \frac{x}{x + y \cdot e^{2 \cdot \left(\left(b - c\right) \cdot -0.8333333333333334\right)}}\\ \mathbf{if}\;t \leq -2 \cdot 10^{-285}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-74}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{c \cdot -0.6666666666666666}{t}}}\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{+218}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \end{array} \]

Alternative 9
Error	21.6%
Cost	7625

\[\begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{-285} \lor \neg \left(t \leq 7 \cdot 10^{-75}\right):\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(b - c\right) \cdot \left(-0.8333333333333334 - a\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{c \cdot -0.6666666666666666}{t}}}\\ \end{array} \]

Alternative 10
Error	35.19%
Cost	7624

\[\begin{array}{l} \mathbf{if}\;b - c \leq -100000000:\\ \;\;\;\;\frac{x}{y \cdot e^{\left(b - c\right) \cdot -1.6666666666666667}}\\ \mathbf{elif}\;b - c \leq 4 \cdot 10^{-68}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot a\right)}}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 11
Error	34.85%
Cost	7624

\[\begin{array}{l} \mathbf{if}\;b - c \leq -200000:\\ \;\;\;\;\frac{x}{y \cdot e^{\left(b - c\right) \cdot -1.6666666666666667}}\\ \mathbf{elif}\;b - c \leq 4 \cdot 10^{-68}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{-2 \cdot \left(b \cdot a\right)}}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 12
Error	37.76%
Cost	7236

\[\begin{array}{l} \mathbf{if}\;b - c \leq -100000000:\\ \;\;\;\;\frac{x}{y \cdot e^{\left(b - c\right) \cdot -1.6666666666666667}}\\ \mathbf{elif}\;b - c \leq 10^{-128}:\\ \;\;\;\;\frac{x}{y \cdot y - x \cdot x} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 13
Error	46.31%
Cost	2396

\[\begin{array}{l} t_1 := \frac{x}{x + y \cdot \left(1 + 2 \cdot \left(c \cdot a + \left(c \cdot c\right) \cdot \left(a \cdot a\right)\right)\right)}\\ t_2 := \frac{x}{x + \left(y + \left(2 \cdot a\right) \cdot \frac{y \cdot \left(\left(c - b\right) \cdot \left(b + c\right)\right)}{b + c}\right)}\\ \mathbf{if}\;c \leq -4.9 \cdot 10^{+89}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -2.15 \cdot 10^{-68}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -4.4 \cdot 10^{-126}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -6.6 \cdot 10^{-145}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.6 \cdot 10^{-9}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 5.9 \cdot 10^{+87}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.6 \cdot 10^{+149}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 14
Error	51.26%
Cost	2017

\[\begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{+219}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{+160}:\\ \;\;\;\;\frac{x}{y \cdot y - x \cdot x} \cdot \left(y - x\right)\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{-84}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{-125}:\\ \;\;\;\;\frac{x}{x + \left(y + \left(2 \cdot a\right) \cdot \left(y \cdot \left(c - b\right)\right)\right)}\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{-240}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-141} \lor \neg \left(x \leq 6.8 \cdot 10^{-53}\right) \land x \leq 3.45 \cdot 10^{+25}:\\ \;\;\;\;\frac{x}{x + y \cdot \left(1 - -2 \cdot \left(c \cdot \left(a + 0.8333333333333334\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 15
Error	51.21%
Cost	2016

\[\begin{array}{l} \mathbf{if}\;x \leq -7.6 \cdot 10^{+220}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{+160}:\\ \;\;\;\;\frac{x}{y \cdot y - x \cdot x} \cdot \left(y - x\right)\\ \mathbf{elif}\;x \leq -1.4 \cdot 10^{-84}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -5.1 \cdot 10^{-123}:\\ \;\;\;\;\frac{x}{x + \left(y + \left(2 \cdot a\right) \cdot \left(y \cdot \left(c - b\right)\right)\right)}\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{-240}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 6.6 \cdot 10^{-145}:\\ \;\;\;\;\frac{x}{x + y \cdot \left(1 + -2 \cdot \left(c \cdot \left(-0.8333333333333334 - \left(a + \frac{-0.6666666666666666}{t}\right)\right)\right)\right)}\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-57}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+25}:\\ \;\;\;\;\frac{x}{x + y \cdot \left(1 - -2 \cdot \left(c \cdot \left(a + 0.8333333333333334\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 16
Error	50.82%
Cost	1888

\[\begin{array}{l} t_1 := \frac{x}{y \cdot y - x \cdot x} \cdot \left(y - x\right)\\ \mathbf{if}\;x \leq -5.2 \cdot 10^{+220}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -2.2 \cdot 10^{+160}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{-84}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -1.35 \cdot 10^{-122}:\\ \;\;\;\;\frac{x}{x + \left(y + \left(2 \cdot a\right) \cdot \left(y \cdot \left(c - b\right)\right)\right)}\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{-240}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-143}:\\ \;\;\;\;\frac{x}{x - y \cdot \left(-1 + \left(b - c\right) \cdot \left(a + a\right)\right)}\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-58}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{+43}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 17
Error	51.7%
Cost	1632

\[\begin{array}{l} t_1 := \frac{x}{y \cdot y - x \cdot x} \cdot \left(y - x\right)\\ \mathbf{if}\;y \leq -1.1 \cdot 10^{+33}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -2.25 \cdot 10^{+17}:\\ \;\;\;\;\frac{\frac{x}{y}}{1 + \left(b - c\right) \cdot \left(a \cdot -2\right)}\\ \mathbf{elif}\;y \leq 9.6 \cdot 10^{-273}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-152}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-74}:\\ \;\;\;\;\frac{x}{x + \left(2 \cdot c\right) \cdot \left(y \cdot a\right)}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-10}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+285}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+306}:\\ \;\;\;\;x \cdot \frac{-0.75}{\frac{y \cdot c}{t}}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 18
Error	49.77%
Cost	1496

\[\begin{array}{l} t_1 := \frac{x}{y \cdot y - x \cdot x} \cdot \left(y - x\right)\\ \mathbf{if}\;z \leq -2 \cdot 10^{-110}:\\ \;\;\;\;1\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-205}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-139}:\\ \;\;\;\;1\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-103}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+105}:\\ \;\;\;\;1\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+236}:\\ \;\;\;\;\frac{x}{x + \frac{-1.3333333333333333}{\frac{t}{y \cdot c}}}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 19
Error	47.48%
Cost	708

\[\begin{array}{l} \mathbf{if}\;c \leq 8.6 \cdot 10^{+206}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{-0.75}{y} \cdot \left(x \cdot \frac{t}{c}\right)\\ \end{array} \]

Alternative 20
Error	49.05%
Cost	584

\[\begin{array}{l} \mathbf{if}\;x \leq 5.2 \cdot 10^{-240}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-142}:\\ \;\;\;\;\frac{x}{x + y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 21
Error	48.38%
Cost	456

\[\begin{array}{l} \mathbf{if}\;x \leq 5.4 \cdot 10^{-240}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 5.7 \cdot 10^{-209}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 22
Error	47.82%
Cost	64

\[1 \]

Reproduce

herbie shell --seed 2023088 
(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)))))))))))