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

Average Error: 4.0 → 2.4

Time: 1.1min

Precision: binary64

Cost: 22468

Math

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

↓

\[\begin{array}{l} t_1 := \frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + 0.8333333333333334\right) - \frac{2}{t \cdot 3}\right)\\ \mathbf{if}\;t_1 \leq \infty:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot t_1}}\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \]

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
         (-
          (/ (* z (sqrt (+ t a))) t)
          (* (- b c) (- (+ a 0.8333333333333334) (/ 2.0 (* t 3.0)))))))
   (if (<= t_1 INFINITY) (/ x (+ x (* y (exp (* 2.0 t_1))))) 0.0)))

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 = ((z * sqrt((t + a))) / t) - ((b - c) * ((a + 0.8333333333333334) - (2.0 / (t * 3.0))));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = x / (x + (y * exp((2.0 * t_1))));
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return x / (x + (y * Math.exp((2.0 * (((z * Math.sqrt((t + a))) / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0)))))))));
}

↓

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((z * Math.sqrt((t + a))) / t) - ((b - c) * ((a + 0.8333333333333334) - (2.0 / (t * 3.0))));
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = x / (x + (y * Math.exp((2.0 * t_1))));
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	return x / (x + (y * math.exp((2.0 * (((z * math.sqrt((t + a))) / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0)))))))))

↓

def code(x, y, z, t, a, b, c):
	t_1 = ((z * math.sqrt((t + a))) / t) - ((b - c) * ((a + 0.8333333333333334) - (2.0 / (t * 3.0))))
	tmp = 0
	if t_1 <= math.inf:
		tmp = x / (x + (y * math.exp((2.0 * t_1))))
	else:
		tmp = 0.0
	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 = Float64(Float64(Float64(z * sqrt(Float64(t + a))) / t) - Float64(Float64(b - c) * Float64(Float64(a + 0.8333333333333334) - Float64(2.0 / Float64(t * 3.0)))))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * t_1)))));
	else
		tmp = 0.0;
	end
	return tmp
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = x / (x + (y * exp((2.0 * (((z * sqrt((t + a))) / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0)))))))));
end

↓

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = ((z * sqrt((t + a))) / t) - ((b - c) * ((a + 0.8333333333333334) - (2.0 / (t * 3.0))));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = x / (x + (y * exp((2.0 * t_1))));
	else
		tmp = 0.0;
	end
	tmp_2 = 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[(N[(N[(z * N[Sqrt[N[(t + a), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision] - N[(N[(b - c), $MachinePrecision] * N[(N[(a + 0.8333333333333334), $MachinePrecision] - N[(2.0 / N[(t * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * t$95$1), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 0.0]]

Target

Original	4.0
Target	2.9
Herbie	2.4

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

Derivation

1. Split input into 2 regimes

2. if (-.f64 (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t) (*.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 5 6)) (/.f64 2 (*.f64 t 3))))) < +inf.0

   1. Initial program 0.8

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

   2. Simplified 0.8

      \[\leadsto \color{blue}{\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + 0.8333333333333334\right) - \frac{2}{t \cdot 3}\right)\right)}}} \]
      Proof

      [Start] 0.8	\[ \frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]
      metadata-eval [=>] 0.8	\[ \frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \color{blue}{0.8333333333333334}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   if +inf.0 < (-.f64 (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t) (*.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 5 6)) (/.f64 2 (*.f64 t 3)))))

   1. Initial program 64.0

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

   2. Simplified 64.0

      \[\leadsto \color{blue}{\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + 0.8333333333333334\right) - \frac{2}{t \cdot 3}\right)\right)}}} \]
      Proof

      [Start] 64.0	\[ \frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]
      metadata-eval [=>] 64.0	\[ \frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \color{blue}{0.8333333333333334}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   3. Taylor expanded in a around inf 25.4

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

   4. Applied egg-rr 24.5

      \[\leadsto \color{blue}{\left(0 - \left(-1 - \frac{x}{y \cdot e^{\left(c - b\right) \cdot \left(a + a\right)} + x}\right)\right) - 1} \]

   5. Taylor expanded in a around 0 30.7

      \[\leadsto \left(0 - \left(-1 - \frac{x}{\color{blue}{y} + x}\right)\right) - 1 \]

   6. Taylor expanded in x around 0 31.7

      \[\leadsto \left(0 - \color{blue}{-1}\right) - 1 \]
3. Recombined 2 regimes into one program.

4. Final simplification 2.4

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + 0.8333333333333334\right) - \frac{2}{t \cdot 3}\right) \leq \infty:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + 0.8333333333333334\right) - \frac{2}{t \cdot 3}\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \]

Alternatives

Alternative 1
Error	17.9
Cost	15080

\[\begin{array}{l} t_1 := \frac{1}{t} \cdot 0.6666666666666666\\ t_2 := \left(a + 0.8333333333333334\right) \cdot \left(a + 0.8333333333333334\right)\\ t_3 := \frac{x}{x + y \cdot e^{2 \cdot \left(\left(0.6666666666666666 \cdot \frac{1}{t} - \left(0.8333333333333334 + a\right)\right) \cdot b\right)}}\\ t_4 := \frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z}{t} \cdot \sqrt{a + t}\right)}}\\ t_5 := \left(0 - \left(-1 - \frac{x}{y \cdot e^{\left(c - b\right) \cdot \left(a + a\right)} + x}\right)\right) - 1\\ \mathbf{if}\;a \leq -8 \cdot 10^{-248}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(b - c\right) \cdot \left(-0.8333333333333334 - a\right)\right)}}\\ \mathbf{elif}\;a \leq -1.6 \cdot 10^{-282}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq 8.8 \cdot 10^{-281}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-238}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(\left(a + 0.8333333333333334\right) - t_1\right)\right)}}\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{-199}:\\ \;\;\;\;\frac{x}{x + e^{\left(0.8333333333333334 + a\right) \cdot \left(b \cdot -2\right)} \cdot y}\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-67}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(\left(t_2 \cdot t_2\right) \cdot \frac{\frac{1}{a + 0.8333333333333334}}{t_2} - t_1\right)\right)}}\\ \mathbf{elif}\;a \leq 4 \cdot 10^{-21}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;a \leq 10^{+71}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{+122}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;a \leq 1.22 \cdot 10^{+169}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \end{array} \]

Alternative 2
Error	15.3
Cost	8520

\[\begin{array}{l} \mathbf{if}\;b \leq -5.5 \cdot 10^{+22}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(0.6666666666666666 \cdot \frac{1}{t} - \left(0.8333333333333334 + a\right)\right) \cdot b\right)}}\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{-5}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(\frac{1}{a + 0.8333333333333334} \cdot \left(\left(a + 0.8333333333333334\right) \cdot \left(a + 0.8333333333333334\right)\right) - \frac{1}{t} \cdot 0.6666666666666666\right)\right)}}\\ \mathbf{elif}\;b \leq 7 \cdot 10^{+123}:\\ \;\;\;\;\left(0 - \left(-1 - \frac{x}{y \cdot e^{\left(c - b\right) \cdot \left(a + a\right)} + x}\right)\right) - 1\\ \mathbf{elif}\;b \leq 1.45 \cdot 10^{+200}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(0.6666666666666666 \cdot \frac{b}{t}\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(b - c\right) \cdot \left(-0.8333333333333334 - a\right)\right)}}\\ \end{array} \]

Alternative 3
Error	20.0
Cost	8420

\[\begin{array}{l} t_1 := \frac{x}{x + e^{\left(b - c\right) \cdot -1.6666666666666667} \cdot y}\\ t_2 := \frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{if}\;a \leq -0.85:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -9.6 \cdot 10^{-190}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -8.8 \cdot 10^{-297}:\\ \;\;\;\;\left(0 - \left(-1 - \frac{x}{y + x}\right)\right) - 1\\ \mathbf{elif}\;a \leq 2 \cdot 10^{-283}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{-249}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(-0.6666666666666666 \cdot \frac{c}{t}\right)}}\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{-21}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{+21}:\\ \;\;\;\;0\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+74}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(0.6666666666666666 \cdot \frac{b}{t}\right)}}\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{+83}:\\ \;\;\;\;0\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 4
Error	20.0
Cost	8420

\[\begin{array}{l} t_1 := \frac{x}{x + e^{\left(b - c\right) \cdot -1.6666666666666667} \cdot y}\\ t_2 := \frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{if}\;a \leq -0.85:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -2.85 \cdot 10^{-190}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{-296}:\\ \;\;\;\;\left(0 - \left(-1 - \frac{x}{y + x}\right)\right) - 1\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-281}:\\ \;\;\;\;\frac{x}{x + e^{\left(0.8333333333333334 + a\right) \cdot \left(b \cdot -2\right)} \cdot y}\\ \mathbf{elif}\;a \leq 4 \cdot 10^{-249}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(-0.6666666666666666 \cdot \frac{c}{t}\right)}}\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{-21}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{+20}:\\ \;\;\;\;0\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{+70}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(0.6666666666666666 \cdot \frac{b}{t}\right)}}\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{+83}:\\ \;\;\;\;0\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 5
Error	24.0
Cost	8292

\[\begin{array}{l} t_1 := \frac{x}{x + e^{\left(b - c\right) \cdot -1.6666666666666667} \cdot y}\\ \mathbf{if}\;a \leq -0.85:\\ \;\;\;\;1\\ \mathbf{elif}\;a \leq -1.15 \cdot 10^{-190}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -7.2 \cdot 10^{-297}:\\ \;\;\;\;\left(0 - \left(-1 - \frac{x}{y + x}\right)\right) - 1\\ \mathbf{elif}\;a \leq 5.1 \cdot 10^{-282}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{-249}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(-0.6666666666666666 \cdot \frac{c}{t}\right)}}\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{-21}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{+20}:\\ \;\;\;\;0\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{+73}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(0.6666666666666666 \cdot \frac{b}{t}\right)}}\\ \mathbf{elif}\;a \leq 8.6 \cdot 10^{+108}:\\ \;\;\;\;0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	15.2
Cost	8012

\[\begin{array}{l} \mathbf{if}\;b \leq -1.25 \cdot 10^{+21}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(0.6666666666666666 \cdot \frac{1}{t} - \left(0.8333333333333334 + a\right)\right) \cdot b\right)}}\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{-7}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(\left(a + 0.8333333333333334\right) - \frac{1}{t} \cdot 0.6666666666666666\right)\right)}}\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{+121}:\\ \;\;\;\;\left(0 - \left(-1 - \frac{x}{y \cdot e^{\left(c - b\right) \cdot \left(a + a\right)} + x}\right)\right) - 1\\ \mathbf{elif}\;b \leq 1.75 \cdot 10^{+200}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(0.6666666666666666 \cdot \frac{b}{t}\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(b - c\right) \cdot \left(-0.8333333333333334 - a\right)\right)}}\\ \end{array} \]

Alternative 7
Error	14.0
Cost	7748

\[\begin{array}{l} \mathbf{if}\;t \leq -2.25 \cdot 10^{-297}:\\ \;\;\;\;\left(0 - \left(-1 - \frac{x}{y \cdot e^{\left(c - b\right) \cdot \left(a + a\right)} + x}\right)\right) - 1\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{-77}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(0.6666666666666666 \cdot \frac{b}{t}\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(b - c\right) \cdot \left(-0.8333333333333334 - a\right)\right)}}\\ \end{array} \]

Alternative 8
Error	20.4
Cost	7632

\[\begin{array}{l} t_1 := \frac{x}{x + e^{\left(b - c\right) \cdot -1.6666666666666667} \cdot y}\\ \mathbf{if}\;t \leq -5.1 \cdot 10^{-250}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 10^{-225}:\\ \;\;\;\;0\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-197}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-54}:\\ \;\;\;\;\left(0 - \left(-1 - \frac{x}{\left(y + y \cdot \left(2 \cdot \left(a \cdot \left(c - b\right)\right)\right)\right) + x}\right)\right) - 1\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 9
Error	19.6
Cost	7632

\[\begin{array}{l} t_1 := \frac{x}{x + e^{\left(b - c\right) \cdot -1.6666666666666667} \cdot y}\\ \mathbf{if}\;t \leq -5.4 \cdot 10^{-250}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.05 \cdot 10^{-276}:\\ \;\;\;\;0\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-164}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(-0.6666666666666666 \cdot \frac{c}{t}\right)}}\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{-52}:\\ \;\;\;\;\left(0 - \left(-1 - \frac{x}{\left(y + y \cdot \left(2 \cdot \left(a \cdot \left(c - b\right)\right)\right)\right) + x}\right)\right) - 1\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 10
Error	13.8
Cost	7624

\[\begin{array}{l} t_1 := \frac{x}{x + y \cdot e^{2 \cdot \left(\left(b - c\right) \cdot \left(-0.8333333333333334 - a\right)\right)}}\\ \mathbf{if}\;t \leq -1.5 \cdot 10^{-298}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-76}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(0.6666666666666666 \cdot \frac{b}{t}\right)}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 11
Error	31.7
Cost	2280

\[\begin{array}{l} t_1 := \frac{x}{x + \left(y + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)\right)}\\ \mathbf{if}\;t \leq -5 \cdot 10^{-86}:\\ \;\;\;\;0\\ \mathbf{elif}\;t \leq -3.4 \cdot 10^{-248}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 10^{-225}:\\ \;\;\;\;0\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-197}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 9.6 \cdot 10^{-181}:\\ \;\;\;\;0\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-66}:\\ \;\;\;\;\left(0 - \left(-1 - \frac{x}{y + x}\right)\right) - 1\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{+14}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+81}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{+167}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+209}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+265}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \]

Alternative 12
Error	31.0
Cost	2152

\[\begin{array}{l} t_1 := \left(0 - \left(-1 - \frac{x}{y + x}\right)\right) - 1\\ \mathbf{if}\;t \leq -5 \cdot 10^{-86}:\\ \;\;\;\;0\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-248}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 1.32 \cdot 10^{-225}:\\ \;\;\;\;0\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-197}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 10^{-180}:\\ \;\;\;\;0\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-61}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1550000000000:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+66}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+167}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{+208}:\\ \;\;\;\;\frac{x}{x + \left(y + -1.3333333333333333 \cdot \frac{c \cdot y}{t}\right)}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+265}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \]

Alternative 13
Error	31.7
Cost	2152

\[\begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{-86}:\\ \;\;\;\;0\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-247}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-225}:\\ \;\;\;\;0\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-197}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-180}:\\ \;\;\;\;0\\ \mathbf{elif}\;t \leq 4.7 \cdot 10^{-63}:\\ \;\;\;\;\left(0 - \left(-1 - \frac{x}{y + x}\right)\right) - 1\\ \mathbf{elif}\;t \leq 1.32 \cdot 10^{+14}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+81}:\\ \;\;\;\;\frac{x}{x + \left(y + \left(y \cdot a\right) \cdot \left(c \cdot 2\right)\right)}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+167}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{+208}:\\ \;\;\;\;\frac{x}{x + \left(y + -1.3333333333333333 \cdot \frac{c \cdot y}{t}\right)}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+265}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \]

Alternative 14
Error	31.9
Cost	2148

\[\begin{array}{l} t_1 := \frac{x}{x + \left(y + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)\right)}\\ \mathbf{if}\;t \leq -5 \cdot 10^{-86}:\\ \;\;\;\;0\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-248}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-225}:\\ \;\;\;\;0\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-197}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 2.85 \cdot 10^{-64}:\\ \;\;\;\;\left(0 - \left(-1 - \frac{x}{\left(y + y \cdot \left(2 \cdot \left(a \cdot \left(c - b\right)\right)\right)\right) + x}\right)\right) - 1\\ \mathbf{elif}\;t \leq 23500000000000:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{+81}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{+167}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{+210}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{+266}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \]

Alternative 15
Error	30.9
Cost	2024

\[\begin{array}{l} t_1 := \left(0 - \left(-1 - \frac{x}{y + x}\right)\right) - 1\\ \mathbf{if}\;t \leq -5 \cdot 10^{-86}:\\ \;\;\;\;0\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-249}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 10^{-225}:\\ \;\;\;\;0\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-197}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-180}:\\ \;\;\;\;0\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{-61}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{+14}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{+67}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{+170}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+208}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+266}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \]

Alternative 16
Error	31.9
Cost	1516

\[\begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+249}:\\ \;\;\;\;0\\ \mathbf{elif}\;x \leq -5 \cdot 10^{+164}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -5 \cdot 10^{+102}:\\ \;\;\;\;0\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{+65}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -5000000000:\\ \;\;\;\;0\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{-85}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{-205}:\\ \;\;\;\;0\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-265}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 2 \cdot 10^{-219}:\\ \;\;\;\;0\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-109}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 10^{+182}:\\ \;\;\;\;0\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 17
Error	27.8
Cost	988

\[\begin{array}{l} \mathbf{if}\;c \leq -50000000000:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -5 \cdot 10^{-74}:\\ \;\;\;\;0\\ \mathbf{elif}\;c \leq -1.7 \cdot 10^{-105}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -7 \cdot 10^{-133}:\\ \;\;\;\;0\\ \mathbf{elif}\;c \leq -6.8 \cdot 10^{-157}:\\ \;\;\;\;\frac{x}{y + x}\\ \mathbf{elif}\;c \leq -5.1 \cdot 10^{-217}:\\ \;\;\;\;0\\ \mathbf{elif}\;c \leq 7 \cdot 10^{-162}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \]

Alternative 18
Error	30.9
Cost	64

\[1 \]

Reproduce

herbie shell --seed 2023077 
(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)))))))))))