Numeric.SpecFunctions:incompleteBetaWorker from math-functions-0.1.5.2, A

Average Accuracy: 97.2% → 96.8%

Time: 30.4s

Precision: binary64

Cost: 33736

Math

\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

↓

\[\begin{array}{l} t_1 := \left(t + -1\right) \cdot \log a\\ \mathbf{if}\;t_1 \leq -628:\\ \;\;\;\;\frac{{a}^{\left(t + -1\right)}}{y} \cdot x\\ \mathbf{elif}\;t_1 \leq -400:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t_1 + y \cdot \log z\right) - b}}{y}\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y))

↓

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (+ t -1.0) (log a))))
   (if (<= t_1 -628.0)
     (* (/ (pow a (+ t -1.0)) y) x)
     (if (<= t_1 -400.0)
       (/ x (* a (* y (exp b))))
       (/ (* x (exp (- (+ t_1 (* y (log z))) b))) y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return (x * exp((((y * log(z)) + ((t - 1.0) * log(a))) - b))) / y;
}

↓

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t + -1.0) * log(a);
	double tmp;
	if (t_1 <= -628.0) {
		tmp = (pow(a, (t + -1.0)) / y) * x;
	} else if (t_1 <= -400.0) {
		tmp = x / (a * (y * exp(b)));
	} else {
		tmp = (x * exp(((t_1 + (y * log(z))) - b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = (x * exp((((y * log(z)) + ((t - 1.0d0) * log(a))) - b))) / y
end function

↓

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t + (-1.0d0)) * log(a)
    if (t_1 <= (-628.0d0)) then
        tmp = ((a ** (t + (-1.0d0))) / y) * x
    else if (t_1 <= (-400.0d0)) then
        tmp = x / (a * (y * exp(b)))
    else
        tmp = (x * exp(((t_1 + (y * log(z))) - b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return (x * Math.exp((((y * Math.log(z)) + ((t - 1.0) * Math.log(a))) - b))) / y;
}

↓

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t + -1.0) * Math.log(a);
	double tmp;
	if (t_1 <= -628.0) {
		tmp = (Math.pow(a, (t + -1.0)) / y) * x;
	} else if (t_1 <= -400.0) {
		tmp = x / (a * (y * Math.exp(b)));
	} else {
		tmp = (x * Math.exp(((t_1 + (y * Math.log(z))) - b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	return (x * math.exp((((y * math.log(z)) + ((t - 1.0) * math.log(a))) - b))) / y

↓

def code(x, y, z, t, a, b):
	t_1 = (t + -1.0) * math.log(a)
	tmp = 0
	if t_1 <= -628.0:
		tmp = (math.pow(a, (t + -1.0)) / y) * x
	elif t_1 <= -400.0:
		tmp = x / (a * (y * math.exp(b)))
	else:
		tmp = (x * math.exp(((t_1 + (y * math.log(z))) - b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(x * exp(Float64(Float64(Float64(y * log(z)) + Float64(Float64(t - 1.0) * log(a))) - b))) / y)
end

↓

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t + -1.0) * log(a))
	tmp = 0.0
	if (t_1 <= -628.0)
		tmp = Float64(Float64((a ^ Float64(t + -1.0)) / y) * x);
	elseif (t_1 <= -400.0)
		tmp = Float64(x / Float64(a * Float64(y * exp(b))));
	else
		tmp = Float64(Float64(x * exp(Float64(Float64(t_1 + Float64(y * log(z))) - b))) / y);
	end
	return tmp
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = (x * exp((((y * log(z)) + ((t - 1.0) * log(a))) - b))) / y;
end

↓

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t + -1.0) * log(a);
	tmp = 0.0;
	if (t_1 <= -628.0)
		tmp = ((a ^ (t + -1.0)) / y) * x;
	elseif (t_1 <= -400.0)
		tmp = x / (a * (y * exp(b)));
	else
		tmp = (x * exp(((t_1 + (y * log(z))) - b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(x * N[Exp[N[(N[(N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision] + N[(N[(t - 1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]

↓

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t + -1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -628.0], N[(N[(N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[t$95$1, -400.0], N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[Exp[N[(N[(t$95$1 + N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]]

Target

Original	97.2%
Target	82.5%
Herbie	96.8%

\[\begin{array}{l} \mathbf{if}\;t < -0.8845848504127471:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t - 1\right)}}{y}}{\left(b + 1\right) - y \cdot \log z}\\ \mathbf{elif}\;t < 852031.2288374073:\\ \;\;\;\;\frac{\frac{x}{y} \cdot {a}^{\left(t - 1\right)}}{e^{b - \log z \cdot y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t - 1\right)}}{y}}{\left(b + 1\right) - y \cdot \log z}\\ \end{array} \]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 t 1) (log.f64 a)) < -628

   1. Initial program 99.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

   2. Taylor expanded in y around 0 96.7%

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

   3. Simplified 85.5%

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

      [Start] 96.7	\[ \frac{e^{\left(t - 1\right) \cdot \log a - b} \cdot x}{y} \]
      associate-/l* [=>] 85.7	\[ \color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a - b}}{\frac{y}{x}}} \]
      associate-/r/ [=>] 97.8	\[ \color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a - b}}{y} \cdot x} \]
      exp-diff [=>] 85.3	\[ \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y} \cdot x \]
      log-pow [<=] 85.3	\[ \frac{\frac{e^{\color{blue}{\log \left({a}^{\left(t - 1\right)}\right)}}}{e^{b}}}{y} \cdot x \]
      sub-neg [=>] 85.3	\[ \frac{\frac{e^{\log \left({a}^{\color{blue}{\left(t + \left(-1\right)\right)}}\right)}}{e^{b}}}{y} \cdot x \]
      metadata-eval [=>] 85.3	\[ \frac{\frac{e^{\log \left({a}^{\left(t + \color{blue}{-1}\right)}\right)}}{e^{b}}}{y} \cdot x \]
      rem-exp-log [=>] 85.5	\[ \frac{\frac{\color{blue}{{a}^{\left(t + -1\right)}}}{e^{b}}}{y} \cdot x \]

   4. Taylor expanded in b around 0 98.3%

      \[\leadsto \color{blue}{\frac{{a}^{\left(t - 1\right)}}{y}} \cdot x \]

   if -628 < (*.f64 (-.f64 t 1) (log.f64 a)) < -400

   1. Initial program 90.3%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

   2. Taylor expanded in y around 0 76.3%

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

   3. Simplified 90.0%

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

      [Start] 76.3	\[ \frac{e^{\left(t - 1\right) \cdot \log a - b} \cdot x}{y} \]
      associate-/l* [=>] 70.0	\[ \color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a - b}}{\frac{y}{x}}} \]
      associate-/r/ [=>] 87.2	\[ \color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a - b}}{y} \cdot x} \]
      exp-diff [=>] 87.2	\[ \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y} \cdot x \]
      log-pow [<=] 87.2	\[ \frac{\frac{e^{\color{blue}{\log \left({a}^{\left(t - 1\right)}\right)}}}{e^{b}}}{y} \cdot x \]
      sub-neg [=>] 87.2	\[ \frac{\frac{e^{\log \left({a}^{\color{blue}{\left(t + \left(-1\right)\right)}}\right)}}{e^{b}}}{y} \cdot x \]
      metadata-eval [=>] 87.2	\[ \frac{\frac{e^{\log \left({a}^{\left(t + \color{blue}{-1}\right)}\right)}}{e^{b}}}{y} \cdot x \]
      rem-exp-log [=>] 90.0	\[ \frac{\frac{\color{blue}{{a}^{\left(t + -1\right)}}}{e^{b}}}{y} \cdot x \]

   4. Taylor expanded in t around 0 89.0%

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

   if -400 < (*.f64 (-.f64 t 1) (log.f64 a))

   1. Initial program 97.2%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
3. Recombined 3 regimes into one program.

4. Final simplification 96.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(t + -1\right) \cdot \log a \leq -628:\\ \;\;\;\;\frac{{a}^{\left(t + -1\right)}}{y} \cdot x\\ \mathbf{elif}\;\left(t + -1\right) \cdot \log a \leq -400:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(\left(t + -1\right) \cdot \log a + y \cdot \log z\right) - b}}{y}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	96.1%
Cost	26692

\[\begin{array}{l} \mathbf{if}\;\left(t + -1\right) \cdot \log a \leq -530:\\ \;\;\;\;\frac{{a}^{\left(t + -1\right)}}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \end{array} \]

Alternative 2
Accuracy	89.5%
Cost	20228

\[\begin{array}{l} \mathbf{if}\;\left(t + -1\right) \cdot \log a \leq -550:\\ \;\;\;\;\frac{{a}^{\left(t + -1\right)}}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{{z}^{y}}{a} \cdot \frac{x}{y \cdot e^{b}}\\ \end{array} \]

Alternative 3
Accuracy	83.0%
Cost	13836

\[\begin{array}{l} \mathbf{if}\;b \leq 2.2 \cdot 10^{-223}:\\ \;\;\;\;\frac{\frac{x}{\frac{y}{{a}^{t}}}}{a}\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{-163}:\\ \;\;\;\;{z}^{y} \cdot \frac{\frac{x}{y}}{a}\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{-19}:\\ \;\;\;\;x \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \]

Alternative 4
Accuracy	82.4%
Cost	7440

\[\begin{array}{l} t_1 := {z}^{y} \cdot \frac{\frac{x}{y}}{a}\\ t_2 := \frac{{a}^{\left(t + -1\right)}}{y} \cdot x\\ \mathbf{if}\;b \leq -7.5 \cdot 10^{-287}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 1.16 \cdot 10^{-163}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{-45}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 6 \cdot 10^{-9}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \]

Alternative 5
Accuracy	81.8%
Cost	7440

\[\begin{array}{l} t_1 := {z}^{y} \cdot \frac{\frac{x}{y}}{a}\\ \mathbf{if}\;b \leq -9.4 \cdot 10^{-287}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{t}}{a}}{y}\\ \mathbf{elif}\;b \leq 9 \cdot 10^{-163}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{-45}:\\ \;\;\;\;\frac{{a}^{\left(t + -1\right)}}{y} \cdot x\\ \mathbf{elif}\;b \leq 120:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \]

Alternative 6
Accuracy	80.2%
Cost	7308

\[\begin{array}{l} t_1 := \frac{{a}^{\left(t + -1\right)}}{y} \cdot x\\ \mathbf{if}\;b \leq -6.9 \cdot 10^{-307}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 4 \cdot 10^{-190}:\\ \;\;\;\;\frac{x}{y} \cdot \left(-\frac{b}{a}\right)\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{-19}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \]

Alternative 7
Accuracy	83.0%
Cost	7308

\[\begin{array}{l} \mathbf{if}\;b \leq 8.5 \cdot 10^{-225}:\\ \;\;\;\;\frac{\frac{x}{\frac{y}{{a}^{t}}}}{a}\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{-163}:\\ \;\;\;\;{z}^{y} \cdot \frac{\frac{x}{y}}{a}\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{-19}:\\ \;\;\;\;\frac{{a}^{\left(t + -1\right)}}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \]

Alternative 8
Accuracy	64.2%
Cost	7244

\[\begin{array}{l} t_1 := \frac{1}{y} + \frac{b}{y}\\ \mathbf{if}\;b \leq -5.6 \cdot 10^{-37}:\\ \;\;\;\;x \cdot \frac{\frac{y}{b} - y}{a \cdot \left(y \cdot \frac{y}{b}\right)}\\ \mathbf{elif}\;b \leq -4.7 \cdot 10^{-262}:\\ \;\;\;\;\frac{t_1}{\frac{t_1 \cdot \frac{a}{x}}{\frac{1 - b}{y}}}\\ \mathbf{elif}\;b \leq 7 \cdot 10^{-194}:\\ \;\;\;\;\frac{x}{y} \cdot \left(-\frac{b}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \]

Alternative 9
Accuracy	39.1%
Cost	1864

\[\begin{array}{l} t_1 := \frac{\frac{1}{a}}{\frac{y}{x}}\\ t_2 := \frac{1}{y} + \frac{b}{y}\\ \mathbf{if}\;x \leq -9 \cdot 10^{-58}:\\ \;\;\;\;x \cdot \frac{\frac{y}{b} - y}{a \cdot \left(y \cdot \frac{y}{b}\right)}\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{-228}:\\ \;\;\;\;\frac{t_2}{\frac{t_2 \cdot \frac{a}{x}}{\frac{1 - b}{y}}}\\ \mathbf{elif}\;x \leq 1.28 \cdot 10^{-160}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-97}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{elif}\;x \leq 2 \cdot 10^{+34}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+248} \lor \neg \left(x \leq 2.7 \cdot 10^{+299}\right):\\ \;\;\;\;\frac{y - y \cdot b}{\frac{a \cdot \left(y \cdot y\right)}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot y}\\ \end{array} \]

Alternative 10
Accuracy	38.9%
Cost	1625

\[\begin{array}{l} t_1 := \frac{y - y \cdot b}{\frac{a \cdot \left(y \cdot y\right)}{x}}\\ \mathbf{if}\;x \leq -4.5 \cdot 10^{+146}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{-222}:\\ \;\;\;\;\frac{1}{y} \cdot \frac{1}{\frac{a}{x}}\\ \mathbf{elif}\;x \leq 1.26 \cdot 10^{-160}:\\ \;\;\;\;\frac{\frac{1}{a}}{\frac{y}{x}}\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-48}:\\ \;\;\;\;\frac{1}{\frac{y}{\frac{x}{a}}}\\ \mathbf{elif}\;x \leq 3.05 \cdot 10^{+249} \lor \neg \left(x \leq 2.8 \cdot 10^{+299}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot y}\\ \end{array} \]

Alternative 11
Accuracy	36.6%
Cost	844

\[\begin{array}{l} t_1 := \frac{\frac{x}{a}}{y}\\ \mathbf{if}\;x \leq -1.25 \cdot 10^{-238}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-161}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-81}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{a \cdot y}\\ \end{array} \]

Alternative 12
Accuracy	36.8%
Cost	844

\[\begin{array}{l} t_1 := \frac{1}{\frac{y}{\frac{x}{a}}}\\ \mathbf{if}\;x \leq -2 \cdot 10^{-223}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{-160}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-81}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{a \cdot y}\\ \end{array} \]

Alternative 13
Accuracy	37.0%
Cost	844

\[\begin{array}{l} t_1 := \frac{1}{\frac{y}{\frac{x}{a}}}\\ \mathbf{if}\;x \leq -8 \cdot 10^{-223}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{-162}:\\ \;\;\;\;\frac{\frac{1}{a}}{\frac{y}{x}}\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{-81}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{a \cdot y}\\ \end{array} \]

Alternative 14
Accuracy	37.0%
Cost	844

\[\begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{-237}:\\ \;\;\;\;\frac{1}{y} \cdot \frac{1}{\frac{a}{x}}\\ \mathbf{elif}\;x \leq 2.12 \cdot 10^{-162}:\\ \;\;\;\;\frac{\frac{1}{a}}{\frac{y}{x}}\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{-86}:\\ \;\;\;\;\frac{1}{\frac{y}{\frac{x}{a}}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{a \cdot y}\\ \end{array} \]

Alternative 15
Accuracy	36.6%
Cost	716

\[\begin{array}{l} t_1 := \frac{\frac{x}{a}}{y}\\ \mathbf{if}\;x \leq -1 \cdot 10^{-237}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-160}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-71}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot y}\\ \end{array} \]

Alternative 16
Accuracy	35.6%
Cost	452

\[\begin{array}{l} \mathbf{if}\;x \leq 6 \cdot 10^{-84}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot y}\\ \end{array} \]

Alternative 17
Accuracy	34.6%
Cost	320

\[\frac{x}{a \cdot y} \]

Reproduce

herbie shell --seed 2023138 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:incompleteBetaWorker from math-functions-0.1.5.2, A"
  :precision binary64

  :herbie-target
  (if (< t -0.8845848504127471) (/ (* x (/ (pow a (- t 1.0)) y)) (- (+ b 1.0) (* y (log z)))) (if (< t 852031.2288374073) (/ (* (/ x y) (pow a (- t 1.0))) (exp (- b (* (log z) y)))) (/ (* x (/ (pow a (- t 1.0)) y)) (- (+ b 1.0) (* y (log z))))))

  (/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y))