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

Average Error: 3.8 → 2.2

Time: 57.7s

Precision: binary64

Cost: 22468

Math

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

↓

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

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)
          (* (- c b) (+ (+ a 0.8333333333333334) (/ -2.0 (* t 3.0)))))))
   (if (<= t_1 INFINITY)
     (/ x (+ x (* y (exp (* 2.0 t_1)))))
     (/ x (+ x (* y (exp (* 2.0 (/ c (/ t -0.6666666666666666))))))))))

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) + ((c - b) * ((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 = x / (x + (y * exp((2.0 * (c / (t / -0.6666666666666666))))));
	}
	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) + ((c - b) * ((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 = x / (x + (y * Math.exp((2.0 * (c / (t / -0.6666666666666666))))));
	}
	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) + ((c - b) * ((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 = x / (x + (y * math.exp((2.0 * (c / (t / -0.6666666666666666))))))
	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(c - b) * 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 = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(c / Float64(t / -0.6666666666666666)))))));
	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) + ((c - b) * ((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 = x / (x + (y * exp((2.0 * (c / (t / -0.6666666666666666))))));
	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[(c - b), $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], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(c / N[(t / -0.6666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Target

Original	3.8
Target	3.0
Herbie	2.2

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

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

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

   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. Taylor expanded in c around inf 28.7

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(c \cdot \left(\left(0.8333333333333334 + a\right) - 0.6666666666666666 \cdot \frac{1}{t}\right)\right)}}} \]

   3. Simplified 28.7

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(c \cdot \left(\frac{-0.6666666666666666}{t} - \left(-0.8333333333333334 - a\right)\right)\right)}}} \]
      Proof
      (*.f64 c (-.f64 (/.f64 -2/3 t) (-.f64 -5/6 a))): 0 points increase in error, 0 points decrease in error
      (*.f64 c (-.f64 (/.f64 (Rewrite<= metadata-eval (neg.f64 2/3)) t) (-.f64 -5/6 a))): 0 points increase in error, 0 points decrease in error
      (*.f64 c (-.f64 (Rewrite<= distribute-neg-frac_binary64 (neg.f64 (/.f64 2/3 t))) (-.f64 -5/6 a))): 0 points increase in error, 0 points decrease in error
      (*.f64 c (-.f64 (neg.f64 (/.f64 (Rewrite<= metadata-eval (*.f64 2/3 1)) t)) (-.f64 -5/6 a))): 0 points increase in error, 0 points decrease in error
      (*.f64 c (-.f64 (neg.f64 (Rewrite<= associate-*r/_binary64 (*.f64 2/3 (/.f64 1 t)))) (-.f64 -5/6 a))): 12 points increase in error, 6 points decrease in error
      (*.f64 c (-.f64 (neg.f64 (*.f64 2/3 (/.f64 1 t))) (-.f64 (Rewrite<= metadata-eval (neg.f64 5/6)) a))): 0 points increase in error, 0 points decrease in error
      (*.f64 c (-.f64 (neg.f64 (*.f64 2/3 (/.f64 1 t))) (Rewrite<= unsub-neg_binary64 (+.f64 (neg.f64 5/6) (neg.f64 a))))): 0 points increase in error, 0 points decrease in error
      (*.f64 c (-.f64 (neg.f64 (*.f64 2/3 (/.f64 1 t))) (Rewrite<= distribute-neg-in_binary64 (neg.f64 (+.f64 5/6 a))))): 0 points increase in error, 0 points decrease in error
      (*.f64 c (Rewrite<= unsub-neg_binary64 (+.f64 (neg.f64 (*.f64 2/3 (/.f64 1 t))) (neg.f64 (neg.f64 (+.f64 5/6 a)))))): 0 points increase in error, 0 points decrease in error
      (*.f64 c (Rewrite<= distribute-neg-in_binary64 (neg.f64 (+.f64 (*.f64 2/3 (/.f64 1 t)) (neg.f64 (+.f64 5/6 a)))))): 0 points increase in error, 0 points decrease in error
      (*.f64 c (neg.f64 (Rewrite<= sub-neg_binary64 (-.f64 (*.f64 2/3 (/.f64 1 t)) (+.f64 5/6 a))))): 0 points increase in error, 0 points decrease in error
      (*.f64 c (Rewrite=> neg-sub0_binary64 (-.f64 0 (-.f64 (*.f64 2/3 (/.f64 1 t)) (+.f64 5/6 a))))): 0 points increase in error, 0 points decrease in error
      (*.f64 c (Rewrite<= associate-+l-_binary64 (+.f64 (-.f64 0 (*.f64 2/3 (/.f64 1 t))) (+.f64 5/6 a)))): 0 points increase in error, 0 points decrease in error
      (*.f64 c (+.f64 (Rewrite<= neg-sub0_binary64 (neg.f64 (*.f64 2/3 (/.f64 1 t)))) (+.f64 5/6 a))): 0 points increase in error, 0 points decrease in error
      (*.f64 c (Rewrite<= +-commutative_binary64 (+.f64 (+.f64 5/6 a) (neg.f64 (*.f64 2/3 (/.f64 1 t)))))): 0 points increase in error, 0 points decrease in error
      (*.f64 c (Rewrite<= sub-neg_binary64 (-.f64 (+.f64 5/6 a) (*.f64 2/3 (/.f64 1 t))))): 0 points increase in error, 0 points decrease in error

   4. Taylor expanded in t around 0 30.8

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

   5. Simplified 30.8

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\frac{c}{\frac{t}{-0.6666666666666666}}}}} \]
      Proof
      (/.f64 c (/.f64 t -2/3)): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 c -2/3) t)): 31 points increase in error, 24 points decrease in error
      (Rewrite<= associate-*l/_binary64 (*.f64 (/.f64 c t) -2/3)): 22 points increase in error, 31 points decrease in error
      (Rewrite<= *-commutative_binary64 (*.f64 -2/3 (/.f64 c t))): 0 points increase in error, 0 points decrease in error
3. Recombined 2 regimes into one program.

4. Final simplification 2.2

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

Alternatives

Alternative 1
Error	2.1
Cost	33408

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

Alternative 2
Error	14.8
Cost	14424

\[\begin{array}{l} \mathbf{if}\;t \leq -2.75 \cdot 10^{+48}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{-2 \cdot \left(a \cdot \left(b - c\right)\right)}}\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{-197}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{\sqrt{a} \cdot \frac{2}{\frac{t}{z}}}}\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-278}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{\left(c - b\right) \cdot 1.6666666666666667}}\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-268}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{c}{\frac{t}{-0.6666666666666666}}}}\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{-66}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \left(\left(-0.8333333333333334 - a\right) + \frac{0.6666666666666666}{t}\right)\right)}}\\ \mathbf{elif}\;t \leq 5.047617163262378 \cdot 10^{+39}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(z \cdot \sqrt{\frac{1}{t}}\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(c - b\right) \cdot \left(a + 0.8333333333333334\right)\right)}}\\ \end{array} \]

Alternative 3
Error	14.1
Cost	13896

\[\begin{array}{l} t_1 := \left(-0.8333333333333334 - a\right) + \frac{0.6666666666666666}{t}\\ \mathbf{if}\;t \leq -2.75 \cdot 10^{+48}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{-2 \cdot \left(a \cdot \left(b - c\right)\right)}}\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{-197}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{\sqrt{a} \cdot \frac{2}{\frac{t}{z}}}}\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-278}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{\left(c - b\right) \cdot 1.6666666666666667}}\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-268}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{c}{\frac{t}{-0.6666666666666666}}}}\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-82}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot t_1\right)}}\\ \mathbf{elif}\;t \leq 2.3566062960922383 \cdot 10^{-19}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{-2 \cdot \left(c \cdot t_1\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(c - b\right) \cdot \left(a + 0.8333333333333334\right)\right)}}\\ \end{array} \]

Alternative 4
Error	27.6
Cost	8688

\[\begin{array}{l} t_1 := \frac{x}{x + y \cdot e^{-2 \cdot \left(a \cdot b\right)}}\\ t_2 := \left(1 + \frac{x}{x + y}\right) + -1\\ t_3 := \frac{x}{x + y \cdot e^{\left(c - b\right) \cdot 1.6666666666666667}}\\ \mathbf{if}\;c \leq -1.1725995836373971 \cdot 10^{+241}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq -1.7208896673802977 \cdot 10^{+177}:\\ \;\;\;\;\frac{x}{x - y \cdot \left(-1 + \frac{c}{t} \cdot 1.3333333333333333\right)}\\ \mathbf{elif}\;c \leq -3.6758442492330087 \cdot 10^{+109}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -9.356134833587597 \cdot 10^{-93}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -5.761135588667649 \cdot 10^{-270}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 1.3011256963090851 \cdot 10^{-211}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 2.119111017066928 \cdot 10^{-61}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 2.321696008741337 \cdot 10^{-44}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 3.8396479608220605 \cdot 10^{+40}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 1.3256773454494805 \cdot 10^{+60}:\\ \;\;\;\;\frac{x}{x + y \cdot \left(-2 \cdot \left(a \cdot \left(b - c\right)\right) + 1\right)}\\ \mathbf{elif}\;c \leq 8.054886839554715 \cdot 10^{+85}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{b \cdot -1.6666666666666667}}\\ \mathbf{elif}\;c \leq 2.21711758320824 \cdot 10^{+144}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 5
Error	27.5
Cost	8424

\[\begin{array}{l} t_1 := \frac{x}{x + y \cdot e^{a \cdot \left(2 \cdot c\right)}}\\ t_2 := \left(1 + \frac{x}{x + y}\right) + -1\\ t_3 := \frac{x}{x + y \cdot e^{\left(c - b\right) \cdot 1.6666666666666667}}\\ \mathbf{if}\;c \leq -1.1725995836373971 \cdot 10^{+241}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq -1.7208896673802977 \cdot 10^{+177}:\\ \;\;\;\;\frac{x}{x - y \cdot \left(-1 + \frac{c}{t} \cdot 1.3333333333333333\right)}\\ \mathbf{elif}\;c \leq -3.6758442492330087 \cdot 10^{+109}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -9.356134833587597 \cdot 10^{-93}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -5.761135588667649 \cdot 10^{-270}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 1.3011256963090851 \cdot 10^{-211}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{-2 \cdot \left(a \cdot b\right)}}\\ \mathbf{elif}\;c \leq 1.557555851725478 \cdot 10^{-71}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 2.321696008741337 \cdot 10^{-44}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 2.21711758320824 \cdot 10^{+144}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 5.092756513384547 \cdot 10^{+263}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	29.5
Cost	8160

\[\begin{array}{l} t_1 := \left(1 + \frac{x}{x + y}\right) + -1\\ t_2 := \frac{x}{x + y \cdot e^{-2 \cdot \left(a \cdot b\right)}}\\ \mathbf{if}\;c \leq -1.1725995836373971 \cdot 10^{+241}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -1.7208896673802977 \cdot 10^{+177}:\\ \;\;\;\;\frac{x}{x - y \cdot \left(-1 + \frac{c}{t} \cdot 1.3333333333333333\right)}\\ \mathbf{elif}\;c \leq -3.6758442492330087 \cdot 10^{+109}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -2.4358016307878852 \cdot 10^{-98}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -1.662035118286602 \cdot 10^{-173}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 1.3011256963090851 \cdot 10^{-211}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 2.119111017066928 \cdot 10^{-61}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 2.321696008741337 \cdot 10^{-44}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 8.614929170902509 \cdot 10^{+181}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 3.550120588900296 \cdot 10^{+223}:\\ \;\;\;\;\frac{x}{x - \left(2 \cdot \left(c \cdot \left(y \cdot \left(\left(-0.8333333333333334 - a\right) + -0.6666666666666666 \cdot \frac{-1}{t}\right)\right)\right) - y\right)}\\ \mathbf{elif}\;c \leq 2.9538150459376286 \cdot 10^{+245}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 1.473987653672599 \cdot 10^{+290}:\\ \;\;\;\;\frac{x}{x - \left(-2 \cdot \left(y \cdot \left(a \cdot c\right)\right) - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y \cdot c} \cdot 0.5}{a}\\ \end{array} \]

Alternative 7
Error	13.0
Cost	8016

\[\begin{array}{l} t_1 := \left(-0.8333333333333334 - a\right) + \frac{0.6666666666666666}{t}\\ \mathbf{if}\;t \leq -9.5 \cdot 10^{-249}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{-2 \cdot \left(a \cdot \left(b - c\right)\right)}}\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-268}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{c}{\frac{t}{-0.6666666666666666}}}}\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-82}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot t_1\right)}}\\ \mathbf{elif}\;t \leq 2.3566062960922383 \cdot 10^{-19}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{-2 \cdot \left(c \cdot t_1\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(c - b\right) \cdot \left(a + 0.8333333333333334\right)\right)}}\\ \end{array} \]

Alternative 8
Error	12.8
Cost	7884

\[\begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{-249}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{-2 \cdot \left(a \cdot \left(b - c\right)\right)}}\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-268}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{c}{\frac{t}{-0.6666666666666666}}}}\\ \mathbf{elif}\;t \leq 2.3566062960922383 \cdot 10^{-19}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \left(\left(-0.8333333333333334 - a\right) + \frac{0.6666666666666666}{t}\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(c - b\right) \cdot \left(a + 0.8333333333333334\right)\right)}}\\ \end{array} \]

Alternative 9
Error	29.8
Cost	7768

\[\begin{array}{l} t_1 := \left(1 + \frac{x}{x + y}\right) + -1\\ \mathbf{if}\;c \leq -1.1725995836373971 \cdot 10^{+241}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -1.7208896673802977 \cdot 10^{+177}:\\ \;\;\;\;\frac{x}{x - y \cdot \left(-1 + \frac{c}{t} \cdot 1.3333333333333333\right)}\\ \mathbf{elif}\;c \leq -3.6758442492330087 \cdot 10^{+109}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -4989875506.102526:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -8.816029827212251 \cdot 10^{-71}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -3.8305608343216727 \cdot 10^{-296}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{b \cdot -1.6666666666666667}}\\ \mathbf{elif}\;c \leq 1.242516648342018 \cdot 10^{-187}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.2669678678776232 \cdot 10^{-163}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 1.3970871563695118 \cdot 10^{-103}:\\ \;\;\;\;\frac{x}{x + \left(y - -2 \cdot \left(\left(\left(-0.8333333333333334 - a\right) + -0.6666666666666666 \cdot \frac{-1}{t}\right) \cdot \left(y \cdot b\right)\right)\right)}\\ \mathbf{elif}\;c \leq 1.5065817831596674 \cdot 10^{-22}:\\ \;\;\;\;\frac{x}{x + \left(y - y \cdot \left(b \cdot \left(2 \cdot a - b \cdot \left(a \cdot \left(2 \cdot a\right)\right)\right)\right)\right)}\\ \mathbf{elif}\;c \leq 8.614929170902509 \cdot 10^{+181}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + \left(y + -2 \cdot \left(a \cdot \left(y \cdot \left(b - c\right)\right)\right)\right)}\\ \end{array} \]

Alternative 10
Error	18.2
Cost	7628

\[\begin{array}{l} t_1 := \frac{x}{x + y \cdot e^{-2 \cdot \left(a \cdot \left(b - c\right)\right)}}\\ \mathbf{if}\;t \leq -9.5 \cdot 10^{-249}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.3566062960922383 \cdot 10^{-19}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{c}{\frac{t}{-0.6666666666666666}}}}\\ \mathbf{elif}\;t \leq 1.4795410044986885 \cdot 10^{+180}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{\left(c - b\right) \cdot 1.6666666666666667}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 11
Error	14.0
Cost	7624

\[\begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{-249}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{-2 \cdot \left(a \cdot \left(b - c\right)\right)}}\\ \mathbf{elif}\;t \leq 2.3566062960922383 \cdot 10^{-19}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{c}{\frac{t}{-0.6666666666666666}}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(c - b\right) \cdot \left(a + 0.8333333333333334\right)\right)}}\\ \end{array} \]

Alternative 12
Error	20.0
Cost	7496

\[\begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{-36}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{-2 \cdot \left(a \cdot b\right)}}\\ \mathbf{elif}\;t \leq 2.3566062960922383 \cdot 10^{-19}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{c}{\frac{t}{-0.6666666666666666}}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{\left(c - b\right) \cdot 1.6666666666666667}}\\ \end{array} \]

Alternative 13
Error	30.9
Cost	2664

\[\begin{array}{l} t_1 := \left(1 + \frac{x}{x + y}\right) + -1\\ \mathbf{if}\;c \leq -1.1725995836373971 \cdot 10^{+241}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -1.7208896673802977 \cdot 10^{+177}:\\ \;\;\;\;\frac{x}{x - y \cdot \left(-1 + \frac{c}{t} \cdot 1.3333333333333333\right)}\\ \mathbf{elif}\;c \leq -3.6758442492330087 \cdot 10^{+109}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -2.4358016307878852 \cdot 10^{-98}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -1.662035118286602 \cdot 10^{-173}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -1.9619285191157696 \cdot 10^{-247}:\\ \;\;\;\;\frac{x}{x + \left(y - y \cdot \left(b \cdot \left(2 \cdot a - b \cdot \left(a \cdot \left(2 \cdot a\right)\right)\right)\right)\right)}\\ \mathbf{elif}\;c \leq 1.242516648342018 \cdot 10^{-187}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 5.912631151232379 \cdot 10^{-117}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 8.614929170902509 \cdot 10^{+181}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 3.550120588900296 \cdot 10^{+223}:\\ \;\;\;\;\frac{x}{x - \left(2 \cdot \left(c \cdot \left(y \cdot \left(\left(-0.8333333333333334 - a\right) + -0.6666666666666666 \cdot \frac{-1}{t}\right)\right)\right) - y\right)}\\ \mathbf{elif}\;c \leq 2.631982616432177 \cdot 10^{+229}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 2.7258403196216133 \cdot 10^{+298}:\\ \;\;\;\;\frac{x}{x - \left(-2 \cdot \left(y \cdot \left(a \cdot c\right)\right) - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y \cdot c} \cdot 0.5}{a}\\ \end{array} \]

Alternative 14
Error	32.1
Cost	2148

\[\begin{array}{l} t_1 := \frac{x}{y + \left(x + 2 \cdot \left(c \cdot \left(y \cdot \left(a + 0.8333333333333334\right)\right)\right)\right)}\\ \mathbf{if}\;b \leq -8.834726077126417 \cdot 10^{+226}:\\ \;\;\;\;\frac{x}{2 \cdot \left(y \cdot \left(b \cdot \left(-0.8333333333333334 - a\right)\right)\right) + \left(x + y\right)}\\ \mathbf{elif}\;b \leq -4.53237884736535 \cdot 10^{+113}:\\ \;\;\;\;1\\ \mathbf{elif}\;b \leq -3.508520408243781 \cdot 10^{+35}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -7.35766385820754 \cdot 10^{-115}:\\ \;\;\;\;\frac{x}{x \cdot x - y \cdot y} \cdot \left(x - y\right)\\ \mathbf{elif}\;b \leq -9.522610399515452 \cdot 10^{-183}:\\ \;\;\;\;\frac{x}{x + \left(y + 2 \cdot \left(c \cdot \left(y \cdot \frac{-0.6666666666666666}{t}\right)\right)\right)}\\ \mathbf{elif}\;b \leq 2.1443801227077677 \cdot 10^{-257}:\\ \;\;\;\;1\\ \mathbf{elif}\;b \leq 4.361454192309311 \cdot 10^{-203}:\\ \;\;\;\;\frac{x}{x - y \cdot \left(-1 + \frac{c}{t} \cdot 1.3333333333333333\right)}\\ \mathbf{elif}\;b \leq 1.1132838900560066 \cdot 10^{-124}:\\ \;\;\;\;1\\ \mathbf{elif}\;b \leq 2.019037682657588 \cdot 10^{-15}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 2.1645315622360428 \cdot 10^{+30}:\\ \;\;\;\;1\\ \mathbf{elif}\;b \leq 5.163260717307116 \cdot 10^{+72}:\\ \;\;\;\;\left(1 + \frac{x}{x + y}\right) + -1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 15
Error	31.9
Cost	2148

\[\begin{array}{l} t_1 := \frac{x}{x + \left(y + -2 \cdot \left(a \cdot \left(y \cdot \left(b - c\right)\right)\right)\right)}\\ \mathbf{if}\;b \leq -8.834726077126417 \cdot 10^{+226}:\\ \;\;\;\;\frac{x}{2 \cdot \left(y \cdot \left(b \cdot \left(-0.8333333333333334 - a\right)\right)\right) + \left(x + y\right)}\\ \mathbf{elif}\;b \leq -4.53237884736535 \cdot 10^{+113}:\\ \;\;\;\;1\\ \mathbf{elif}\;b \leq -3.508520408243781 \cdot 10^{+35}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -7.35766385820754 \cdot 10^{-115}:\\ \;\;\;\;\frac{x}{x \cdot x - y \cdot y} \cdot \left(x - y\right)\\ \mathbf{elif}\;b \leq -9.522610399515452 \cdot 10^{-183}:\\ \;\;\;\;\frac{x}{x + \left(y + 2 \cdot \left(c \cdot \left(y \cdot \frac{-0.6666666666666666}{t}\right)\right)\right)}\\ \mathbf{elif}\;b \leq 2.1443801227077677 \cdot 10^{-257}:\\ \;\;\;\;1\\ \mathbf{elif}\;b \leq 4.361454192309311 \cdot 10^{-203}:\\ \;\;\;\;\frac{x}{x - y \cdot \left(-1 + \frac{c}{t} \cdot 1.3333333333333333\right)}\\ \mathbf{elif}\;b \leq 4.9183514619891046 \cdot 10^{-92}:\\ \;\;\;\;1\\ \mathbf{elif}\;b \leq 2.019037682657588 \cdot 10^{-15}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 2.1645315622360428 \cdot 10^{+30}:\\ \;\;\;\;1\\ \mathbf{elif}\;b \leq 5.163260717307116 \cdot 10^{+72}:\\ \;\;\;\;\left(1 + \frac{x}{x + y}\right) + -1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 16
Error	30.7
Cost	2148

\[\begin{array}{l} t_1 := \left(1 + \frac{x}{x + y}\right) + -1\\ \mathbf{if}\;b \leq -8.834726077126417 \cdot 10^{+226}:\\ \;\;\;\;\frac{x}{2 \cdot \left(y \cdot \left(b \cdot \left(-0.8333333333333334 - a\right)\right)\right) + \left(x + y\right)}\\ \mathbf{elif}\;b \leq -8.615539385396031 \cdot 10^{+120}:\\ \;\;\;\;1\\ \mathbf{elif}\;b \leq -1.1171761965174481 \cdot 10^{+95}:\\ \;\;\;\;\frac{x}{x + \left(y - y \cdot \left(b \cdot \left(2 \cdot a - b \cdot \left(a \cdot \left(2 \cdot a\right)\right)\right)\right)\right)}\\ \mathbf{elif}\;b \leq -7.35766385820754 \cdot 10^{-115}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -9.522610399515452 \cdot 10^{-183}:\\ \;\;\;\;\frac{x}{x + \left(y + 2 \cdot \left(c \cdot \left(y \cdot \frac{-0.6666666666666666}{t}\right)\right)\right)}\\ \mathbf{elif}\;b \leq 2.1443801227077677 \cdot 10^{-257}:\\ \;\;\;\;1\\ \mathbf{elif}\;b \leq 4.361454192309311 \cdot 10^{-203}:\\ \;\;\;\;\frac{x}{x - y \cdot \left(-1 + \frac{c}{t} \cdot 1.3333333333333333\right)}\\ \mathbf{elif}\;b \leq 4.9183514619891046 \cdot 10^{-92}:\\ \;\;\;\;1\\ \mathbf{elif}\;b \leq 2.019037682657588 \cdot 10^{-15}:\\ \;\;\;\;\frac{x}{x + \left(y + -2 \cdot \left(a \cdot \left(y \cdot \left(b - c\right)\right)\right)\right)}\\ \mathbf{elif}\;b \leq 2.1645315622360428 \cdot 10^{+30}:\\ \;\;\;\;1\\ \mathbf{elif}\;b \leq 5.163260717307116 \cdot 10^{+72}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 17
Error	32.5
Cost	1888

\[\begin{array}{l} t_1 := \left(1 + \frac{x}{x + y}\right) + -1\\ \mathbf{if}\;z \leq -0.9781855756324187:\\ \;\;\;\;1\\ \mathbf{elif}\;z \leq -9.886007033711489 \cdot 10^{-45}:\\ \;\;\;\;\frac{x}{x - \left(2 \cdot \left(b \cdot \frac{y \cdot -0.6666666666666666}{t}\right) - y\right)}\\ \mathbf{elif}\;z \leq -6.162160145843347 \cdot 10^{-102}:\\ \;\;\;\;1\\ \mathbf{elif}\;z \leq 6.050776073012503 \cdot 10^{-264}:\\ \;\;\;\;\frac{x}{x - y \cdot \left(-1 + \frac{c}{t} \cdot 1.3333333333333333\right)}\\ \mathbf{elif}\;z \leq 4.28040321033226 \cdot 10^{-43}:\\ \;\;\;\;1\\ \mathbf{elif}\;z \leq 8.240495795013377 \cdot 10^{+20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.8263588692666994 \cdot 10^{+95}:\\ \;\;\;\;1\\ \mathbf{elif}\;z \leq 2.5352005297251414 \cdot 10^{+168}:\\ \;\;\;\;\frac{x}{x \cdot x - y \cdot y} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 18
Error	30.9
Cost	1632

\[\begin{array}{l} t_1 := \left(1 + \frac{x}{x + y}\right) + -1\\ \mathbf{if}\;c \leq -1.1725995836373971 \cdot 10^{+241}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -1.7208896673802977 \cdot 10^{+177}:\\ \;\;\;\;\frac{x}{x - y \cdot \left(-1 + \frac{c}{t} \cdot 1.3333333333333333\right)}\\ \mathbf{elif}\;c \leq -3.6758442492330087 \cdot 10^{+109}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -2.4358016307878852 \cdot 10^{-98}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -1.662035118286602 \cdot 10^{-173}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -1.9619285191157696 \cdot 10^{-247}:\\ \;\;\;\;\frac{x}{x + \left(y + -2 \cdot \left(y \cdot \left(a \cdot b\right)\right)\right)}\\ \mathbf{elif}\;c \leq 1.242516648342018 \cdot 10^{-187}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 5.912631151232379 \cdot 10^{-117}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 19
Error	31.2
Cost	1632

\[\begin{array}{l} t_1 := \left(1 + \frac{x}{x + y}\right) + -1\\ \mathbf{if}\;c \leq -1.1725995836373971 \cdot 10^{+241}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -1.7208896673802977 \cdot 10^{+177}:\\ \;\;\;\;\frac{x}{x - y \cdot \left(-1 + \frac{c}{t} \cdot 1.3333333333333333\right)}\\ \mathbf{elif}\;c \leq -3.6758442492330087 \cdot 10^{+109}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -2.4358016307878852 \cdot 10^{-98}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -6.13570516171969 \cdot 10^{-174}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -1.9619285191157696 \cdot 10^{-247}:\\ \;\;\;\;\frac{x}{x \cdot x - y \cdot y} \cdot \left(x - y\right)\\ \mathbf{elif}\;c \leq 1.242516648342018 \cdot 10^{-187}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 5.912631151232379 \cdot 10^{-117}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 20
Error	30.5
Cost	1236

\[\begin{array}{l} t_1 := \left(1 + \frac{x}{x + y}\right) + -1\\ \mathbf{if}\;b \leq -8.834726077126417 \cdot 10^{+226}:\\ \;\;\;\;-0.5 \cdot \frac{x}{y \cdot \left(a \cdot b\right)}\\ \mathbf{elif}\;b \leq -8.615539385396031 \cdot 10^{+120}:\\ \;\;\;\;1\\ \mathbf{elif}\;b \leq -3.080152254026196 \cdot 10^{-79}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 2.6868885406698625 \cdot 10^{-128}:\\ \;\;\;\;1\\ \mathbf{elif}\;b \leq 5.163260717307116 \cdot 10^{+72}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 21
Error	30.5
Cost	1236

\[\begin{array}{l} t_1 := \left(1 + \frac{x}{x + y}\right) + -1\\ \mathbf{if}\;c \leq -1.1725995836373971 \cdot 10^{+241}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -1.7208896673802977 \cdot 10^{+177}:\\ \;\;\;\;\frac{x}{x - y \cdot \left(-1 + \frac{c}{t} \cdot 1.3333333333333333\right)}\\ \mathbf{elif}\;c \leq -3.6758442492330087 \cdot 10^{+109}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 1.242516648342018 \cdot 10^{-187}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 5.912631151232379 \cdot 10^{-117}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 22
Error	30.4
Cost	708

\[\begin{array}{l} \mathbf{if}\;b \leq -8.834726077126417 \cdot 10^{+226}:\\ \;\;\;\;-0.5 \cdot \frac{x}{y \cdot \left(a \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 23
Error	30.9
Cost	64

\[1 \]

Reproduce

herbie shell --seed 2022300 
(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)))))))))))