\[1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \]

↓

\[\begin{array}{l} t_0 := x + \frac{x + -1}{-1 - y}\\ \mathbf{if}\;y \leq -0.3547015236528428:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 4.5647550601383184 \cdot 10^{-5}:\\ \;\;\;\;\mathsf{fma}\left(1 - x, \frac{y}{-1 - y}, 1\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

(FPCore (x y) :precision binary64 (- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0))))

↓

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ x (/ (+ x -1.0) (- -1.0 y)))))
   (if (<= y -0.3547015236528428)
     t_0
     (if (<= y 4.5647550601383184e-5)
       (fma (- 1.0 x) (/ y (- -1.0 y)) 1.0)
       t_0))))

double code(double x, double y) {
	return 1.0 - (((1.0 - x) * y) / (y + 1.0));
}

↓

double code(double x, double y) {
	double t_0 = x + ((x + -1.0) / (-1.0 - y));
	double tmp;
	if (y <= -0.3547015236528428) {
		tmp = t_0;
	} else if (y <= 4.5647550601383184e-5) {
		tmp = fma((1.0 - x), (y / (-1.0 - y)), 1.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

function code(x, y)
	return Float64(1.0 - Float64(Float64(Float64(1.0 - x) * y) / Float64(y + 1.0)))
end

↓

function code(x, y)
	t_0 = Float64(x + Float64(Float64(x + -1.0) / Float64(-1.0 - y)))
	tmp = 0.0
	if (y <= -0.3547015236528428)
		tmp = t_0;
	elseif (y <= 4.5647550601383184e-5)
		tmp = fma(Float64(1.0 - x), Float64(y / Float64(-1.0 - y)), 1.0);
	else
		tmp = t_0;
	end
	return tmp
end

code[x_, y_] := N[(1.0 - N[(N[(N[(1.0 - x), $MachinePrecision] * y), $MachinePrecision] / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_] := Block[{t$95$0 = N[(x + N[(N[(x + -1.0), $MachinePrecision] / N[(-1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -0.3547015236528428], t$95$0, If[LessEqual[y, 4.5647550601383184e-5], N[(N[(1.0 - x), $MachinePrecision] * N[(y / N[(-1.0 - y), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision], t$95$0]]]

1 - \frac{\left(1 - x\right) \cdot y}{y + 1}

↓

\begin{array}{l}
t_0 := x + \frac{x + -1}{-1 - y}\\
\mathbf{if}\;y \leq -0.3547015236528428:\\
\;\;\;\;t_0\\

\mathbf{elif}\;y \leq 4.5647550601383184 \cdot 10^{-5}:\\
\;\;\;\;\mathsf{fma}\left(1 - x, \frac{y}{-1 - y}, 1\right)\\

\mathbf{else}:\\
\;\;\;\;t_0\\


\end{array}

Original	22.6
Target	0.2
Herbie	0.0

Derivation

Split input into 2 regimes
if y < -0.3547015236528428 or 4.56475506013831838e-5 < y
1. Initial program 44.7
  \[1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \]
2. Taylor expanded in y around inf 0.9
  \[\leadsto \color{blue}{\left(\frac{1}{y} + \left(-1 \cdot \frac{1 + -1 \cdot x}{{y}^{2}} + x\right)\right) - \frac{x}{y}} \]
3. Simplified0.9
  \[\leadsto \color{blue}{x + \frac{-1 + x}{y} \cdot \left(\frac{1}{y} + -1\right)} \]
  Proof
  (+.f64 x (*.f64 (/.f64 (+.f64 -1 x) y) (+.f64 (/.f64 1 y) -1))): 0 points increase in error, 0 points decrease in error
  (+.f64 x (*.f64 (/.f64 (Rewrite<= +-commutative_binary64 (+.f64 x -1)) y) (+.f64 (/.f64 1 y) -1))): 0 points increase in error, 0 points decrease in error
  (+.f64 x (*.f64 (/.f64 (+.f64 x (Rewrite<= metadata-eval (neg.f64 1))) y) (+.f64 (/.f64 1 y) -1))): 0 points increase in error, 0 points decrease in error
  (+.f64 x (*.f64 (/.f64 (Rewrite<= sub-neg_binary64 (-.f64 x 1)) y) (+.f64 (/.f64 1 y) -1))): 0 points increase in error, 0 points decrease in error
  (+.f64 x (Rewrite<= distribute-rgt-out_binary64 (+.f64 (*.f64 (/.f64 1 y) (/.f64 (-.f64 x 1) y)) (*.f64 -1 (/.f64 (-.f64 x 1) y))))): 1 points increase in error, 2 points decrease in error
  (+.f64 x (+.f64 (Rewrite<= times-frac_binary64 (/.f64 (*.f64 1 (-.f64 x 1)) (*.f64 y y))) (*.f64 -1 (/.f64 (-.f64 x 1) y)))): 4 points increase in error, 12 points decrease in error
  (+.f64 x (+.f64 (/.f64 (*.f64 1 (-.f64 x 1)) (Rewrite<= unpow2_binary64 (pow.f64 y 2))) (*.f64 -1 (/.f64 (-.f64 x 1) y)))): 0 points increase in error, 0 points decrease in error
  (+.f64 x (+.f64 (/.f64 (*.f64 1 (-.f64 x 1)) (Rewrite<= *-lft-identity_binary64 (*.f64 1 (pow.f64 y 2)))) (*.f64 -1 (/.f64 (-.f64 x 1) y)))): 0 points increase in error, 0 points decrease in error
  (+.f64 x (+.f64 (Rewrite=> times-frac_binary64 (*.f64 (/.f64 1 1) (/.f64 (-.f64 x 1) (pow.f64 y 2)))) (*.f64 -1 (/.f64 (-.f64 x 1) y)))): 0 points increase in error, 0 points decrease in error
  (+.f64 x (+.f64 (*.f64 (Rewrite=> metadata-eval 1) (/.f64 (-.f64 x 1) (pow.f64 y 2))) (*.f64 -1 (/.f64 (-.f64 x 1) y)))): 0 points increase in error, 0 points decrease in error
  (+.f64 x (+.f64 (Rewrite=> *-lft-identity_binary64 (/.f64 (-.f64 x 1) (pow.f64 y 2))) (*.f64 -1 (/.f64 (-.f64 x 1) y)))): 0 points increase in error, 0 points decrease in error
  (Rewrite<= associate-+l+_binary64 (+.f64 (+.f64 x (/.f64 (-.f64 x 1) (pow.f64 y 2))) (*.f64 -1 (/.f64 (-.f64 x 1) y)))): 1 points increase in error, 0 points decrease in error
  (+.f64 (Rewrite=> +-commutative_binary64 (+.f64 (/.f64 (-.f64 x 1) (pow.f64 y 2)) x)) (*.f64 -1 (/.f64 (-.f64 x 1) y))): 0 points increase in error, 0 points decrease in error
  (Rewrite=> associate-+l+_binary64 (+.f64 (/.f64 (-.f64 x 1) (pow.f64 y 2)) (+.f64 x (*.f64 -1 (/.f64 (-.f64 x 1) y))))): 0 points increase in error, 1 points decrease in error
  (+.f64 (/.f64 (-.f64 x 1) (pow.f64 y 2)) (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 -1 (/.f64 (-.f64 x 1) y)) x))): 0 points increase in error, 0 points decrease in error
  (Rewrite<= +-commutative_binary64 (+.f64 (+.f64 (*.f64 -1 (/.f64 (-.f64 x 1) y)) x) (/.f64 (-.f64 x 1) (pow.f64 y 2)))): 0 points increase in error, 0 points decrease in error
  (+.f64 (+.f64 (*.f64 -1 (/.f64 (-.f64 x 1) y)) x) (Rewrite=> div-sub_binary64 (-.f64 (/.f64 x (pow.f64 y 2)) (/.f64 1 (pow.f64 y 2))))): 2 points increase in error, 0 points decrease in error
  (Rewrite<= associate--l+_binary64 (-.f64 (+.f64 (+.f64 (*.f64 -1 (/.f64 (-.f64 x 1) y)) x) (/.f64 x (pow.f64 y 2))) (/.f64 1 (pow.f64 y 2)))): 0 points increase in error, 0 points decrease in error
  (-.f64 (Rewrite<= +-commutative_binary64 (+.f64 (/.f64 x (pow.f64 y 2)) (+.f64 (*.f64 -1 (/.f64 (-.f64 x 1) y)) x))) (/.f64 1 (pow.f64 y 2))): 0 points increase in error, 0 points decrease in error
  (Rewrite=> associate--l+_binary64 (+.f64 (/.f64 x (pow.f64 y 2)) (-.f64 (+.f64 (*.f64 -1 (/.f64 (-.f64 x 1) y)) x) (/.f64 1 (pow.f64 y 2))))): 0 points increase in error, 0 points decrease in error
  (Rewrite=> +-commutative_binary64 (+.f64 (-.f64 (+.f64 (*.f64 -1 (/.f64 (-.f64 x 1) y)) x) (/.f64 1 (pow.f64 y 2))) (/.f64 x (pow.f64 y 2)))): 0 points increase in error, 0 points decrease in error
  (+.f64 (Rewrite=> associate--l+_binary64 (+.f64 (*.f64 -1 (/.f64 (-.f64 x 1) y)) (-.f64 x (/.f64 1 (pow.f64 y 2))))) (/.f64 x (pow.f64 y 2))): 0 points increase in error, 0 points decrease in error
  (Rewrite=> associate-+l+_binary64 (+.f64 (*.f64 -1 (/.f64 (-.f64 x 1) y)) (+.f64 (-.f64 x (/.f64 1 (pow.f64 y 2))) (/.f64 x (pow.f64 y 2))))): 1 points increase in error, 0 points decrease in error
  (+.f64 (*.f64 -1 (/.f64 (-.f64 x 1) y)) (Rewrite<= associate--r-_binary64 (-.f64 x (-.f64 (/.f64 1 (pow.f64 y 2)) (/.f64 x (pow.f64 y 2)))))): 0 points increase in error, 0 points decrease in error
  (+.f64 (*.f64 -1 (/.f64 (-.f64 x 1) y)) (-.f64 x (Rewrite<= div-sub_binary64 (/.f64 (-.f64 1 x) (pow.f64 y 2))))): 0 points increase in error, 2 points decrease in error
  (+.f64 (*.f64 -1 (/.f64 (-.f64 x 1) y)) (-.f64 x (/.f64 (Rewrite=> sub-neg_binary64 (+.f64 1 (neg.f64 x))) (pow.f64 y 2)))): 0 points increase in error, 0 points decrease in error
  (+.f64 (*.f64 -1 (/.f64 (-.f64 x 1) y)) (-.f64 x (/.f64 (+.f64 1 (Rewrite<= mul-1-neg_binary64 (*.f64 -1 x))) (pow.f64 y 2)))): 0 points increase in error, 0 points decrease in error
  (+.f64 (*.f64 -1 (/.f64 (-.f64 x 1) y)) (Rewrite<= unsub-neg_binary64 (+.f64 x (neg.f64 (/.f64 (+.f64 1 (*.f64 -1 x)) (pow.f64 y 2)))))): 0 points increase in error, 0 points decrease in error
  (+.f64 (*.f64 -1 (/.f64 (-.f64 x 1) y)) (+.f64 x (Rewrite<= mul-1-neg_binary64 (*.f64 -1 (/.f64 (+.f64 1 (*.f64 -1 x)) (pow.f64 y 2)))))): 0 points increase in error, 0 points decrease in error
  (+.f64 (*.f64 -1 (/.f64 (-.f64 x 1) y)) (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 -1 (/.f64 (+.f64 1 (*.f64 -1 x)) (pow.f64 y 2))) x))): 0 points increase in error, 0 points decrease in error
  (Rewrite<= +-commutative_binary64 (+.f64 (+.f64 (*.f64 -1 (/.f64 (+.f64 1 (*.f64 -1 x)) (pow.f64 y 2))) x) (*.f64 -1 (/.f64 (-.f64 x 1) y)))): 0 points increase in error, 0 points decrease in error
  (+.f64 (+.f64 (*.f64 -1 (/.f64 (+.f64 1 (*.f64 -1 x)) (pow.f64 y 2))) x) (Rewrite=> mul-1-neg_binary64 (neg.f64 (/.f64 (-.f64 x 1) y)))): 0 points increase in error, 0 points decrease in error
  (Rewrite=> unsub-neg_binary64 (-.f64 (+.f64 (*.f64 -1 (/.f64 (+.f64 1 (*.f64 -1 x)) (pow.f64 y 2))) x) (/.f64 (-.f64 x 1) y))): 0 points increase in error, 0 points decrease in error
  (-.f64 (+.f64 (*.f64 -1 (/.f64 (+.f64 1 (*.f64 -1 x)) (pow.f64 y 2))) x) (Rewrite=> div-sub_binary64 (-.f64 (/.f64 x y) (/.f64 1 y)))): 0 points increase in error, 0 points decrease in error
  (Rewrite<= associate-+l-_binary64 (+.f64 (-.f64 (+.f64 (*.f64 -1 (/.f64 (+.f64 1 (*.f64 -1 x)) (pow.f64 y 2))) x) (/.f64 x y)) (/.f64 1 y))): 0 points increase in error, 0 points decrease in error
  (Rewrite<= +-commutative_binary64 (+.f64 (/.f64 1 y) (-.f64 (+.f64 (*.f64 -1 (/.f64 (+.f64 1 (*.f64 -1 x)) (pow.f64 y 2))) x) (/.f64 x y)))): 0 points increase in error, 0 points decrease in error
  (Rewrite<= associate--l+_binary64 (-.f64 (+.f64 (/.f64 1 y) (+.f64 (*.f64 -1 (/.f64 (+.f64 1 (*.f64 -1 x)) (pow.f64 y 2))) x)) (/.f64 x y))): 0 points increase in error, 0 points decrease in error
4. Applied egg-rr0.9
  \[\leadsto x + \color{blue}{\frac{-1 + x}{\frac{y}{-1 + \frac{1}{y}}}} \]
5. Taylor expanded in y around inf 0.0
  \[\leadsto x + \frac{-1 + x}{\color{blue}{-1 \cdot y - 1}} \]
6. Simplified0.0
  \[\leadsto x + \frac{-1 + x}{\color{blue}{-1 - y}} \]
  Proof
  (-.f64 -1 y): 0 points increase in error, 0 points decrease in error
  (Rewrite<= unsub-neg_binary64 (+.f64 -1 (neg.f64 y))): 0 points increase in error, 0 points decrease in error
  (+.f64 -1 (Rewrite<= mul-1-neg_binary64 (*.f64 -1 y))): 0 points increase in error, 0 points decrease in error
  (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 -1 y) -1)): 0 points increase in error, 0 points decrease in error
  (+.f64 (*.f64 -1 y) (Rewrite<= metadata-eval (neg.f64 1))): 0 points increase in error, 0 points decrease in error
  (Rewrite<= sub-neg_binary64 (-.f64 (*.f64 -1 y) 1)): 0 points increase in error, 0 points decrease in error
if -0.3547015236528428 < y < 4.56475506013831838e-5
1. Initial program 0.0
  \[1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \]
2. Simplified0.0
  \[\leadsto \color{blue}{\mathsf{fma}\left(1 - x, \frac{y}{-1 - y}, 1\right)} \]
  Proof
  (fma.f64 (-.f64 1 x) (/.f64 y (-.f64 -1 y)) 1): 0 points increase in error, 0 points decrease in error
  (fma.f64 (-.f64 1 x) (/.f64 y (Rewrite=> sub-neg_binary64 (+.f64 -1 (neg.f64 y)))) 1): 0 points increase in error, 0 points decrease in error
  (fma.f64 (-.f64 1 x) (/.f64 y (+.f64 (Rewrite<= metadata-eval (*.f64 -1 1)) (neg.f64 y))) 1): 0 points increase in error, 0 points decrease in error
  (fma.f64 (-.f64 1 x) (/.f64 y (+.f64 (*.f64 -1 1) (Rewrite=> neg-mul-1_binary64 (*.f64 -1 y)))) 1): 0 points increase in error, 0 points decrease in error
  (fma.f64 (-.f64 1 x) (/.f64 y (Rewrite<= distribute-lft-in_binary64 (*.f64 -1 (+.f64 1 y)))) 1): 0 points increase in error, 0 points decrease in error
  (fma.f64 (-.f64 1 x) (/.f64 y (*.f64 -1 (Rewrite<= +-commutative_binary64 (+.f64 y 1)))) 1): 0 points increase in error, 0 points decrease in error
  (fma.f64 (-.f64 1 x) (/.f64 y (*.f64 (Rewrite<= metadata-eval (/.f64 1 -1)) (+.f64 y 1))) 1): 0 points increase in error, 0 points decrease in error
  (fma.f64 (-.f64 1 x) (/.f64 y (Rewrite<= associate-/r/_binary64 (/.f64 1 (/.f64 -1 (+.f64 y 1))))) 1): 17 points increase in error, 6 points decrease in error
  (fma.f64 (-.f64 1 x) (/.f64 y (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 1 (+.f64 y 1)) -1))) 1): 6 points increase in error, 17 points decrease in error
  (fma.f64 (-.f64 1 x) (/.f64 y (/.f64 (Rewrite<= *-commutative_binary64 (*.f64 (+.f64 y 1) 1)) -1)) 1): 0 points increase in error, 0 points decrease in error
  (fma.f64 (-.f64 1 x) (/.f64 y (Rewrite=> associate-/l*_binary64 (/.f64 (+.f64 y 1) (/.f64 -1 1)))) 1): 0 points increase in error, 0 points decrease in error
  (fma.f64 (-.f64 1 x) (/.f64 y (/.f64 (+.f64 y 1) (Rewrite=> metadata-eval -1))) 1): 0 points increase in error, 0 points decrease in error
  (fma.f64 (-.f64 1 x) (Rewrite=> associate-/r/_binary64 (*.f64 (/.f64 y (+.f64 y 1)) -1)) 1): 0 points increase in error, 0 points decrease in error
  (fma.f64 (-.f64 1 x) (Rewrite=> *-commutative_binary64 (*.f64 -1 (/.f64 y (+.f64 y 1)))) 1): 0 points increase in error, 0 points decrease in error
  (fma.f64 (-.f64 1 x) (Rewrite<= neg-mul-1_binary64 (neg.f64 (/.f64 y (+.f64 y 1)))) 1): 0 points increase in error, 0 points decrease in error
  (fma.f64 (-.f64 1 x) (neg.f64 (/.f64 (Rewrite<= *-lft-identity_binary64 (*.f64 1 y)) (+.f64 y 1))) 1): 0 points increase in error, 0 points decrease in error
  (fma.f64 (-.f64 1 x) (neg.f64 (Rewrite=> associate-/l*_binary64 (/.f64 1 (/.f64 (+.f64 y 1) y)))) 1): 4 points increase in error, 0 points decrease in error
  (Rewrite<= fma-def_binary64 (+.f64 (*.f64 (-.f64 1 x) (neg.f64 (/.f64 1 (/.f64 (+.f64 y 1) y)))) 1)): 2 points increase in error, 0 points decrease in error
  (+.f64 (*.f64 (-.f64 1 x) (neg.f64 (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 1 y) (+.f64 y 1))))) 1): 0 points increase in error, 4 points decrease in error
  (+.f64 (*.f64 (-.f64 1 x) (neg.f64 (/.f64 (Rewrite=> *-lft-identity_binary64 y) (+.f64 y 1)))) 1): 0 points increase in error, 0 points decrease in error
  (+.f64 (*.f64 (-.f64 1 x) (Rewrite=> distribute-neg-frac_binary64 (/.f64 (neg.f64 y) (+.f64 y 1)))) 1): 0 points increase in error, 0 points decrease in error
  (+.f64 (Rewrite=> associate-*r/_binary64 (/.f64 (*.f64 (-.f64 1 x) (neg.f64 y)) (+.f64 y 1))) 1): 47 points increase in error, 0 points decrease in error
  (+.f64 (/.f64 (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 (-.f64 1 x) y))) (+.f64 y 1)) 1): 0 points increase in error, 0 points decrease in error
  (+.f64 (Rewrite<= distribute-neg-frac_binary64 (neg.f64 (/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1)))) 1): 0 points increase in error, 0 points decrease in error
  (Rewrite<= +-commutative_binary64 (+.f64 1 (neg.f64 (/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1))))): 0 points increase in error, 0 points decrease in error
  (Rewrite<= sub-neg_binary64 (-.f64 1 (/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1)))): 0 points increase in error, 0 points decrease in error
Recombined 2 regimes into one program.
Final simplification0.0
\[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.3547015236528428:\\ \;\;\;\;x + \frac{x + -1}{-1 - y}\\ \mathbf{elif}\;y \leq 4.5647550601383184 \cdot 10^{-5}:\\ \;\;\;\;\mathsf{fma}\left(1 - x, \frac{y}{-1 - y}, 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{x + -1}{-1 - y}\\ \end{array} \]

Alternatives

Alternative 1
Error	0.0
Cost	1352

\[\begin{array}{l} t_0 := x + \frac{x + -1}{-1 - y}\\ \mathbf{if}\;y \leq -0.3547015236528428:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 4.5647550601383184 \cdot 10^{-5}:\\ \;\;\;\;1 + y \cdot \left(\frac{1 - x}{1 - y \cdot y} \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	0.0
Cost	968

\[\begin{array}{l} t_0 := x + \frac{x + -1}{-1 - y}\\ \mathbf{if}\;y \leq -52992.58597404602:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 4.5647550601383184 \cdot 10^{-5}:\\ \;\;\;\;1 + y \cdot \frac{x + -1}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Error	0.0
Cost	968

\[\begin{array}{l} t_0 := x + \frac{x + -1}{-1 - y}\\ \mathbf{if}\;y \leq -0.3547015236528428:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 4.5647550601383184 \cdot 10^{-5}:\\ \;\;\;\;1 + \frac{y \cdot \left(x + -1\right)}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 4
Error	0.3
Cost	840

\[\begin{array}{l} t_0 := x + \frac{x + -1}{-1 - y}\\ \mathbf{if}\;y \leq -0.3547015236528428:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 2.19134100414984 \cdot 10^{-10}:\\ \;\;\;\;1 + \left(y \cdot x - y\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 5
Error	0.2
Cost	840

\[\begin{array}{l} t_0 := x + \frac{x + -1}{-1 - y}\\ \mathbf{if}\;y \leq -0.3547015236528428:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.5881646322858982 \cdot 10^{-8}:\\ \;\;\;\;1 + \frac{y \cdot x}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 6
Error	1.2
Cost	712

\[\begin{array}{l} t_0 := x + \frac{1}{y}\\ \mathbf{if}\;y \leq -243.95786548580054:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 4.5647550601383184 \cdot 10^{-5}:\\ \;\;\;\;1 + \left(y \cdot x - y\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 7
Error	1.0
Cost	712

\[\begin{array}{l} t_0 := x + \frac{1 - x}{y}\\ \mathbf{if}\;y \leq -243.95786548580054:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 4.5647550601383184 \cdot 10^{-5}:\\ \;\;\;\;1 + \left(y \cdot x - y\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 8
Error	16.5
Cost	584

\[\begin{array}{l} t_0 := x - \frac{x}{y}\\ \mathbf{if}\;y \leq -243.95786548580054:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 4.5647550601383184 \cdot 10^{-5}:\\ \;\;\;\;1 - y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 9
Error	8.9
Cost	584

\[\begin{array}{l} t_0 := x + \frac{1}{y}\\ \mathbf{if}\;y \leq -243.95786548580054:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 4.5647550601383184 \cdot 10^{-5}:\\ \;\;\;\;1 - y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 10
Error	1.4
Cost	584

\[\begin{array}{l} t_0 := x + \frac{1}{y}\\ \mathbf{if}\;y \leq -243.95786548580054:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 4.5647550601383184 \cdot 10^{-5}:\\ \;\;\;\;1 + y \cdot x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 11
Error	16.7
Cost	456

\[\begin{array}{l} \mathbf{if}\;y \leq -243.95786548580054:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.5647550601383184 \cdot 10^{-5}:\\ \;\;\;\;1 - y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12
Error	16.8
Cost	328

\[\begin{array}{l} \mathbf{if}\;y \leq -243.95786548580054:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.5647550601383184 \cdot 10^{-5}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 13
Error	39.1
Cost	64

\[x \]

Error

Target

Derivation

`if y < -0.3547015236528428 or 4.56475506013831838e-5 < y`

`if -0.3547015236528428 < y < 4.56475506013831838e-5`

Alternatives

Error

Reproduce