Diagrams.Trail:splitAtParam from diagrams-lib-1.3.0.3, D

Average Error: 22.2 → 0.1

Time: 10.9s

Precision: binary64

Cost: 7880

Math

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

↓

\[\begin{array}{l} t_0 := \frac{x + -1}{y \cdot y}\\ t_1 := 1 + \frac{-1}{y}\\ \mathbf{if}\;y \leq -43529.630834191135:\\ \;\;\;\;\left(x - \frac{x + -1}{y}\right) + t_0 \cdot t_1\\ \mathbf{elif}\;y \leq 7.444779409057008:\\ \;\;\;\;\mathsf{fma}\left(1 - x, \frac{y}{-1 - y}, 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + \mathsf{fma}\left(t_1, t_0, \frac{1 - x}{y}\right)\\ \end{array} \]

FPCore

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

↓

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (+ x -1.0) (* y y))) (t_1 (+ 1.0 (/ -1.0 y))))
   (if (<= y -43529.630834191135)
     (+ (- x (/ (+ x -1.0) y)) (* t_0 t_1))
     (if (<= y 7.444779409057008)
       (fma (- 1.0 x) (/ y (- -1.0 y)) 1.0)
       (+ x (fma t_1 t_0 (/ (- 1.0 x) y)))))))

C

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 + -1.0) / (y * y);
	double t_1 = 1.0 + (-1.0 / y);
	double tmp;
	if (y <= -43529.630834191135) {
		tmp = (x - ((x + -1.0) / y)) + (t_0 * t_1);
	} else if (y <= 7.444779409057008) {
		tmp = fma((1.0 - x), (y / (-1.0 - y)), 1.0);
	} else {
		tmp = x + fma(t_1, t_0, ((1.0 - x) / y));
	}
	return tmp;
}

Julia

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(Float64(x + -1.0) / Float64(y * y))
	t_1 = Float64(1.0 + Float64(-1.0 / y))
	tmp = 0.0
	if (y <= -43529.630834191135)
		tmp = Float64(Float64(x - Float64(Float64(x + -1.0) / y)) + Float64(t_0 * t_1));
	elseif (y <= 7.444779409057008)
		tmp = fma(Float64(1.0 - x), Float64(y / Float64(-1.0 - y)), 1.0);
	else
		tmp = Float64(x + fma(t_1, t_0, Float64(Float64(1.0 - x) / y)));
	end
	return tmp
end

Wolfram

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[(N[(x + -1.0), $MachinePrecision] / N[(y * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(1.0 + N[(-1.0 / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -43529.630834191135], N[(N[(x - N[(N[(x + -1.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] + N[(t$95$0 * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.444779409057008], N[(N[(1.0 - x), $MachinePrecision] * N[(y / N[(-1.0 - y), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision], N[(x + N[(t$95$1 * t$95$0 + N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Target

Original	22.2
Target	0.2
Herbie	0.1

\[\begin{array}{l} \mathbf{if}\;y < -3693.8482788297247:\\ \;\;\;\;\frac{1}{y} - \left(\frac{x}{y} - x\right)\\ \mathbf{elif}\;y < 6799310503.41891:\\ \;\;\;\;1 - \frac{\left(1 - x\right) \cdot y}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{y} - \left(\frac{x}{y} - x\right)\\ \end{array} \]

Derivation

1. Split input into 3 regimes

2. if y < -43529.630834191135

   1. Initial program 45.4

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

   2. Taylor expanded in y around -inf 0.0

      \[\leadsto \color{blue}{\left(\frac{x}{{y}^{2}} + \left(-1 \cdot \frac{x - 1}{y} + \left(-1 \cdot \frac{x - 1}{{y}^{3}} + x\right)\right)\right) - \frac{1}{{y}^{2}}} \]

   3. Simplified 0.0

      \[\leadsto \color{blue}{\left(x + \frac{1 - x}{y}\right) + \frac{-1 + x}{y \cdot y} \cdot \left(\frac{-1}{y} + 1\right)} \]
      Proof
      (+.f64 (+.f64 x (/.f64 (-.f64 1 x) y)) (*.f64 (/.f64 (+.f64 -1 x) (*.f64 y y)) (+.f64 (/.f64 -1 y) 1))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 x (Rewrite=> div-sub_binary64 (-.f64 (/.f64 1 y) (/.f64 x y)))) (*.f64 (/.f64 (+.f64 -1 x) (*.f64 y y)) (+.f64 (/.f64 -1 y) 1))): 0 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite<= associate--l+_binary64 (-.f64 (+.f64 x (/.f64 1 y)) (/.f64 x y))) (*.f64 (/.f64 (+.f64 -1 x) (*.f64 y y)) (+.f64 (/.f64 -1 y) 1))): 0 points increase in error, 0 points decrease in error
      (+.f64 (-.f64 (Rewrite<= +-commutative_binary64 (+.f64 (/.f64 1 y) x)) (/.f64 x y)) (*.f64 (/.f64 (+.f64 -1 x) (*.f64 y y)) (+.f64 (/.f64 -1 y) 1))): 0 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite=> associate--l+_binary64 (+.f64 (/.f64 1 y) (-.f64 x (/.f64 x y)))) (*.f64 (/.f64 (+.f64 -1 x) (*.f64 y y)) (+.f64 (/.f64 -1 y) 1))): 0 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite=> +-commutative_binary64 (+.f64 (-.f64 x (/.f64 x y)) (/.f64 1 y))) (*.f64 (/.f64 (+.f64 -1 x) (*.f64 y y)) (+.f64 (/.f64 -1 y) 1))): 0 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite<= associate--r-_binary64 (-.f64 x (-.f64 (/.f64 x y) (/.f64 1 y)))) (*.f64 (/.f64 (+.f64 -1 x) (*.f64 y y)) (+.f64 (/.f64 -1 y) 1))): 0 points increase in error, 0 points decrease in error
      (+.f64 (-.f64 x (Rewrite<= div-sub_binary64 (/.f64 (-.f64 x 1) y))) (*.f64 (/.f64 (+.f64 -1 x) (*.f64 y y)) (+.f64 (/.f64 -1 y) 1))): 0 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite<= unsub-neg_binary64 (+.f64 x (neg.f64 (/.f64 (-.f64 x 1) y)))) (*.f64 (/.f64 (+.f64 -1 x) (*.f64 y y)) (+.f64 (/.f64 -1 y) 1))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 x (Rewrite<= mul-1-neg_binary64 (*.f64 -1 (/.f64 (-.f64 x 1) y)))) (*.f64 (/.f64 (+.f64 -1 x) (*.f64 y y)) (+.f64 (/.f64 -1 y) 1))): 0 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 -1 (/.f64 (-.f64 x 1) y)) x)) (*.f64 (/.f64 (+.f64 -1 x) (*.f64 y y)) (+.f64 (/.f64 -1 y) 1))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (*.f64 -1 (/.f64 (-.f64 x 1) y)) x) (*.f64 (/.f64 (Rewrite<= +-commutative_binary64 (+.f64 x -1)) (*.f64 y y)) (+.f64 (/.f64 -1 y) 1))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (*.f64 -1 (/.f64 (-.f64 x 1) y)) x) (*.f64 (/.f64 (+.f64 x (Rewrite<= metadata-eval (neg.f64 1))) (*.f64 y y)) (+.f64 (/.f64 -1 y) 1))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (*.f64 -1 (/.f64 (-.f64 x 1) y)) x) (*.f64 (/.f64 (Rewrite<= sub-neg_binary64 (-.f64 x 1)) (*.f64 y y)) (+.f64 (/.f64 -1 y) 1))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (*.f64 -1 (/.f64 (-.f64 x 1) y)) x) (*.f64 (/.f64 (-.f64 x 1) (Rewrite<= unpow2_binary64 (pow.f64 y 2))) (+.f64 (/.f64 -1 y) 1))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (*.f64 -1 (/.f64 (-.f64 x 1) y)) x) (*.f64 (/.f64 (-.f64 x 1) (pow.f64 y 2)) (+.f64 (/.f64 (Rewrite<= metadata-eval (neg.f64 1)) y) 1))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (*.f64 -1 (/.f64 (-.f64 x 1) y)) x) (*.f64 (/.f64 (-.f64 x 1) (pow.f64 y 2)) (+.f64 (Rewrite<= distribute-neg-frac_binary64 (neg.f64 (/.f64 1 y))) 1))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (*.f64 -1 (/.f64 (-.f64 x 1) y)) x) (Rewrite<= distribute-rgt-out_binary64 (+.f64 (*.f64 (neg.f64 (/.f64 1 y)) (/.f64 (-.f64 x 1) (pow.f64 y 2))) (*.f64 1 (/.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) (+.f64 (*.f64 (Rewrite=> distribute-neg-frac_binary64 (/.f64 (neg.f64 1) y)) (/.f64 (-.f64 x 1) (pow.f64 y 2))) (*.f64 1 (/.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) (+.f64 (*.f64 (/.f64 (Rewrite=> metadata-eval -1) y) (/.f64 (-.f64 x 1) (pow.f64 y 2))) (*.f64 1 (/.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) (+.f64 (Rewrite<= times-frac_binary64 (/.f64 (*.f64 -1 (-.f64 x 1)) (*.f64 y (pow.f64 y 2)))) (*.f64 1 (/.f64 (-.f64 x 1) (pow.f64 y 2))))): 13 points increase in error, 6 points decrease in error
      (+.f64 (+.f64 (*.f64 -1 (/.f64 (-.f64 x 1) y)) x) (+.f64 (/.f64 (*.f64 -1 (-.f64 x 1)) (*.f64 y (Rewrite=> unpow2_binary64 (*.f64 y y)))) (*.f64 1 (/.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) (+.f64 (/.f64 (*.f64 -1 (-.f64 x 1)) (Rewrite<= cube-mult_binary64 (pow.f64 y 3))) (*.f64 1 (/.f64 (-.f64 x 1) (pow.f64 y 2))))): 1 points increase in error, 4 points decrease in error
      (+.f64 (+.f64 (*.f64 -1 (/.f64 (-.f64 x 1) y)) x) (+.f64 (Rewrite<= associate-*r/_binary64 (*.f64 -1 (/.f64 (-.f64 x 1) (pow.f64 y 3)))) (*.f64 1 (/.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) (+.f64 (*.f64 -1 (/.f64 (-.f64 x 1) (pow.f64 y 3))) (Rewrite=> *-lft-identity_binary64 (/.f64 (-.f64 x 1) (pow.f64 y 2))))): 0 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 -1 (/.f64 (-.f64 x 1) (pow.f64 y 3)))) (/.f64 (-.f64 x 1) (pow.f64 y 2)))): 1 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite<= associate-+r+_binary64 (+.f64 (*.f64 -1 (/.f64 (-.f64 x 1) y)) (+.f64 x (*.f64 -1 (/.f64 (-.f64 x 1) (pow.f64 y 3)))))) (/.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)) (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 -1 (/.f64 (-.f64 x 1) (pow.f64 y 3))) 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)) (+.f64 (*.f64 -1 (/.f64 (-.f64 x 1) (pow.f64 y 3))) x)) (Rewrite=> div-sub_binary64 (-.f64 (/.f64 x (pow.f64 y 2)) (/.f64 1 (pow.f64 y 2))))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate--l+_binary64 (-.f64 (+.f64 (+.f64 (*.f64 -1 (/.f64 (-.f64 x 1) y)) (+.f64 (*.f64 -1 (/.f64 (-.f64 x 1) (pow.f64 y 3))) 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)) (+.f64 (*.f64 -1 (/.f64 (-.f64 x 1) (pow.f64 y 3))) x)))) (/.f64 1 (pow.f64 y 2))): 0 points increase in error, 0 points decrease in error

   if -43529.630834191135 < y < 7.4447794090570083

   1. Initial program 0.0

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

   2. Simplified 0.0

      \[\leadsto \color{blue}{\mathsf{fma}\left(1 - x, \frac{y}{-1 - y}, 1\right)} \]
      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): 19 points increase in error, 7 points decrease in error
      (fma.f64 (-.f64 1 x) (/.f64 y (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 1 (+.f64 y 1)) -1))) 1): 7 points increase in error, 19 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): 9 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)): 0 points increase in error, 1 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, 9 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): 45 points increase in error, 1 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

   if 7.4447794090570083 < y

   1. Initial program 45.3

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

   2. Taylor expanded in y around -inf 0.4

      \[\leadsto \color{blue}{\left(\frac{x}{{y}^{2}} + \left(-1 \cdot \frac{x - 1}{y} + \left(-1 \cdot \frac{x - 1}{{y}^{3}} + x\right)\right)\right) - \frac{1}{{y}^{2}}} \]

   3. Simplified 0.4

      \[\leadsto \color{blue}{\left(x + \frac{1 - x}{y}\right) + \frac{-1 + x}{y \cdot y} \cdot \left(\frac{-1}{y} + 1\right)} \]
      Proof
      (+.f64 (+.f64 x (/.f64 (-.f64 1 x) y)) (*.f64 (/.f64 (+.f64 -1 x) (*.f64 y y)) (+.f64 (/.f64 -1 y) 1))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 x (Rewrite=> div-sub_binary64 (-.f64 (/.f64 1 y) (/.f64 x y)))) (*.f64 (/.f64 (+.f64 -1 x) (*.f64 y y)) (+.f64 (/.f64 -1 y) 1))): 0 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite<= associate--l+_binary64 (-.f64 (+.f64 x (/.f64 1 y)) (/.f64 x y))) (*.f64 (/.f64 (+.f64 -1 x) (*.f64 y y)) (+.f64 (/.f64 -1 y) 1))): 0 points increase in error, 0 points decrease in error
      (+.f64 (-.f64 (Rewrite<= +-commutative_binary64 (+.f64 (/.f64 1 y) x)) (/.f64 x y)) (*.f64 (/.f64 (+.f64 -1 x) (*.f64 y y)) (+.f64 (/.f64 -1 y) 1))): 0 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite=> associate--l+_binary64 (+.f64 (/.f64 1 y) (-.f64 x (/.f64 x y)))) (*.f64 (/.f64 (+.f64 -1 x) (*.f64 y y)) (+.f64 (/.f64 -1 y) 1))): 0 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite=> +-commutative_binary64 (+.f64 (-.f64 x (/.f64 x y)) (/.f64 1 y))) (*.f64 (/.f64 (+.f64 -1 x) (*.f64 y y)) (+.f64 (/.f64 -1 y) 1))): 0 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite<= associate--r-_binary64 (-.f64 x (-.f64 (/.f64 x y) (/.f64 1 y)))) (*.f64 (/.f64 (+.f64 -1 x) (*.f64 y y)) (+.f64 (/.f64 -1 y) 1))): 0 points increase in error, 0 points decrease in error
      (+.f64 (-.f64 x (Rewrite<= div-sub_binary64 (/.f64 (-.f64 x 1) y))) (*.f64 (/.f64 (+.f64 -1 x) (*.f64 y y)) (+.f64 (/.f64 -1 y) 1))): 0 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite<= unsub-neg_binary64 (+.f64 x (neg.f64 (/.f64 (-.f64 x 1) y)))) (*.f64 (/.f64 (+.f64 -1 x) (*.f64 y y)) (+.f64 (/.f64 -1 y) 1))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 x (Rewrite<= mul-1-neg_binary64 (*.f64 -1 (/.f64 (-.f64 x 1) y)))) (*.f64 (/.f64 (+.f64 -1 x) (*.f64 y y)) (+.f64 (/.f64 -1 y) 1))): 0 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 -1 (/.f64 (-.f64 x 1) y)) x)) (*.f64 (/.f64 (+.f64 -1 x) (*.f64 y y)) (+.f64 (/.f64 -1 y) 1))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (*.f64 -1 (/.f64 (-.f64 x 1) y)) x) (*.f64 (/.f64 (Rewrite<= +-commutative_binary64 (+.f64 x -1)) (*.f64 y y)) (+.f64 (/.f64 -1 y) 1))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (*.f64 -1 (/.f64 (-.f64 x 1) y)) x) (*.f64 (/.f64 (+.f64 x (Rewrite<= metadata-eval (neg.f64 1))) (*.f64 y y)) (+.f64 (/.f64 -1 y) 1))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (*.f64 -1 (/.f64 (-.f64 x 1) y)) x) (*.f64 (/.f64 (Rewrite<= sub-neg_binary64 (-.f64 x 1)) (*.f64 y y)) (+.f64 (/.f64 -1 y) 1))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (*.f64 -1 (/.f64 (-.f64 x 1) y)) x) (*.f64 (/.f64 (-.f64 x 1) (Rewrite<= unpow2_binary64 (pow.f64 y 2))) (+.f64 (/.f64 -1 y) 1))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (*.f64 -1 (/.f64 (-.f64 x 1) y)) x) (*.f64 (/.f64 (-.f64 x 1) (pow.f64 y 2)) (+.f64 (/.f64 (Rewrite<= metadata-eval (neg.f64 1)) y) 1))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (*.f64 -1 (/.f64 (-.f64 x 1) y)) x) (*.f64 (/.f64 (-.f64 x 1) (pow.f64 y 2)) (+.f64 (Rewrite<= distribute-neg-frac_binary64 (neg.f64 (/.f64 1 y))) 1))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (*.f64 -1 (/.f64 (-.f64 x 1) y)) x) (Rewrite<= distribute-rgt-out_binary64 (+.f64 (*.f64 (neg.f64 (/.f64 1 y)) (/.f64 (-.f64 x 1) (pow.f64 y 2))) (*.f64 1 (/.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) (+.f64 (*.f64 (Rewrite=> distribute-neg-frac_binary64 (/.f64 (neg.f64 1) y)) (/.f64 (-.f64 x 1) (pow.f64 y 2))) (*.f64 1 (/.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) (+.f64 (*.f64 (/.f64 (Rewrite=> metadata-eval -1) y) (/.f64 (-.f64 x 1) (pow.f64 y 2))) (*.f64 1 (/.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) (+.f64 (Rewrite<= times-frac_binary64 (/.f64 (*.f64 -1 (-.f64 x 1)) (*.f64 y (pow.f64 y 2)))) (*.f64 1 (/.f64 (-.f64 x 1) (pow.f64 y 2))))): 13 points increase in error, 6 points decrease in error
      (+.f64 (+.f64 (*.f64 -1 (/.f64 (-.f64 x 1) y)) x) (+.f64 (/.f64 (*.f64 -1 (-.f64 x 1)) (*.f64 y (Rewrite=> unpow2_binary64 (*.f64 y y)))) (*.f64 1 (/.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) (+.f64 (/.f64 (*.f64 -1 (-.f64 x 1)) (Rewrite<= cube-mult_binary64 (pow.f64 y 3))) (*.f64 1 (/.f64 (-.f64 x 1) (pow.f64 y 2))))): 1 points increase in error, 4 points decrease in error
      (+.f64 (+.f64 (*.f64 -1 (/.f64 (-.f64 x 1) y)) x) (+.f64 (Rewrite<= associate-*r/_binary64 (*.f64 -1 (/.f64 (-.f64 x 1) (pow.f64 y 3)))) (*.f64 1 (/.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) (+.f64 (*.f64 -1 (/.f64 (-.f64 x 1) (pow.f64 y 3))) (Rewrite=> *-lft-identity_binary64 (/.f64 (-.f64 x 1) (pow.f64 y 2))))): 0 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 -1 (/.f64 (-.f64 x 1) (pow.f64 y 3)))) (/.f64 (-.f64 x 1) (pow.f64 y 2)))): 1 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite<= associate-+r+_binary64 (+.f64 (*.f64 -1 (/.f64 (-.f64 x 1) y)) (+.f64 x (*.f64 -1 (/.f64 (-.f64 x 1) (pow.f64 y 3)))))) (/.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)) (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 -1 (/.f64 (-.f64 x 1) (pow.f64 y 3))) 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)) (+.f64 (*.f64 -1 (/.f64 (-.f64 x 1) (pow.f64 y 3))) x)) (Rewrite=> div-sub_binary64 (-.f64 (/.f64 x (pow.f64 y 2)) (/.f64 1 (pow.f64 y 2))))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate--l+_binary64 (-.f64 (+.f64 (+.f64 (*.f64 -1 (/.f64 (-.f64 x 1) y)) (+.f64 (*.f64 -1 (/.f64 (-.f64 x 1) (pow.f64 y 3))) 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)) (+.f64 (*.f64 -1 (/.f64 (-.f64 x 1) (pow.f64 y 3))) x)))) (/.f64 1 (pow.f64 y 2))): 0 points increase in error, 0 points decrease in error

   4. Taylor expanded in x around 0 0.4

      \[\leadsto \color{blue}{\left(\left(1 + \frac{1}{{y}^{2}}\right) - \left(\frac{1}{y} + \frac{1}{{y}^{3}}\right)\right) \cdot x + \left(\frac{1}{y} + -1 \cdot \frac{1 - \frac{1}{y}}{{y}^{2}}\right)} \]

   5. Simplified 0.4

      \[\leadsto \color{blue}{x + \mathsf{fma}\left(1 + \frac{-1}{y}, \frac{-1 + x}{y \cdot y}, \frac{1 - x}{y}\right)} \]
      Proof
      (+.f64 x (fma.f64 (+.f64 1 (/.f64 -1 y)) (/.f64 (+.f64 -1 x) (*.f64 y y)) (/.f64 (-.f64 1 x) y))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (fma.f64 (+.f64 1 (/.f64 (Rewrite<= metadata-eval (neg.f64 1)) y)) (/.f64 (+.f64 -1 x) (*.f64 y y)) (/.f64 (-.f64 1 x) y))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (fma.f64 (+.f64 1 (Rewrite<= distribute-neg-frac_binary64 (neg.f64 (/.f64 1 y)))) (/.f64 (+.f64 -1 x) (*.f64 y y)) (/.f64 (-.f64 1 x) y))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (fma.f64 (Rewrite<= sub-neg_binary64 (-.f64 1 (/.f64 1 y))) (/.f64 (+.f64 -1 x) (*.f64 y y)) (/.f64 (-.f64 1 x) y))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (fma.f64 (-.f64 1 (/.f64 1 y)) (/.f64 (Rewrite<= +-commutative_binary64 (+.f64 x -1)) (*.f64 y y)) (/.f64 (-.f64 1 x) y))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (fma.f64 (-.f64 1 (/.f64 1 y)) (/.f64 (+.f64 x (Rewrite<= metadata-eval (neg.f64 1))) (*.f64 y y)) (/.f64 (-.f64 1 x) y))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (fma.f64 (-.f64 1 (/.f64 1 y)) (/.f64 (Rewrite<= sub-neg_binary64 (-.f64 x 1)) (*.f64 y y)) (/.f64 (-.f64 1 x) y))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (fma.f64 (-.f64 1 (/.f64 1 y)) (/.f64 (-.f64 x 1) (Rewrite<= unpow2_binary64 (pow.f64 y 2))) (/.f64 (-.f64 1 x) y))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (fma.f64 (-.f64 1 (/.f64 1 y)) (/.f64 (-.f64 x 1) (pow.f64 y 2)) (Rewrite=> div-sub_binary64 (-.f64 (/.f64 1 y) (/.f64 x y))))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (fma.f64 (-.f64 1 (/.f64 1 y)) (/.f64 (-.f64 x 1) (pow.f64 y 2)) (Rewrite<= unsub-neg_binary64 (+.f64 (/.f64 1 y) (neg.f64 (/.f64 x y)))))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (fma.f64 (-.f64 1 (/.f64 1 y)) (/.f64 (-.f64 x 1) (pow.f64 y 2)) (Rewrite=> +-commutative_binary64 (+.f64 (neg.f64 (/.f64 x y)) (/.f64 1 y))))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (fma.f64 (-.f64 1 (/.f64 1 y)) (/.f64 (-.f64 x 1) (pow.f64 y 2)) (+.f64 (Rewrite=> neg-sub0_binary64 (-.f64 0 (/.f64 x y))) (/.f64 1 y)))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (fma.f64 (-.f64 1 (/.f64 1 y)) (/.f64 (-.f64 x 1) (pow.f64 y 2)) (Rewrite=> associate-+l-_binary64 (-.f64 0 (-.f64 (/.f64 x y) (/.f64 1 y)))))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (fma.f64 (-.f64 1 (/.f64 1 y)) (/.f64 (-.f64 x 1) (pow.f64 y 2)) (-.f64 0 (Rewrite<= div-sub_binary64 (/.f64 (-.f64 x 1) y))))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (fma.f64 (-.f64 1 (/.f64 1 y)) (/.f64 (-.f64 x 1) (pow.f64 y 2)) (Rewrite<= neg-sub0_binary64 (neg.f64 (/.f64 (-.f64 x 1) y))))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (Rewrite<= fma-neg_binary64 (-.f64 (*.f64 (-.f64 1 (/.f64 1 y)) (/.f64 (-.f64 x 1) (pow.f64 y 2))) (/.f64 (-.f64 x 1) y)))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (-.f64 (*.f64 (Rewrite=> sub-neg_binary64 (+.f64 1 (neg.f64 (/.f64 1 y)))) (/.f64 (-.f64 x 1) (pow.f64 y 2))) (/.f64 (-.f64 x 1) y))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (-.f64 (*.f64 (Rewrite=> +-commutative_binary64 (+.f64 (neg.f64 (/.f64 1 y)) 1)) (/.f64 (-.f64 x 1) (pow.f64 y 2))) (/.f64 (-.f64 x 1) y))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (-.f64 (Rewrite<= distribute-lft1-in_binary64 (+.f64 (*.f64 (neg.f64 (/.f64 1 y)) (/.f64 (-.f64 x 1) (pow.f64 y 2))) (/.f64 (-.f64 x 1) (pow.f64 y 2)))) (/.f64 (-.f64 x 1) y))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (-.f64 (+.f64 (*.f64 (Rewrite=> distribute-neg-frac_binary64 (/.f64 (neg.f64 1) y)) (/.f64 (-.f64 x 1) (pow.f64 y 2))) (/.f64 (-.f64 x 1) (pow.f64 y 2))) (/.f64 (-.f64 x 1) y))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (-.f64 (+.f64 (*.f64 (/.f64 (Rewrite=> metadata-eval -1) y) (/.f64 (-.f64 x 1) (pow.f64 y 2))) (/.f64 (-.f64 x 1) (pow.f64 y 2))) (/.f64 (-.f64 x 1) y))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (-.f64 (+.f64 (Rewrite<= times-frac_binary64 (/.f64 (*.f64 -1 (-.f64 x 1)) (*.f64 y (pow.f64 y 2)))) (/.f64 (-.f64 x 1) (pow.f64 y 2))) (/.f64 (-.f64 x 1) y))): 13 points increase in error, 6 points decrease in error
      (+.f64 x (-.f64 (+.f64 (/.f64 (*.f64 -1 (-.f64 x 1)) (*.f64 y (Rewrite=> unpow2_binary64 (*.f64 y y)))) (/.f64 (-.f64 x 1) (pow.f64 y 2))) (/.f64 (-.f64 x 1) y))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (-.f64 (+.f64 (/.f64 (*.f64 -1 (-.f64 x 1)) (Rewrite<= cube-mult_binary64 (pow.f64 y 3))) (/.f64 (-.f64 x 1) (pow.f64 y 2))) (/.f64 (-.f64 x 1) y))): 1 points increase in error, 4 points decrease in error
      (+.f64 x (-.f64 (+.f64 (Rewrite<= associate-*r/_binary64 (*.f64 -1 (/.f64 (-.f64 x 1) (pow.f64 y 3)))) (/.f64 (-.f64 x 1) (pow.f64 y 2))) (/.f64 (-.f64 x 1) y))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (-.f64 (+.f64 (*.f64 -1 (/.f64 (-.f64 x 1) (pow.f64 y 3))) (Rewrite=> div-sub_binary64 (-.f64 (/.f64 x (pow.f64 y 2)) (/.f64 1 (pow.f64 y 2))))) (/.f64 (-.f64 x 1) y))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (-.f64 (Rewrite<= associate--l+_binary64 (-.f64 (+.f64 (*.f64 -1 (/.f64 (-.f64 x 1) (pow.f64 y 3))) (/.f64 x (pow.f64 y 2))) (/.f64 1 (pow.f64 y 2)))) (/.f64 (-.f64 x 1) y))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (-.f64 (-.f64 (Rewrite<= +-commutative_binary64 (+.f64 (/.f64 x (pow.f64 y 2)) (*.f64 -1 (/.f64 (-.f64 x 1) (pow.f64 y 3))))) (/.f64 1 (pow.f64 y 2))) (/.f64 (-.f64 x 1) y))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (-.f64 (-.f64 (+.f64 (/.f64 x (pow.f64 y 2)) (*.f64 -1 (/.f64 (-.f64 x 1) (pow.f64 y 3)))) (/.f64 1 (pow.f64 y 2))) (Rewrite=> div-sub_binary64 (-.f64 (/.f64 x y) (/.f64 1 y))))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (Rewrite<= associate-+l-_binary64 (+.f64 (-.f64 (-.f64 (+.f64 (/.f64 x (pow.f64 y 2)) (*.f64 -1 (/.f64 (-.f64 x 1) (pow.f64 y 3)))) (/.f64 1 (pow.f64 y 2))) (/.f64 x y)) (/.f64 1 y)))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (+.f64 (Rewrite<= associate--r+_binary64 (-.f64 (+.f64 (/.f64 x (pow.f64 y 2)) (*.f64 -1 (/.f64 (-.f64 x 1) (pow.f64 y 3)))) (+.f64 (/.f64 1 (pow.f64 y 2)) (/.f64 x y)))) (/.f64 1 y))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (+.f64 (-.f64 (+.f64 (/.f64 x (pow.f64 y 2)) (*.f64 -1 (/.f64 (-.f64 x 1) (pow.f64 y 3)))) (Rewrite=> +-commutative_binary64 (+.f64 (/.f64 x y) (/.f64 1 (pow.f64 y 2))))) (/.f64 1 y))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (+.f64 (Rewrite=> associate--r+_binary64 (-.f64 (-.f64 (+.f64 (/.f64 x (pow.f64 y 2)) (*.f64 -1 (/.f64 (-.f64 x 1) (pow.f64 y 3)))) (/.f64 x y)) (/.f64 1 (pow.f64 y 2)))) (/.f64 1 y))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (Rewrite=> associate-+l-_binary64 (-.f64 (-.f64 (+.f64 (/.f64 x (pow.f64 y 2)) (*.f64 -1 (/.f64 (-.f64 x 1) (pow.f64 y 3)))) (/.f64 x y)) (-.f64 (/.f64 1 (pow.f64 y 2)) (/.f64 1 y))))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate--l+_binary64 (-.f64 (+.f64 x (-.f64 (+.f64 (/.f64 x (pow.f64 y 2)) (*.f64 -1 (/.f64 (-.f64 x 1) (pow.f64 y 3)))) (/.f64 x y))) (-.f64 (/.f64 1 (pow.f64 y 2)) (/.f64 1 y)))): 0 points increase in error, 0 points decrease in error
      (-.f64 (Rewrite<= associate--l+_binary64 (-.f64 (+.f64 x (+.f64 (/.f64 x (pow.f64 y 2)) (*.f64 -1 (/.f64 (-.f64 x 1) (pow.f64 y 3))))) (/.f64 x y))) (-.f64 (/.f64 1 (pow.f64 y 2)) (/.f64 1 y))): 1 points increase in error, 0 points decrease in error
      (-.f64 (-.f64 (Rewrite<= +-commutative_binary64 (+.f64 (+.f64 (/.f64 x (pow.f64 y 2)) (*.f64 -1 (/.f64 (-.f64 x 1) (pow.f64 y 3)))) x)) (/.f64 x y)) (-.f64 (/.f64 1 (pow.f64 y 2)) (/.f64 1 y))): 0 points increase in error, 0 points decrease in error
      (-.f64 (-.f64 (Rewrite<= associate-+r+_binary64 (+.f64 (/.f64 x (pow.f64 y 2)) (+.f64 (*.f64 -1 (/.f64 (-.f64 x 1) (pow.f64 y 3))) x))) (/.f64 x y)) (-.f64 (/.f64 1 (pow.f64 y 2)) (/.f64 1 y))): 0 points increase in error, 0 points decrease in error
      (-.f64 (-.f64 (Rewrite=> associate-+r+_binary64 (+.f64 (+.f64 (/.f64 x (pow.f64 y 2)) (*.f64 -1 (/.f64 (-.f64 x 1) (pow.f64 y 3)))) x)) (/.f64 x y)) (-.f64 (/.f64 1 (pow.f64 y 2)) (/.f64 1 y))): 0 points increase in error, 0 points decrease in error
      (-.f64 (-.f64 (+.f64 (Rewrite=> +-commutative_binary64 (+.f64 (*.f64 -1 (/.f64 (-.f64 x 1) (pow.f64 y 3))) (/.f64 x (pow.f64 y 2)))) x) (/.f64 x y)) (-.f64 (/.f64 1 (pow.f64 y 2)) (/.f64 1 y))): 0 points increase in error, 0 points decrease in error
      (-.f64 (-.f64 (Rewrite=> associate-+l+_binary64 (+.f64 (*.f64 -1 (/.f64 (-.f64 x 1) (pow.f64 y 3))) (+.f64 (/.f64 x (pow.f64 y 2)) x))) (/.f64 x y)) (-.f64 (/.f64 1 (pow.f64 y 2)) (/.f64 1 y))): 0 points increase in error, 0 points decrease in error
      (-.f64 (Rewrite=> associate--l+_binary64 (+.f64 (*.f64 -1 (/.f64 (-.f64 x 1) (pow.f64 y 3))) (-.f64 (+.f64 (/.f64 x (pow.f64 y 2)) x) (/.f64 x y)))) (-.f64 (/.f64 1 (pow.f64 y 2)) (/.f64 1 y))): 0 points increase in error, 0 points decrease in error
      (-.f64 (Rewrite=> +-commutative_binary64 (+.f64 (-.f64 (+.f64 (/.f64 x (pow.f64 y 2)) x) (/.f64 x y)) (*.f64 -1 (/.f64 (-.f64 x 1) (pow.f64 y 3))))) (-.f64 (/.f64 1 (pow.f64 y 2)) (/.f64 1 y))): 0 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (-.f64 (+.f64 (/.f64 x (pow.f64 y 2)) x) (/.f64 x y)) (Rewrite=> associate-*r/_binary64 (/.f64 (*.f64 -1 (-.f64 x 1)) (pow.f64 y 3)))) (-.f64 (/.f64 1 (pow.f64 y 2)) (/.f64 1 y))): 0 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (-.f64 (+.f64 (/.f64 x (pow.f64 y 2)) x) (/.f64 x y)) (Rewrite<= associate-*l/_binary64 (*.f64 (/.f64 -1 (pow.f64 y 3)) (-.f64 x 1)))) (-.f64 (/.f64 1 (pow.f64 y 2)) (/.f64 1 y))): 2 points increase in error, 3 points decrease in error
      (-.f64 (+.f64 (-.f64 (+.f64 (/.f64 x (pow.f64 y 2)) x) (/.f64 x y)) (*.f64 (/.f64 (Rewrite<= metadata-eval (neg.f64 1)) (pow.f64 y 3)) (-.f64 x 1))) (-.f64 (/.f64 1 (pow.f64 y 2)) (/.f64 1 y))): 0 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (-.f64 (+.f64 (/.f64 x (pow.f64 y 2)) x) (/.f64 x y)) (*.f64 (Rewrite<= distribute-neg-frac_binary64 (neg.f64 (/.f64 1 (pow.f64 y 3)))) (-.f64 x 1))) (-.f64 (/.f64 1 (pow.f64 y 2)) (/.f64 1 y))): 0 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (-.f64 (+.f64 (/.f64 x (pow.f64 y 2)) x) (/.f64 x y)) (*.f64 (neg.f64 (/.f64 1 (pow.f64 y 3))) (Rewrite=> sub-neg_binary64 (+.f64 x (neg.f64 1))))) (-.f64 (/.f64 1 (pow.f64 y 2)) (/.f64 1 y))): 0 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (-.f64 (+.f64 (/.f64 x (pow.f64 y 2)) x) (/.f64 x y)) (*.f64 (neg.f64 (/.f64 1 (pow.f64 y 3))) (+.f64 x (Rewrite=> metadata-eval -1)))) (-.f64 (/.f64 1 (pow.f64 y 2)) (/.f64 1 y))): 0 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (-.f64 (+.f64 (/.f64 x (pow.f64 y 2)) x) (/.f64 x y)) (Rewrite=> distribute-rgt-in_binary64 (+.f64 (*.f64 x (neg.f64 (/.f64 1 (pow.f64 y 3)))) (*.f64 -1 (neg.f64 (/.f64 1 (pow.f64 y 3))))))) (-.f64 (/.f64 1 (pow.f64 y 2)) (/.f64 1 y))): 0 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (-.f64 (+.f64 (/.f64 x (pow.f64 y 2)) x) (/.f64 x y)) (+.f64 (Rewrite<= *-commutative_binary64 (*.f64 (neg.f64 (/.f64 1 (pow.f64 y 3))) x)) (*.f64 -1 (neg.f64 (/.f64 1 (pow.f64 y 3)))))) (-.f64 (/.f64 1 (pow.f64 y 2)) (/.f64 1 y))): 0 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (-.f64 (+.f64 (/.f64 x (pow.f64 y 2)) x) (/.f64 x y)) (+.f64 (*.f64 (neg.f64 (/.f64 1 (pow.f64 y 3))) x) (Rewrite<= neg-mul-1_binary64 (neg.f64 (neg.f64 (/.f64 1 (pow.f64 y 3))))))) (-.f64 (/.f64 1 (pow.f64 y 2)) (/.f64 1 y))): 0 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (-.f64 (+.f64 (/.f64 x (pow.f64 y 2)) x) (/.f64 x y)) (Rewrite=> unsub-neg_binary64 (-.f64 (*.f64 (neg.f64 (/.f64 1 (pow.f64 y 3))) x) (neg.f64 (/.f64 1 (pow.f64 y 3)))))) (-.f64 (/.f64 1 (pow.f64 y 2)) (/.f64 1 y))): 0 points increase in error, 0 points decrease in error
      (-.f64 (Rewrite<= associate--l+_binary64 (-.f64 (+.f64 (-.f64 (+.f64 (/.f64 x (pow.f64 y 2)) x) (/.f64 x y)) (*.f64 (neg.f64 (/.f64 1 (pow.f64 y 3))) x)) (neg.f64 (/.f64 1 (pow.f64 y 3))))) (-.f64 (/.f64 1 (pow.f64 y 2)) (/.f64 1 y))): 0 points increase in error, 0 points decrease in error
      (-.f64 (-.f64 (+.f64 (-.f64 (+.f64 (/.f64 (Rewrite<= *-rgt-identity_binary64 (*.f64 x 1)) (pow.f64 y 2)) x) (/.f64 x y)) (*.f64 (neg.f64 (/.f64 1 (pow.f64 y 3))) x)) (neg.f64 (/.f64 1 (pow.f64 y 3)))) (-.f64 (/.f64 1 (pow.f64 y 2)) (/.f64 1 y))): 0 points increase in error, 0 points decrease in error
      (-.f64 (-.f64 (+.f64 (-.f64 (+.f64 (Rewrite<= associate-*r/_binary64 (*.f64 x (/.f64 1 (pow.f64 y 2)))) x) (/.f64 x y)) (*.f64 (neg.f64 (/.f64 1 (pow.f64 y 3))) x)) (neg.f64 (/.f64 1 (pow.f64 y 3)))) (-.f64 (/.f64 1 (pow.f64 y 2)) (/.f64 1 y))): 0 points increase in error, 0 points decrease in error
      (-.f64 (-.f64 (+.f64 (-.f64 (+.f64 (*.f64 x (/.f64 1 (pow.f64 y 2))) (Rewrite<= *-rgt-identity_binary64 (*.f64 x 1))) (/.f64 x y)) (*.f64 (neg.f64 (/.f64 1 (pow.f64 y 3))) x)) (neg.f64 (/.f64 1 (pow.f64 y 3)))) (-.f64 (/.f64 1 (pow.f64 y 2)) (/.f64 1 y))): 0 points increase in error, 0 points decrease in error
      (-.f64 (-.f64 (+.f64 (-.f64 (Rewrite<= distribute-lft-in_binary64 (*.f64 x (+.f64 (/.f64 1 (pow.f64 y 2)) 1))) (/.f64 x y)) (*.f64 (neg.f64 (/.f64 1 (pow.f64 y 3))) x)) (neg.f64 (/.f64 1 (pow.f64 y 3)))) (-.f64 (/.f64 1 (pow.f64 y 2)) (/.f64 1 y))): 1 points increase in error, 0 points decrease in error
      (-.f64 (-.f64 (+.f64 (-.f64 (*.f64 x (Rewrite<= +-commutative_binary64 (+.f64 1 (/.f64 1 (pow.f64 y 2))))) (/.f64 x y)) (*.f64 (neg.f64 (/.f64 1 (pow.f64 y 3))) x)) (neg.f64 (/.f64 1 (pow.f64 y 3)))) (-.f64 (/.f64 1 (pow.f64 y 2)) (/.f64 1 y))): 0 points increase in error, 0 points decrease in error
      (-.f64 (-.f64 (+.f64 (-.f64 (*.f64 x (+.f64 1 (/.f64 1 (pow.f64 y 2)))) (/.f64 (Rewrite<= *-rgt-identity_binary64 (*.f64 x 1)) y)) (*.f64 (neg.f64 (/.f64 1 (pow.f64 y 3))) x)) (neg.f64 (/.f64 1 (pow.f64 y 3)))) (-.f64 (/.f64 1 (pow.f64 y 2)) (/.f64 1 y))): 0 points increase in error, 0 points decrease in error
      (-.f64 (-.f64 (+.f64 (-.f64 (*.f64 x (+.f64 1 (/.f64 1 (pow.f64 y 2)))) (Rewrite<= associate-*r/_binary64 (*.f64 x (/.f64 1 y)))) (*.f64 (neg.f64 (/.f64 1 (pow.f64 y 3))) x)) (neg.f64 (/.f64 1 (pow.f64 y 3)))) (-.f64 (/.f64 1 (pow.f64 y 2)) (/.f64 1 y))): 0 points increase in error, 0 points decrease in error
      (-.f64 (-.f64 (+.f64 (Rewrite=> distribute-lft-out--_binary64 (*.f64 x (-.f64 (+.f64 1 (/.f64 1 (pow.f64 y 2))) (/.f64 1 y)))) (*.f64 (neg.f64 (/.f64 1 (pow.f64 y 3))) x)) (neg.f64 (/.f64 1 (pow.f64 y 3)))) (-.f64 (/.f64 1 (pow.f64 y 2)) (/.f64 1 y))): 0 points increase in error, 0 points decrease in error
      (-.f64 (-.f64 (+.f64 (*.f64 x (-.f64 (+.f64 1 (/.f64 1 (pow.f64 y 2))) (/.f64 1 y))) (Rewrite=> *-commutative_binary64 (*.f64 x (neg.f64 (/.f64 1 (pow.f64 y 3)))))) (neg.f64 (/.f64 1 (pow.f64 y 3)))) (-.f64 (/.f64 1 (pow.f64 y 2)) (/.f64 1 y))): 0 points increase in error, 0 points decrease in error
      (-.f64 (-.f64 (Rewrite=> distribute-lft-out_binary64 (*.f64 x (+.f64 (-.f64 (+.f64 1 (/.f64 1 (pow.f64 y 2))) (/.f64 1 y)) (neg.f64 (/.f64 1 (pow.f64 y 3)))))) (neg.f64 (/.f64 1 (pow.f64 y 3)))) (-.f64 (/.f64 1 (pow.f64 y 2)) (/.f64 1 y))): 0 points increase in error, 0 points decrease in error
      (-.f64 (-.f64 (*.f64 x (Rewrite<= sub-neg_binary64 (-.f64 (-.f64 (+.f64 1 (/.f64 1 (pow.f64 y 2))) (/.f64 1 y)) (/.f64 1 (pow.f64 y 3))))) (neg.f64 (/.f64 1 (pow.f64 y 3)))) (-.f64 (/.f64 1 (pow.f64 y 2)) (/.f64 1 y))): 0 points increase in error, 0 points decrease in error
      (-.f64 (-.f64 (*.f64 x (Rewrite<= associate--r+_binary64 (-.f64 (+.f64 1 (/.f64 1 (pow.f64 y 2))) (+.f64 (/.f64 1 y) (/.f64 1 (pow.f64 y 3)))))) (neg.f64 (/.f64 1 (pow.f64 y 3)))) (-.f64 (/.f64 1 (pow.f64 y 2)) (/.f64 1 y))): 0 points increase in error, 0 points decrease in error
      (-.f64 (-.f64 (Rewrite<= *-commutative_binary64 (*.f64 (-.f64 (+.f64 1 (/.f64 1 (pow.f64 y 2))) (+.f64 (/.f64 1 y) (/.f64 1 (pow.f64 y 3)))) x)) (neg.f64 (/.f64 1 (pow.f64 y 3)))) (-.f64 (/.f64 1 (pow.f64 y 2)) (/.f64 1 y))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate-+l-_binary64 (+.f64 (-.f64 (-.f64 (*.f64 (-.f64 (+.f64 1 (/.f64 1 (pow.f64 y 2))) (+.f64 (/.f64 1 y) (/.f64 1 (pow.f64 y 3)))) x) (neg.f64 (/.f64 1 (pow.f64 y 3)))) (/.f64 1 (pow.f64 y 2))) (/.f64 1 y))): 0 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite<= associate--r+_binary64 (-.f64 (*.f64 (-.f64 (+.f64 1 (/.f64 1 (pow.f64 y 2))) (+.f64 (/.f64 1 y) (/.f64 1 (pow.f64 y 3)))) x) (+.f64 (neg.f64 (/.f64 1 (pow.f64 y 3))) (/.f64 1 (pow.f64 y 2))))) (/.f64 1 y)): 0 points increase in error, 1 points decrease in error
      (+.f64 (-.f64 (*.f64 (-.f64 (+.f64 1 (/.f64 1 (pow.f64 y 2))) (+.f64 (/.f64 1 y) (/.f64 1 (pow.f64 y 3)))) x) (Rewrite<= +-commutative_binary64 (+.f64 (/.f64 1 (pow.f64 y 2)) (neg.f64 (/.f64 1 (pow.f64 y 3)))))) (/.f64 1 y)): 0 points increase in error, 0 points decrease in error
      (+.f64 (-.f64 (*.f64 (-.f64 (+.f64 1 (/.f64 1 (pow.f64 y 2))) (+.f64 (/.f64 1 y) (/.f64 1 (pow.f64 y 3)))) x) (+.f64 (/.f64 1 (pow.f64 y 2)) (neg.f64 (/.f64 1 (Rewrite=> unpow3_binary64 (*.f64 (*.f64 y y) y)))))) (/.f64 1 y)): 4 points increase in error, 1 points decrease in error
      (+.f64 (-.f64 (*.f64 (-.f64 (+.f64 1 (/.f64 1 (pow.f64 y 2))) (+.f64 (/.f64 1 y) (/.f64 1 (pow.f64 y 3)))) x) (+.f64 (/.f64 1 (pow.f64 y 2)) (neg.f64 (/.f64 1 (*.f64 (Rewrite<= unpow2_binary64 (pow.f64 y 2)) y))))) (/.f64 1 y)): 0 points increase in error, 0 points decrease in error
      (+.f64 (-.f64 (*.f64 (-.f64 (+.f64 1 (/.f64 1 (pow.f64 y 2))) (+.f64 (/.f64 1 y) (/.f64 1 (pow.f64 y 3)))) x) (+.f64 (/.f64 1 (pow.f64 y 2)) (neg.f64 (Rewrite<= associate-/l/_binary64 (/.f64 (/.f64 1 y) (pow.f64 y 2)))))) (/.f64 1 y)): 3 points increase in error, 7 points decrease in error
      (+.f64 (-.f64 (*.f64 (-.f64 (+.f64 1 (/.f64 1 (pow.f64 y 2))) (+.f64 (/.f64 1 y) (/.f64 1 (pow.f64 y 3)))) x) (Rewrite<= sub-neg_binary64 (-.f64 (/.f64 1 (pow.f64 y 2)) (/.f64 (/.f64 1 y) (pow.f64 y 2))))) (/.f64 1 y)): 0 points increase in error, 0 points decrease in error
      (+.f64 (-.f64 (*.f64 (-.f64 (+.f64 1 (/.f64 1 (pow.f64 y 2))) (+.f64 (/.f64 1 y) (/.f64 1 (pow.f64 y 3)))) x) (Rewrite<= div-sub_binary64 (/.f64 (-.f64 1 (/.f64 1 y)) (pow.f64 y 2)))) (/.f64 1 y)): 0 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite<= unsub-neg_binary64 (+.f64 (*.f64 (-.f64 (+.f64 1 (/.f64 1 (pow.f64 y 2))) (+.f64 (/.f64 1 y) (/.f64 1 (pow.f64 y 3)))) x) (neg.f64 (/.f64 (-.f64 1 (/.f64 1 y)) (pow.f64 y 2))))) (/.f64 1 y)): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (*.f64 (-.f64 (+.f64 1 (/.f64 1 (pow.f64 y 2))) (+.f64 (/.f64 1 y) (/.f64 1 (pow.f64 y 3)))) x) (Rewrite<= mul-1-neg_binary64 (*.f64 -1 (/.f64 (-.f64 1 (/.f64 1 y)) (pow.f64 y 2))))) (/.f64 1 y)): 0 points increase in error, 0 points decrease in error
      (Rewrite=> associate-+l+_binary64 (+.f64 (*.f64 (-.f64 (+.f64 1 (/.f64 1 (pow.f64 y 2))) (+.f64 (/.f64 1 y) (/.f64 1 (pow.f64 y 3)))) x) (+.f64 (*.f64 -1 (/.f64 (-.f64 1 (/.f64 1 y)) (pow.f64 y 2))) (/.f64 1 y)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 (-.f64 (+.f64 1 (/.f64 1 (pow.f64 y 2))) (+.f64 (/.f64 1 y) (/.f64 1 (pow.f64 y 3)))) x) (Rewrite<= +-commutative_binary64 (+.f64 (/.f64 1 y) (*.f64 -1 (/.f64 (-.f64 1 (/.f64 1 y)) (pow.f64 y 2)))))): 0 points increase in error, 0 points decrease in error
3. Recombined 3 regimes into one program.

4. Final simplification 0.1

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -43529.630834191135:\\ \;\;\;\;\left(x - \frac{x + -1}{y}\right) + \frac{x + -1}{y \cdot y} \cdot \left(1 + \frac{-1}{y}\right)\\ \mathbf{elif}\;y \leq 7.444779409057008:\\ \;\;\;\;\mathsf{fma}\left(1 - x, \frac{y}{-1 - y}, 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + \mathsf{fma}\left(1 + \frac{-1}{y}, \frac{x + -1}{y \cdot y}, \frac{1 - x}{y}\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	0.1
Cost	7240

\[\begin{array}{l} t_0 := \left(x - \frac{x + -1}{y}\right) + \frac{x + -1}{y \cdot y} \cdot \left(1 + \frac{-1}{y}\right)\\ \mathbf{if}\;y \leq -43529.630834191135:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 7.444779409057008:\\ \;\;\;\;\mathsf{fma}\left(1 - x, \frac{y}{-1 - y}, 1\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	0.4
Cost	3276

\[\begin{array}{l} t_0 := \frac{y \cdot \left(1 - x\right)}{y + 1}\\ t_1 := x \cdot \frac{y}{y + 1}\\ \mathbf{if}\;t_0 \leq -1 \cdot 10^{+67}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_0 \leq 0.9:\\ \;\;\;\;1 - t_0\\ \mathbf{elif}\;t_0 \leq 1.0000005:\\ \;\;\;\;\left(x - \frac{x + -1}{y}\right) + \frac{x + -1}{y \cdot y} \cdot \left(1 + \frac{-1}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Error	0.4
Cost	2764

\[\begin{array}{l} t_0 := \frac{y \cdot \left(1 - x\right)}{y + 1}\\ t_1 := x \cdot \frac{y}{y + 1}\\ \mathbf{if}\;t_0 \leq -1 \cdot 10^{+67}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_0 \leq 0.9:\\ \;\;\;\;1 - t_0\\ \mathbf{elif}\;t_0 \leq 1.0000005:\\ \;\;\;\;x + \frac{1 - x}{y} \cdot \left(1 + \frac{-1}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Error	0.4
Cost	2508

\[\begin{array}{l} t_0 := \frac{y \cdot \left(1 - x\right)}{y + 1}\\ t_1 := x \cdot \frac{y}{y + 1}\\ \mathbf{if}\;t_0 \leq -1 \cdot 10^{+67}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_0 \leq 0.9995:\\ \;\;\;\;1 - t_0\\ \mathbf{elif}\;t_0 \leq 1.0000005:\\ \;\;\;\;x + \frac{1 + \frac{-1}{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Error	16.9
Cost	720

\[\begin{array}{l} \mathbf{if}\;y \leq -1.261860562910319 \cdot 10^{+53}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.2100994589355638 \cdot 10^{+38}:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{elif}\;y \leq -43529.630834191135:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7.943791275622311 \cdot 10^{-5}:\\ \;\;\;\;1 - y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6
Error	1.2
Cost	712

\[\begin{array}{l} t_0 := x + \frac{1}{y}\\ \mathbf{if}\;y \leq -43529.630834191135:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 7.943791275622311 \cdot 10^{-5}:\\ \;\;\;\;1 + \left(y \cdot x - y\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 7
Error	1.1
Cost	712

\[\begin{array}{l} t_0 := x - \frac{x + -1}{y}\\ \mathbf{if}\;y \leq -43529.630834191135:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 7.943791275622311 \cdot 10^{-5}:\\ \;\;\;\;1 + \left(y \cdot x - y\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 8
Error	17.1
Cost	592

\[\begin{array}{l} \mathbf{if}\;y \leq -1.261860562910319 \cdot 10^{+53}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.2100994589355638 \cdot 10^{+38}:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{elif}\;y \leq -43529.630834191135:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7.444779409057008:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9
Error	9.1
Cost	584

\[\begin{array}{l} t_0 := x + \frac{1}{y}\\ \mathbf{if}\;y \leq -43529.630834191135:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 7.943791275622311 \cdot 10^{-5}:\\ \;\;\;\;1 - y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 10
Error	1.4
Cost	584

\[\begin{array}{l} t_0 := x + \frac{1}{y}\\ \mathbf{if}\;y \leq -43529.630834191135:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 7.943791275622311 \cdot 10^{-5}:\\ \;\;\;\;1 + y \cdot x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 11
Error	17.0
Cost	328

\[\begin{array}{l} \mathbf{if}\;y \leq -43529.630834191135:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7.444779409057008:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12
Error	39.7
Cost	64

\[x \]

Reproduce

herbie shell --seed 2022302 
(FPCore (x y)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, D"
  :precision binary64

  :herbie-target
  (if (< y -3693.8482788297247) (- (/ 1.0 y) (- (/ x y) x)) (if (< y 6799310503.41891) (- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0))) (- (/ 1.0 y) (- (/ x y) x))))

  (- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0))))