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

Average Error: 21.8 → 0.1

Time: 12.9s

Precision: binary64

Cost: 7304

Math

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

↓

\[\begin{array}{l} t_0 := x + \frac{1 - x}{y} \cdot \left(\frac{-1}{y} + \left(1 + \frac{\frac{1}{y}}{y}\right)\right)\\ \mathbf{if}\;y \leq -70860.27575897537:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 6739.445106154658:\\ \;\;\;\;\mathsf{fma}\left(\frac{1 - x}{y + 1}, -y, 1\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

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 x) y) (+ (/ -1.0 y) (+ 1.0 (/ (/ 1.0 y) y)))))))
   (if (<= y -70860.27575897537)
     t_0
     (if (<= y 6739.445106154658)
       (fma (/ (- 1.0 x) (+ y 1.0)) (- y) 1.0)
       t_0))))

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 - x) / y) * ((-1.0 / y) + (1.0 + ((1.0 / y) / y))));
	double tmp;
	if (y <= -70860.27575897537) {
		tmp = t_0;
	} else if (y <= 6739.445106154658) {
		tmp = fma(((1.0 - x) / (y + 1.0)), -y, 1.0);
	} else {
		tmp = t_0;
	}
	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(x + Float64(Float64(Float64(1.0 - x) / y) * Float64(Float64(-1.0 / y) + Float64(1.0 + Float64(Float64(1.0 / y) / y)))))
	tmp = 0.0
	if (y <= -70860.27575897537)
		tmp = t_0;
	elseif (y <= 6739.445106154658)
		tmp = fma(Float64(Float64(1.0 - x) / Float64(y + 1.0)), Float64(-y), 1.0);
	else
		tmp = t_0;
	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[(x + N[(N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision] * N[(N[(-1.0 / y), $MachinePrecision] + N[(1.0 + N[(N[(1.0 / y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -70860.27575897537], t$95$0, If[LessEqual[y, 6739.445106154658], N[(N[(N[(1.0 - x), $MachinePrecision] / N[(y + 1.0), $MachinePrecision]), $MachinePrecision] * (-y) + 1.0), $MachinePrecision], t$95$0]]]

Target

Original	21.8
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 2 regimes

2. if y < -70860.2757589753746 or 6739.44510615465788 < y

   1. Initial program 44.9

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

   2. Applied egg-rr 28.8

      \[\leadsto 1 - \color{blue}{\frac{1 - x}{1 + y} \cdot y} \]

   3. Applied egg-rr 28.8

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

   4. Taylor expanded in y around inf 28.7

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

   5. Simplified 0.0

      \[\leadsto \color{blue}{x + \frac{-1 + x}{y} \cdot \left(\frac{1}{y} + \left(-1 + \frac{\frac{-1}{y}}{y}\right)\right)} \]
      Proof
      (+.f64 x (*.f64 (/.f64 (+.f64 -1 x) y) (+.f64 (/.f64 1 y) (+.f64 -1 (/.f64 (/.f64 -1 y) y))))): 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) (+.f64 -1 (/.f64 (/.f64 -1 y) y))))): 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) (+.f64 -1 (/.f64 (/.f64 -1 y) y))))): 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) (+.f64 -1 (/.f64 (/.f64 -1 y) y))))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (*.f64 (/.f64 (-.f64 x 1) y) (+.f64 (/.f64 1 y) (+.f64 -1 (Rewrite<= associate-/r*_binary64 (/.f64 -1 (*.f64 y y))))))): 5 points increase in error, 6 points decrease in error
      (+.f64 x (*.f64 (/.f64 (-.f64 x 1) y) (+.f64 (/.f64 1 y) (+.f64 -1 (/.f64 -1 (Rewrite<= unpow2_binary64 (pow.f64 y 2))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (*.f64 (/.f64 (-.f64 x 1) y) (+.f64 (/.f64 1 y) (+.f64 -1 (/.f64 (Rewrite<= metadata-eval (neg.f64 1)) (pow.f64 y 2)))))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (*.f64 (/.f64 (-.f64 x 1) y) (+.f64 (/.f64 1 y) (+.f64 -1 (Rewrite<= distribute-neg-frac_binary64 (neg.f64 (/.f64 1 (pow.f64 y 2)))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (*.f64 (/.f64 (-.f64 x 1) y) (+.f64 (/.f64 1 y) (+.f64 -1 (Rewrite=> neg-mul-1_binary64 (*.f64 -1 (/.f64 1 (pow.f64 y 2)))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (*.f64 (/.f64 (-.f64 x 1) y) (+.f64 (/.f64 1 y) (+.f64 -1 (Rewrite=> *-commutative_binary64 (*.f64 (/.f64 1 (pow.f64 y 2)) -1)))))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (*.f64 (/.f64 (-.f64 x 1) y) (+.f64 (/.f64 1 y) (Rewrite=> distribute-rgt1-in_binary64 (*.f64 (+.f64 (/.f64 1 (pow.f64 y 2)) 1) -1))))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (*.f64 (/.f64 (-.f64 x 1) y) (+.f64 (/.f64 1 y) (Rewrite<= distribute-lft1-in_binary64 (+.f64 (*.f64 (/.f64 1 (pow.f64 y 2)) -1) -1))))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (*.f64 (/.f64 (-.f64 x 1) y) (+.f64 (/.f64 1 y) (+.f64 (Rewrite<= *-commutative_binary64 (*.f64 -1 (/.f64 1 (pow.f64 y 2)))) -1)))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (*.f64 (/.f64 (-.f64 x 1) y) (+.f64 (/.f64 1 y) (+.f64 (Rewrite<= neg-mul-1_binary64 (neg.f64 (/.f64 1 (pow.f64 y 2)))) -1)))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (Rewrite<= distribute-lft-out_binary64 (+.f64 (*.f64 (/.f64 (-.f64 x 1) y) (/.f64 1 y)) (*.f64 (/.f64 (-.f64 x 1) y) (+.f64 (neg.f64 (/.f64 1 (pow.f64 y 2))) -1))))): 2 points increase in error, 2 points decrease in error
      (+.f64 x (+.f64 (*.f64 (/.f64 (-.f64 x 1) y) (/.f64 (Rewrite<= metadata-eval (neg.f64 -1)) y)) (*.f64 (/.f64 (-.f64 x 1) y) (+.f64 (neg.f64 (/.f64 1 (pow.f64 y 2))) -1)))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (+.f64 (*.f64 (/.f64 (-.f64 x 1) y) (Rewrite<= distribute-neg-frac_binary64 (neg.f64 (/.f64 -1 y)))) (*.f64 (/.f64 (-.f64 x 1) y) (+.f64 (neg.f64 (/.f64 1 (pow.f64 y 2))) -1)))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (+.f64 (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 (/.f64 (-.f64 x 1) y) (/.f64 -1 y)))) (*.f64 (/.f64 (-.f64 x 1) y) (+.f64 (neg.f64 (/.f64 1 (pow.f64 y 2))) -1)))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (+.f64 (neg.f64 (Rewrite<= times-frac_binary64 (/.f64 (*.f64 (-.f64 x 1) -1) (*.f64 y y)))) (*.f64 (/.f64 (-.f64 x 1) y) (+.f64 (neg.f64 (/.f64 1 (pow.f64 y 2))) -1)))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (+.f64 (neg.f64 (/.f64 (Rewrite<= *-commutative_binary64 (*.f64 -1 (-.f64 x 1))) (*.f64 y y))) (*.f64 (/.f64 (-.f64 x 1) y) (+.f64 (neg.f64 (/.f64 1 (pow.f64 y 2))) -1)))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (+.f64 (neg.f64 (/.f64 (*.f64 -1 (-.f64 x 1)) (Rewrite<= unpow2_binary64 (pow.f64 y 2)))) (*.f64 (/.f64 (-.f64 x 1) y) (+.f64 (neg.f64 (/.f64 1 (pow.f64 y 2))) -1)))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (+.f64 (neg.f64 (/.f64 (Rewrite=> mul-1-neg_binary64 (neg.f64 (-.f64 x 1))) (pow.f64 y 2))) (*.f64 (/.f64 (-.f64 x 1) y) (+.f64 (neg.f64 (/.f64 1 (pow.f64 y 2))) -1)))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (+.f64 (neg.f64 (/.f64 (Rewrite=> neg-sub0_binary64 (-.f64 0 (-.f64 x 1))) (pow.f64 y 2))) (*.f64 (/.f64 (-.f64 x 1) y) (+.f64 (neg.f64 (/.f64 1 (pow.f64 y 2))) -1)))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (+.f64 (neg.f64 (/.f64 (Rewrite<= associate-+l-_binary64 (+.f64 (-.f64 0 x) 1)) (pow.f64 y 2))) (*.f64 (/.f64 (-.f64 x 1) y) (+.f64 (neg.f64 (/.f64 1 (pow.f64 y 2))) -1)))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (+.f64 (neg.f64 (/.f64 (+.f64 (Rewrite<= neg-sub0_binary64 (neg.f64 x)) 1) (pow.f64 y 2))) (*.f64 (/.f64 (-.f64 x 1) y) (+.f64 (neg.f64 (/.f64 1 (pow.f64 y 2))) -1)))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (+.f64 (neg.f64 (/.f64 (Rewrite<= +-commutative_binary64 (+.f64 1 (neg.f64 x))) (pow.f64 y 2))) (*.f64 (/.f64 (-.f64 x 1) y) (+.f64 (neg.f64 (/.f64 1 (pow.f64 y 2))) -1)))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (+.f64 (neg.f64 (/.f64 (Rewrite<= sub-neg_binary64 (-.f64 1 x)) (pow.f64 y 2))) (*.f64 (/.f64 (-.f64 x 1) y) (+.f64 (neg.f64 (/.f64 1 (pow.f64 y 2))) -1)))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (+.f64 (Rewrite<= mul-1-neg_binary64 (*.f64 -1 (/.f64 (-.f64 1 x) (pow.f64 y 2)))) (*.f64 (/.f64 (-.f64 x 1) y) (+.f64 (neg.f64 (/.f64 1 (pow.f64 y 2))) -1)))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (+.f64 (*.f64 -1 (/.f64 (-.f64 1 x) (pow.f64 y 2))) (Rewrite<= distribute-rgt-out_binary64 (+.f64 (*.f64 (neg.f64 (/.f64 1 (pow.f64 y 2))) (/.f64 (-.f64 x 1) y)) (*.f64 -1 (/.f64 (-.f64 x 1) y)))))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (+.f64 (*.f64 -1 (/.f64 (-.f64 1 x) (pow.f64 y 2))) (+.f64 (*.f64 (Rewrite=> distribute-neg-frac_binary64 (/.f64 (neg.f64 1) (pow.f64 y 2))) (/.f64 (-.f64 x 1) y)) (*.f64 -1 (/.f64 (-.f64 x 1) y))))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (+.f64 (*.f64 -1 (/.f64 (-.f64 1 x) (pow.f64 y 2))) (+.f64 (*.f64 (/.f64 (Rewrite=> metadata-eval -1) (pow.f64 y 2)) (/.f64 (-.f64 x 1) y)) (*.f64 -1 (/.f64 (-.f64 x 1) y))))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (+.f64 (*.f64 -1 (/.f64 (-.f64 1 x) (pow.f64 y 2))) (+.f64 (Rewrite<= times-frac_binary64 (/.f64 (*.f64 -1 (-.f64 x 1)) (*.f64 (pow.f64 y 2) y))) (*.f64 -1 (/.f64 (-.f64 x 1) y))))): 10 points increase in error, 12 points decrease in error
      (+.f64 x (+.f64 (*.f64 -1 (/.f64 (-.f64 1 x) (pow.f64 y 2))) (+.f64 (/.f64 (*.f64 -1 (-.f64 x 1)) (*.f64 (Rewrite=> unpow2_binary64 (*.f64 y y)) y)) (*.f64 -1 (/.f64 (-.f64 x 1) y))))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (+.f64 (*.f64 -1 (/.f64 (-.f64 1 x) (pow.f64 y 2))) (+.f64 (/.f64 (*.f64 -1 (-.f64 x 1)) (Rewrite<= unpow3_binary64 (pow.f64 y 3))) (*.f64 -1 (/.f64 (-.f64 x 1) y))))): 7 points increase in error, 3 points decrease in error
      (+.f64 x (+.f64 (*.f64 -1 (/.f64 (-.f64 1 x) (pow.f64 y 2))) (+.f64 (Rewrite<= associate-*r/_binary64 (*.f64 -1 (/.f64 (-.f64 x 1) (pow.f64 y 3)))) (*.f64 -1 (/.f64 (-.f64 x 1) y))))): 0 points increase in error, 0 points decrease in error
      (+.f64 x (Rewrite<= associate-+l+_binary64 (+.f64 (+.f64 (*.f64 -1 (/.f64 (-.f64 1 x) (pow.f64 y 2))) (*.f64 -1 (/.f64 (-.f64 x 1) (pow.f64 y 3)))) (*.f64 -1 (/.f64 (-.f64 x 1) y))))): 0 points increase in error, 1 points decrease in error
      (+.f64 x (+.f64 (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 -1 (/.f64 (-.f64 x 1) (pow.f64 y 3))) (*.f64 -1 (/.f64 (-.f64 1 x) (pow.f64 y 2))))) (*.f64 -1 (/.f64 (-.f64 x 1) y)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite<= +-lft-identity_binary64 (+.f64 0 x)) (+.f64 (+.f64 (*.f64 -1 (/.f64 (-.f64 x 1) (pow.f64 y 3))) (*.f64 -1 (/.f64 (-.f64 1 x) (pow.f64 y 2)))) (*.f64 -1 (/.f64 (-.f64 x 1) y)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (Rewrite<= metadata-eval (-.f64 1 1)) x) (+.f64 (+.f64 (*.f64 -1 (/.f64 (-.f64 x 1) (pow.f64 y 3))) (*.f64 -1 (/.f64 (-.f64 1 x) (pow.f64 y 2)))) (*.f64 -1 (/.f64 (-.f64 x 1) y)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite<= associate--r-_binary64 (-.f64 1 (-.f64 1 x))) (+.f64 (+.f64 (*.f64 -1 (/.f64 (-.f64 x 1) (pow.f64 y 3))) (*.f64 -1 (/.f64 (-.f64 1 x) (pow.f64 y 2)))) (*.f64 -1 (/.f64 (-.f64 x 1) y)))): 33 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite<= unsub-neg_binary64 (+.f64 1 (neg.f64 (-.f64 1 x)))) (+.f64 (+.f64 (*.f64 -1 (/.f64 (-.f64 x 1) (pow.f64 y 3))) (*.f64 -1 (/.f64 (-.f64 1 x) (pow.f64 y 2)))) (*.f64 -1 (/.f64 (-.f64 x 1) y)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 1 (Rewrite<= mul-1-neg_binary64 (*.f64 -1 (-.f64 1 x)))) (+.f64 (+.f64 (*.f64 -1 (/.f64 (-.f64 x 1) (pow.f64 y 3))) (*.f64 -1 (/.f64 (-.f64 1 x) (pow.f64 y 2)))) (*.f64 -1 (/.f64 (-.f64 x 1) y)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 1 (*.f64 -1 (-.f64 1 x))) (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 -1 (/.f64 (-.f64 x 1) y)) (+.f64 (*.f64 -1 (/.f64 (-.f64 x 1) (pow.f64 y 3))) (*.f64 -1 (/.f64 (-.f64 1 x) (pow.f64 y 2))))))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate-+r+_binary64 (+.f64 1 (+.f64 (*.f64 -1 (-.f64 1 x)) (+.f64 (*.f64 -1 (/.f64 (-.f64 x 1) y)) (+.f64 (*.f64 -1 (/.f64 (-.f64 x 1) (pow.f64 y 3))) (*.f64 -1 (/.f64 (-.f64 1 x) (pow.f64 y 2)))))))): 48 points increase in error, 15 points decrease in error

   if -70860.2757589753746 < y < 6739.44510615465788

   1. Initial program 0.1

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

   2. Applied egg-rr 0.1

      \[\leadsto 1 - \color{blue}{\frac{1 - x}{1 + y} \cdot y} \]

   3. Applied egg-rr 0.1

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{1 - x}{1 + y}, -y, 1\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 0.1

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -70860.27575897537:\\ \;\;\;\;x + \frac{1 - x}{y} \cdot \left(\frac{-1}{y} + \left(1 + \frac{\frac{1}{y}}{y}\right)\right)\\ \mathbf{elif}\;y \leq 6739.445106154658:\\ \;\;\;\;\mathsf{fma}\left(\frac{1 - x}{y + 1}, -y, 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1 - x}{y} \cdot \left(\frac{-1}{y} + \left(1 + \frac{\frac{1}{y}}{y}\right)\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	0.1
Cost	2120

\[\begin{array}{l} t_0 := \frac{y \cdot \left(1 - x\right)}{y + 1}\\ t_1 := 1 - y \cdot \frac{1 - x}{y + 1}\\ \mathbf{if}\;t_0 \leq 0.98:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_0 \leq 1.0001:\\ \;\;\;\;x + \frac{1 + \frac{-1 + \frac{1}{y}}{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	0.0
Cost	1480

\[\begin{array}{l} t_0 := x + \frac{1 - x}{y} \cdot \left(\frac{-1}{y} + \left(1 + \frac{\frac{1}{y}}{y}\right)\right)\\ \mathbf{if}\;y \leq -70860.27575897537:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 6739.445106154658:\\ \;\;\;\;1 + \frac{y \cdot \left(x + -1\right)}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Error	0.3
Cost	968

\[\begin{array}{l} t_0 := x + \frac{1}{y}\\ \mathbf{if}\;y \leq -13307707495.534391:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 26047.069786415846:\\ \;\;\;\;1 - y \cdot \frac{1 - x}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 4
Error	0.3
Cost	968

\[\begin{array}{l} t_0 := x + \frac{1}{y}\\ \mathbf{if}\;y \leq -13307707495.534391:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 26047.069786415846:\\ \;\;\;\;1 + \frac{y \cdot \left(x + -1\right)}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 5
Error	17.2
Cost	848

\[\begin{array}{l} t_0 := x - \frac{x}{y}\\ \mathbf{if}\;y \leq -2.6139404476370336 \cdot 10^{+106}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.5609094979744057 \cdot 10^{+66}:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{elif}\;y \leq -274.6501948732118:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.2673286291819278 \cdot 10^{-6}:\\ \;\;\;\;1 - y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 6
Error	17.3
Cost	720

\[\begin{array}{l} \mathbf{if}\;y \leq -2.6139404476370336 \cdot 10^{+106}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.5609094979744057 \cdot 10^{+66}:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{elif}\;y \leq -274.6501948732118:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.882530211263151 \cdot 10^{-8}:\\ \;\;\;\;1 - y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7
Error	1.2
Cost	712

\[\begin{array}{l} t_0 := x + \frac{1}{y}\\ \mathbf{if}\;y \leq -274.6501948732118:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.2673286291819278 \cdot 10^{-6}:\\ \;\;\;\;1 + \left(y \cdot x - y\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 8
Error	1.1
Cost	712

\[\begin{array}{l} t_0 := x + \frac{1 - x}{y}\\ \mathbf{if}\;y \leq -274.6501948732118:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.2673286291819278 \cdot 10^{-6}:\\ \;\;\;\;1 + \left(y \cdot x - y\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 9
Error	17.4
Cost	592

\[\begin{array}{l} \mathbf{if}\;y \leq -2.6139404476370336 \cdot 10^{+106}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.5609094979744057 \cdot 10^{+66}:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{elif}\;y \leq -274.6501948732118:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 26.15598179250866:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10
Error	9.2
Cost	584

\[\begin{array}{l} t_0 := x + \frac{1}{y}\\ \mathbf{if}\;y \leq -274.6501948732118:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.882530211263151 \cdot 10^{-8}:\\ \;\;\;\;1 - y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 11
Error	1.3
Cost	584

\[\begin{array}{l} t_0 := x + \frac{1}{y}\\ \mathbf{if}\;y \leq -274.6501948732118:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.2673286291819278 \cdot 10^{-6}:\\ \;\;\;\;1 + y \cdot x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 12
Error	16.7
Cost	328

\[\begin{array}{l} \mathbf{if}\;y \leq -274.6501948732118:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 26.15598179250866:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 13
Error	38.8
Cost	64

\[1 \]

Reproduce

herbie shell --seed 2022300 
(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))))