Error

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Target

Derivation

1. Split input into 3 regimes

2. if y < -1.36473141996577e+154 or 1.819193390664124e-192 < y < 4.000116206191754e-176

   1. Initial program 59.8

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

   2. Taylor expanded around 0 4.1

      \[\leadsto \color{blue}{-1}\]

   if -1.36473141996577e+154 < y < -9.928191242845041e-154 or 4.000116206191754e-176 < y

   1. Initial program 0.9

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

   if -9.928191242845041e-154 < y < 1.819193390664124e-192

   1. Initial program 29.2

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

   2. Taylor expanded around -inf 14.4

      \[\leadsto \color{blue}{1}\]
3. Recombined 3 regimes into one program.

4. Final simplification5.5

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -1.36473141996577 \cdot 10^{+154}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \le -9.928191242845041 \cdot 10^{-154}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot \left(y + x\right)}{y \cdot y + x \cdot x}\\ \mathbf{elif}\;y \le 1.819193390664124 \cdot 10^{-192}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \le 4.000116206191754 \cdot 10^{-176}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot \left(y + x\right)}{y \cdot y + x \cdot x}\\ \end{array}\]

Runtime

Time bar (total: 31.1s)Debug logProfile

herbie shell --seed 2018353 
(FPCore (x y)
  :name "Kahan p9 Example"
  :pre (and (< 0 x 1) (< y 1))

  :herbie-target
  (if (< 0.5 (fabs (/ x y)) 2) (/ (* (- x y) (+ x y)) (+ (* x x) (* y y))) (- 1 (/ 2 (+ 1 (* (/ x y) (/ x y))))))

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