quadm (p42, negative)

Average Error: 34.1 → 9.9

Time: 5.2s

Precision: binary64

Math

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↓

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Error

Bits error versus a

Bits error versus b

Bits error versus c

Target

Original	34.1
Target	20.7
Herbie	9.9

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Derivation

1. Split input into 3 regimes

2. if b < -3.6006169463337958e-70

   1. Initial program 53.7

      \[\]

   2. Taylor expanded around -inf 8.8

      \[\leadsto \]

   3. Simplified 8.8

      \[\leadsto \]

   if -3.6006169463337958e-70 < b < 1.8526227140702638e107

   1. Initial program 12.5

      \[\]
   2. Using strategy rm

   3. Applied div-inv 12.6

      \[\leadsto \]

   4. Simplified 12.6

      \[\leadsto \]

   if 1.8526227140702638e107 < b

   1. Initial program 49.7

      \[\]
   2. Using strategy rm

   3. Applied flip-- 63.3

      \[\leadsto \]

   4. Simplified 62.4

      \[\leadsto \]

   5. Simplified 62.4

      \[\leadsto \]

   6. Taylor expanded around 0 4.1

      \[\leadsto \]
3. Recombined 3 regimes into one program.

4. Final simplification 9.9

   \[\leadsto \]

Reproduce

herbie shell --seed 2020181 
(FPCore (a b c)
  :name "quadm (p42, negative)"
  :precision binary64

  :herbie-target
  (if (< b 0.0) (/ c (* a (/ (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a)))) (/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a)))

  (/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a)))