quadm (p42, negative)

Average Error: 34.2 → 6.8

Time: 5.5s

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	34.2
Target	20.8
Herbie	6.8

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Derivation

1. Split input into 4 regimes

2. if b < -9.103844937062704e64

   1. Initial program 57.6

      \[\]

   2. Taylor expanded around -inf 3.7

      \[\leadsto \]

   3. Simplified 3.7

      \[\leadsto \]

   if -9.103844937062704e64 < b < -1.13478872317873976e-303

   1. Initial program 30.8

      \[\]
   2. Using strategy rm

   3. Applied flip-- 30.8

      \[\leadsto \]

   4. Simplified 17.1

      \[\leadsto \]

   5. Simplified 17.1

      \[\leadsto \]
   6. Using strategy rm

   7. Applied clear-num 17.2

      \[\leadsto \]

   8. Simplified 9.7

      \[\leadsto \]

   if -1.13478872317873976e-303 < b < 2.81251542793613095e118

   1. Initial program 9.0

      \[\]

   if 2.81251542793613095e118 < b

   1. Initial program 51.9

      \[\]

   2. Taylor expanded around inf 2.4

      \[\leadsto \]

   3. Simplified 2.4

      \[\leadsto \]
3. Recombined 4 regimes into one program.

4. Final simplification 6.8

   \[\leadsto \]

Reproduce

herbie shell --seed 2020191 
(FPCore (a b c)
  :name "quadm (p42, negative)"
  :precision binary64
  :herbie-expected #f

  :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)))