quadp (p42, positive)

Average Error: 33.6 → 10.6

Time: 5.1s

Precision: binary64

Math

\[\]

↓

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Error

Bits error versus a

Bits error versus b

Bits error versus c

Target

Original	33.6
Target	20.9
Herbie	10.6

\[\]

Derivation

1. Split input into 3 regimes

2. if b < -1.3061538410972681e63

   1. Initial program 39.9

      \[\]

   2. Simplified 39.9

      \[\leadsto \]

   3. Taylor expanded around -inf 5.5

      \[\leadsto \]

   4. Simplified 5.5

      \[\leadsto \]

   if -1.3061538410972681e63 < b < 9.6001021312979276e-81

   1. Initial program 13.7

      \[\]

   2. Simplified 13.7

      \[\leadsto \]
   3. Using strategy rm

   4. Applied clear-num 13.8

      \[\leadsto \]

   5. Simplified 13.8

      \[\leadsto \]

   if 9.6001021312979276e-81 < b

   1. Initial program 52.4

      \[\]

   2. Simplified 52.4

      \[\leadsto \]

   3. Taylor expanded around inf 9.5

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

4. Final simplification 10.6

   \[\leadsto \]

Reproduce

herbie shell --seed 2020192 
(FPCore (a b c)
  :name "quadp (p42, positive)"
  :precision binary64
  :herbie-expected #f

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