quadp (p42, positive)

Average Error: 34.1 → 10.0

Time: 6.0s

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	20.8
Herbie	10.0

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Derivation

1. Split input into 3 regimes

2. if b < -1.38476143180922117e134

   1. Initial program 56.8

      \[\]

   2. Taylor expanded around -inf 10.0

      \[\leadsto \]

   3. Simplified 2.4

      \[\leadsto \]

   if -1.38476143180922117e134 < b < 5.1943629106266941e-122

   1. Initial program 11.3

      \[\]
   2. Using strategy rm

   3. Applied associate-*r* 11.3

      \[\leadsto \]

   if 5.1943629106266941e-122 < b

   1. Initial program 51.5

      \[\]

   2. Taylor expanded around inf 10.8

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

4. Final simplification 10.0

   \[\leadsto \]

Reproduce

herbie shell --seed 2020179 
(FPCore (a b c)
  :name "quadp (p42, positive)"
  :precision binary64

  :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)))