Average Error: 19.5 → 6.5
Time: 5.7s
Precision: binary64
\[\]
↓
\[\]

Error

Bits error versus a

Bits error versus b

Bits error versus c

Derivation

  1. Split input into 3 regimes

  2. if b < -5.3612603850103236e145

    1. Initial program 60.8

      \[\]
    2. Using strategy rm

    3. Applied add-sqr-sqrt60.8

      \[\leadsto \]

    4. Applied sqrt-prod60.8

      \[\leadsto \]

    5. Simplified60.8

      \[\leadsto \]

    6. Simplified60.8

      \[\leadsto \]

    7. Taylor expanded around -inf 11.1

      \[\leadsto \]

    8. Simplified2.2

      \[\leadsto \]

    if -5.3612603850103236e145 < b < 6.94611700570219558e108

    1. Initial program 8.6

      \[\]
    2. Using strategy rm

    3. Applied add-sqr-sqrt8.6

      \[\leadsto \]

    4. Applied sqrt-prod8.7

      \[\leadsto \]

    5. Simplified8.7

      \[\leadsto \]

    6. Simplified8.7

      \[\leadsto \]

    if 6.94611700570219558e108 < b

    1. Initial program 30.3

      \[\]
    2. Using strategy rm

    3. Applied add-sqr-sqrt30.3

      \[\leadsto \]

    4. Applied sqrt-prod30.3

      \[\leadsto \]

    5. Simplified30.3

      \[\leadsto \]

    6. Simplified30.3

      \[\leadsto \]

    7. Taylor expanded around inf 6.6

      \[\leadsto \]

    8. Simplified2.3

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

  4. Final simplification6.5

    \[\leadsto \]

Reproduce

herbie shell --seed 2020192 
(FPCore (a b c)
  :name "jeff quadratic root 2"
  :precision binary64
  (if (>= b 0.0) (/ (* 2.0 c) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))))