Average Error: 34.3 → 8.6
Time: 4.8s
Precision: binary64
\[\]
↓
\[\]

Error

Bits error versus a

Bits error versus b

Bits error versus c

Target

Original34.3
Target20.6
Herbie8.6
\[\]

Derivation

  1. Split input into 4 regimes

  2. if b < -7.40032164261079705e-22

    1. Initial program 55.6

      \[\]

    2. Taylor expanded around -inf 6.7

      \[\leadsto \]

    3. Simplified6.7

      \[\leadsto \]

    if -7.40032164261079705e-22 < b < 1.75851541092494309e-188

    1. Initial program 22.3

      \[\]
    2. Using strategy rm

    3. Applied flip--22.5

      \[\leadsto \]

    4. Simplified17.6

      \[\leadsto \]

    5. Simplified17.6

      \[\leadsto \]
    6. Using strategy rm

    7. Applied *-un-lft-identity17.6

      \[\leadsto \]

    8. Applied times-frac17.6

      \[\leadsto \]

    9. Simplified17.6

      \[\leadsto \]

    10. Simplified15.1

      \[\leadsto \]

    if 1.75851541092494309e-188 < b < 1.22639498028987855e78

    1. Initial program 6.3

      \[\]
    2. Using strategy rm

    3. Applied div-sub6.3

      \[\leadsto \]

    4. Simplified6.3

      \[\leadsto \]

    5. Simplified6.3

      \[\leadsto \]

    if 1.22639498028987855e78 < b

    1. Initial program 43.3

      \[\]

    2. Taylor expanded around inf 11.0

      \[\leadsto \]

    3. Simplified4.9

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

  4. Final simplification8.6

    \[\leadsto \]

Reproduce

herbie shell --seed 2020190 
(FPCore (a b c)
  :name "The quadratic formula (r2)"
  :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)))