Average Error: 52.7 → 6.1
Time: 6.3s
Precision: binary64
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↓
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Error

Bits error versus a

Bits error versus b

Bits error versus c

Derivation

  1. Initial program 52.7

    \[\]

  2. Simplified52.7

    \[\leadsto \]

  3. Taylor expanded around inf 6.1

    \[\leadsto \]

  4. Final simplification6.1

    \[\leadsto \]

Reproduce

herbie shell --seed 2020191 
(FPCore (a b c)
  :name "Quadratic roots, wide range"
  :precision binary64
  :pre (and (< 4.930380657631324e-32 a 2.028240960365167e+31) (< 4.930380657631324e-32 b 2.028240960365167e+31) (< 4.930380657631324e-32 c 2.028240960365167e+31))
  (/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a)))