Average Error: 0.2 → 0.0
Time: 1.6m
Precision: 64
Internal precision: 128
\[\left({\left({a}^2 + {b}^2\right)}^2 + 4 \cdot \left({a}^2 \cdot \left(1 - a\right) + {b}^2 \cdot \left(3 + a\right)\right)\right) - 1\]
⬇
\[\left(\left({b}^{4} + \left({a}^{4} + 2 \cdot \left({b}^2 \cdot {a}^2\right)\right)\right) + 4 \cdot \left({a}^2 \cdot \left(1 - a\right) + {b}^2 \cdot \left(3 + a\right)\right)\right) - 1\]

Error

Bits error versus a

Bits error versus b

Derivation

  1. Initial program 0.2

    \[\left({\left({a}^2 + {b}^2\right)}^2 + 4 \cdot \left({a}^2 \cdot \left(1 - a\right) + {b}^2 \cdot \left(3 + a\right)\right)\right) - 1\]

  2. Applied taylor 0.0

    \[\leadsto \left(\left({b}^{4} + \left({a}^{4} + 2 \cdot \left({b}^2 \cdot {a}^2\right)\right)\right) + 4 \cdot \left({a}^2 \cdot \left(1 - a\right) + {b}^2 \cdot \left(3 + a\right)\right)\right) - 1\]

  3. Taylor expanded around inf 0.0

    \[\leadsto \left(\color{blue}{\left({b}^{4} + \left({a}^{4} + 2 \cdot \left({b}^2 \cdot {a}^2\right)\right)\right)} + 4 \cdot \left({a}^2 \cdot \left(1 - a\right) + {b}^2 \cdot \left(3 + a\right)\right)\right) - 1\]
  4. Removed slow pow expressions

Runtime

Time bar (total: 1.6m) Debug log

Please include this information when filing a bug report:

herbie --seed '#(1491116092 2728141720 1661291233 1656418562 1371115622 1455964555)'
(FPCore (a b)
  :name "Bouland and Aaronson, Equation (24)"
  (- (+ (sqr (+ (sqr a) (sqr b))) (* 4 (+ (* (sqr a) (- 1 a)) (* (sqr b) (+ 3 a))))) 1))