Average Error: 30.4 → 30.4
Time: 15.0s
Precision: 64
Internal Precision: 128
\[{\left(\tan^{-1} \left(a \bmod \left(\sin^{-1} a\right)\right)\right)}^{\left(a \cdot a\right)}\]
↓
\[{\left(\tan^{-1} \left(a \bmod \left(\sin^{-1} a\right)\right)\right)}^{\left(a \cdot a\right)}\]

Error

Bits error versus a

Derivation

  1. Initial program 30.4

    \[{\left(\tan^{-1} \left(a \bmod \left(\sin^{-1} a\right)\right)\right)}^{\left(a \cdot a\right)}\]

  2. Final simplification30.4

    \[\leadsto {\left(\tan^{-1} \left(a \bmod \left(\sin^{-1} a\right)\right)\right)}^{\left(a \cdot a\right)}\]

Reproduce

herbie shell --seed 2019008 +o rules:numerics
(FPCore (a)
  :name "Fuzzer 002"
  (pow (atan (fmod a (asin a))) (* a a)))

Details

Time bar (total: 14.7s)Debug log

sample735.0ms

Algorithm
intervals

simplify1.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

1.0ms
(pow (atan (fmod a (asin a))) (* a a))

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.2b

localize14.0ms

Local error

Found 2 expressions with local error:

28.1b
(pow (atan (fmod a (asin a))) (* a a))
3.1b
(fmod a (asin a))

rewrite2.0ms

Algorithm
rewrite-expression-head
Counts
2 → 25
Calls

2 calls. Slowest were:

2.0ms
(pow (atan (fmod a (asin a))) (* a a))
0.0ms
(fmod a (asin a))

series15.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

14.0ms
(pow (atan (fmod a (asin a))) (* a a))
2.0ms
(fmod a (asin a))

simplify99.0ms

Counts
11 → 31
Calls

11 calls. Slowest were:

83.0ms
(+ (* 1/2 (* (pow a 4) (pow (log (atan (fmod a (asin a)))) 2))) (+ 1 (* (pow a 2) (log (atan (fmod a (asin a)))))))
4.0ms
(* (log (atan (fmod a (asin a)))) (* a a))
2.0ms
(pow (atan (fmod a (asin a))) (pow a 2))

prune324.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 31.2b

end0.0ms

sample13.5s

Algorithm
intervals