Average Error: 31.0 → 31.0
Time: 15.2s
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 31.0

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

  2. Final simplification31.0

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

Reproduce

herbie shell --seed 2019004 +o rules:numerics
(FPCore (a)
  :name "Fuzzer 002"
  (pow (atan (fmod a (asin a))) (* a a)))

Details

Time bar (total: 14.9s)Debug log

sample509.0ms

Algorithm
intervals

simplify2.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

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

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.6b

localize57.0ms

Local error

Found 2 expressions with local error:

31.7b
(pow (atan (fmod a (asin a))) (* a a))
2.2b
(fmod a (asin a))

rewrite4.0ms

Algorithm
rewrite-expression-head
Counts
2 → 25
Calls

2 calls. Slowest were:

3.0ms
(pow (atan (fmod a (asin a))) (* a a))
0.0ms
(fmod a (asin a))

series26.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

24.0ms
(pow (atan (fmod a (asin a))) (* a a))
3.0ms
(fmod a (asin a))

simplify117.0ms

Counts
11 → 31
Calls

11 calls. Slowest were:

89.0ms
(+ (* 1/2 (* (pow a 4) (pow (log (atan (fmod a (asin a)))) 2))) (+ 1 (* (pow a 2) (log (atan (fmod a (asin a)))))))
9.0ms
(* (log (atan (fmod a (asin a)))) (* a a))
3.0ms
(pow 1 (* a a))

prune325.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 27.6b

end0.0ms

sample13.8s

Algorithm
intervals