Average Error: 31.3 → 31.3
Time: 26.0s
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 31.3

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

  2. Final simplification31.3

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

Runtime

Time bar (total: 26.0s)Debug log

start686.0ms

Algorithm
intervals

setup21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.2b

localize54.0ms

Local error

Found 2 expressions with local error:

27.6b
(pow (atan (fmod a (asin a))) (* a a))
2.7b
(fmod a (asin a))

rewrite3.0ms

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))

series30.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

27.0ms
(pow (atan (fmod a (asin a))) (* a a))
3.0ms
(fmod a (asin a))

simplify96.0ms

Counts
11 → 31
Calls

11 calls. Slowest were:

65.0ms
(+ (* 1/2 (* (pow a 4) (pow (log (atan (fmod a (asin a)))) 2))) (+ 1 (* (pow a 2) (log (atan (fmod a (asin a)))))))
10.0ms
(* (log (atan (fmod a (asin a)))) (* a a))
3.0ms
(pow 1 (* a a))

prune351.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 33.2b

herbie shell --seed 2018359 +o rules:numerics
(FPCore (a)
  :name "Fuzzer 002"
  (pow (atan (fmod a (asin a))) (* a a)))