Average Error: 30.8 → 30.8
Time: 26.8s
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 30.8

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

  2. Final simplification30.8

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

Runtime

Time bar (total: 26.8s)Debug logProfile

start741.0ms

Algorithm
intervals

setup11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.5b

localize16.0ms

Local error

Found 2 expressions with local error:

30.8b
(pow (atan (fmod a (asin a))) (* a a))
1.7b
(fmod a (asin a))

rewrite2.0ms

Algorithm
rewrite-expression-head
Counts
2 → 21
Calls

2 calls. Slowest were:

1.0ms
(pow (atan (fmod a (asin a))) (* a a))
0.0ms
(fmod a (asin a))

series40.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

38.0ms
(pow (atan (fmod a (asin a))) (* a a))
2.0ms
(fmod a (asin a))

simplify75.0ms

Counts
11 → 27
Calls

11 calls. Slowest were:

51.0ms
(+ (* 1/2 (* (pow a 4) (pow (log (atan (fmod a (asin a)))) 2))) (+ 1 (* (pow a 2) (log (atan (fmod a (asin a)))))))
6.0ms
(* (log (atan (fmod a (asin a)))) (* a a))
3.0ms
(pow (* (cbrt (atan (fmod a (asin a)))) (cbrt (atan (fmod a (asin a))))) (* a a))

prune286.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 30.5b

herbie shell --seed 2018357 
(FPCore (a)
  :name "Fuzzer 002"
  (pow (atan (fmod a (asin a))) (* a a)))