Average Error: 31.1 → 31.1
Time: 15.5s
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 31.1

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

  2. Final simplification31.1

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

Reproduce

herbie shell --seed 2019010 +o rules:numerics
(FPCore (a)
  :name "Fuzzer 002"
  (pow (atan (fmod a (asin a))) (* a a)))

Details

Time bar (total: 15.1s)Debug log

sample382.0ms

Algorithm
intervals

simplify2.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
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

localize30.0ms

Local error

Found 2 expressions with local error:

32.7b
(pow (atan (fmod a (asin a))) (* a a))
1.2b
(fmod a (asin a))

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
3×add-cube-cbrt
3×add-exp-log
3×*-un-lft-identity
3×unpow-prod-down
3×pow1
3×add-sqr-sqrt
2×add-log-exp
2×log1p-expm1-u
2×add-cbrt-cube
2×expm1-log1p-u
1×pow-exp
1×pow-pow
1×pow-unpow
1×pow-to-exp
Counts
2 → 25
Calls
2 calls:
Slowest
3.0ms
(pow (atan (fmod a (asin a))) (* a a))
0.0ms
(fmod a (asin a))

series25.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
22.0ms
(pow (atan (fmod a (asin a))) (* a a))
3.0ms
(fmod a (asin a))

simplify107.0ms

Counts
11 → 31
Calls
11 calls:
Slowest
78.0ms
(+ (* 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))
3.0ms
(pow (* (cbrt (atan (fmod a (asin a)))) (cbrt (atan (fmod a (asin a))))) (* a a))
3.0ms
(pow (atan (fmod a (asin a))) (pow a 2))

prune314.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 27.6b

end0.0ms

sample14.2s

Algorithm
intervals