Average Error: 31.3 → 31.3
Time: 15.1s
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

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

Reproduce

herbie shell --seed 2019022 
(FPCore (a)
  :name "Fuzzer 002"
  (pow (atan (fmod a (asin a))) (* a a)))

Details

Time bar (total: 14.5s)Debug log

sample376.0ms

Algorithm
intervals
Results
116.0ms89×body2560valid
108.0ms805×body80nan
69.0ms91×body1280valid
31.0ms19×body320valid
26.0ms44×body640valid
3.0ms9×body160valid
1.0ms4×body80valid

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: 31.6b

localize37.0ms

Local error

Found 2 expressions with local error:

29.9b
(pow (atan (fmod a (asin a))) (* a a))
1.7b
(fmod a (asin a))

rewrite2.0ms

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×add-cbrt-cube
1×pow-exp
1×pow-pow
1×pow-unpow
1×pow-to-exp
Counts
2 → 21
Calls
2 calls:
Slowest
2.0ms
(pow (atan (fmod a (asin a))) (* a a))
0.0ms
(fmod a (asin a))

series18.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
17.0ms
(pow (atan (fmod a (asin a))) (* a a))
2.0ms
(fmod a (asin a))

simplify76.0ms

Counts
11 → 27
Calls
11 calls:
Slowest
54.0ms
(+ (* 1/2 (* (pow a 4) (pow (log (atan (fmod a (asin a)))) 2))) (+ 1 (* (pow a 2) (log (atan (fmod a (asin a)))))))
8.0ms
(pow (atan (fmod a (asin a))) (pow a 2))
4.0ms
(* (log (atan (fmod a (asin a)))) (* a a))
2.0ms
(pow (atan (fmod a (asin a))) (pow a 2))
2.0ms
(pow (* (cbrt (atan (fmod a (asin a)))) (cbrt (atan (fmod a (asin a))))) (* a a))

prune292.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 31.6b

end0.0ms

sample13.7s

Algorithm
intervals
Results
4.7s2975×body2560valid
4.7s24239×body80nan
2.4s2496×body1280valid
947.0ms1293×body640valid
301.0ms619×body320valid
128.0ms333×body160valid
52.0ms284×body80valid