Average Error: 30.8 → 30.8
Time: 15.6s
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

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

Reproduce

herbie shell --seed 2019016 +o rules:numerics
(FPCore (a)
  :name "Fuzzer 002"
  (pow (atan (fmod a (asin a))) (* a a)))

Details

Time bar (total: 15.3s)Debug log

sample422.0ms

Algorithm
intervals
Results
1052×(pre true 80)
796×(body nan 80)
101×(body real 2560)
76×(body real 1280)
43×(body real 640)
14×(body real 320)
13×(body real 160)
9×(body real 80)

simplify2.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
2.0ms
(pow (atan (fmod a (asin a))) (* a a))

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.3b

localize14.0ms

Local error

Found 2 expressions with local error:

30.8b
(pow (atan (fmod a (asin a))) (* a a))
2.4b
(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×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
2.0ms
(pow (atan (fmod a (asin a))) (* a a))
0.0ms
(fmod a (asin a))

series27.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
23.0ms
(pow (atan (fmod a (asin a))) (* a a))
3.0ms
(fmod a (asin a))

simplify509.0ms

Counts
11 → 31
Calls
11 calls:
Slowest
475.0ms
(+ (* 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))
5.0ms
(pow (atan (fmod a (asin a))) (pow a 2))
5.0ms
(pow (atan (fmod a (asin a))) (pow a 2))
3.0ms
(pow 1 (* a a))

prune295.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 29.3b

end0.0ms

sample14.0s

Algorithm
intervals
Results
32004×(pre true 80)
24004×(body nan 80)
3037×(body real 2560)
2499×(body real 1280)
1213×(body real 640)
596×(body real 320)
337×(body real 80)
318×(body real 160)