Details

Time bar (total: 32.6s)

sample115.0ms

Algorithm
intervals
Results
43.0ms487×body80nan
33.0ms237×body160nan
20.0ms256×body80valid

simplify20.9s

Counts
1 → 1
Iterations
IterNodes
94745
81502
7489
6252
5117
466
335
219
115
07

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.4b

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ x (sqrt (fma x x -1)))
29.2b
(sqrt (fma x x -1))

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
6×*-un-lft-identity
5×add-sqr-sqrt
4×add-cube-cbrt add-log-exp
3×pow1 fma-def sqrt-prod
2×expm1-log1p-u add-cbrt-cube add-exp-log log1p-expm1-u
1×+-commutative rem-sqrt-square sum-log sqrt-pow1 flip3-+ pow1/2 flip-+ distribute-lft-out
Counts
2 → 32
Calls
2 calls:
4.0ms
(+ x (sqrt (fma x x -1)))
1.0ms
(sqrt (fma x x -1))

series131.0ms

Counts
2 → 6
Calls
2 calls:
75.0ms
(+ x (sqrt (fma x x -1)))
57.0ms
(sqrt (fma x x -1))

simplify1.9s

Counts
38 → 38
Iterations
IterNodes
42841
31031
2406
1168
071

prune327.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize47.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma 2 x (- (/ -1/8 (* x (* x x))) (/ 1/2 x)))
0.0b
(- (/ -1/8 (* x (* x x))) (/ 1/2 x))
0.1b
(* x (* x x))
0.5b
(/ -1/8 (* x (* x x)))

rewrite94.0ms

Algorithm
rewrite-expression-head
Rules
109×times-frac
91×prod-diff
90×add-sqr-sqrt
86×*-un-lft-identity
84×add-cube-cbrt
22×div-inv
18×pow1 add-cbrt-cube add-exp-log
7×fma-neg
6×prod-exp cbrt-unprod add-log-exp
5×pow-prod-up
4×expm1-log1p-u log1p-expm1-u
3×cbrt-undiv div-exp associate-*l* pow-prod-down associate-/l*
2×difference-of-squares
1×pow2 clear-num associate-/r* sub-neg frac-2neg pow-plus flip3-- diff-log cube-unmult associate-*r* pow-sqr *-commutative frac-sub fma-udef flip-- distribute-lft-out-- unswap-sqr
Counts
4 → 177
Calls
4 calls:
0.0ms
(fma 2 x (- (/ -1/8 (* x (* x x))) (/ 1/2 x)))
53.0ms
(- (/ -1/8 (* x (* x x))) (/ 1/2 x))
14.0ms
(* x (* x x))
23.0ms
(/ -1/8 (* x (* x x)))

series292.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(fma 2 x (- (/ -1/8 (* x (* x x))) (/ 1/2 x)))
138.0ms
(- (/ -1/8 (* x (* x x))) (/ 1/2 x))
50.0ms
(* x (* x x))
50.0ms
(/ -1/8 (* x (* x x)))

simplify2.8s

Counts
189 → 189
Iterations
IterNodes
35723
21712
1662
0288

prune2.0s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes23.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Iterations
IterNodes
212
112
011

end0.0ms

sample4.1s

Algorithm
intervals
Results
1.6s16330×body80nan
1.3s7790×body160nan
749.0ms8000×body80valid