Details

Time bar (total: 21.7s)

sample267.0ms

Algorithm
intervals
Results
145.0ms57×body5120valid
59.0ms44×body2560valid
22.0ms126×body80valid
16.0ms17×body1280valid
5.0msbody640valid
3.0msbody320valid
0.0msbody160valid

simplify1.2s

Counts
1 → 1
Iterations
IterNodes
52434
4731
3204
266
129
011

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 55.5b

localize37.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (* x x) 2)
0.1b
(* (* x x) (* x x))
0.5b
(- (- 1 (/ (* x x) 2)) (cos x))
49.2b
(/ (- (- 1 (/ (* x x) 2)) (cos x)) (* (* x x) (* x x)))

rewrite427.0ms

Algorithm
rewrite-expression-head
Rules
115×pow1
39×add-cbrt-cube add-exp-log
36×pow-prod-up
23×*-un-lft-identity pow-prod-down
22×pow-sqr
18×pow-plus
17×prod-exp cbrt-unprod
14×add-sqr-sqrt
13×pow2
times-frac distribute-lft-out-- add-log-exp
add-cube-cbrt
cbrt-undiv div-exp associate-/l*
associate-/r* insert-posit16
diff-log difference-of-squares
clear-num sub-neg frac-2neg flip3-- associate--l+ div-inv flip-- associate-/l/
associate--l- div-sub swap-sqr associate-*r* associate-*l* *-commutative unswap-sqr
Counts
4 → 143
Calls
4 calls:
23.0ms
(/ (* x x) 2)
54.0ms
(* (* x x) (* x x))
104.0ms
(- (- 1 (/ (* x x) 2)) (cos x))
241.0ms
(/ (- (- 1 (/ (* x x) 2)) (cos x)) (* (* x x) (* x x)))

series596.0ms

Counts
4 → 12
Calls
4 calls:
56.0ms
(/ (* x x) 2)
73.0ms
(* (* x x) (* x x))
171.0ms
(- (- 1 (/ (* x x) 2)) (cos x))
295.0ms
(/ (- (- 1 (/ (* x x) 2)) (cos x)) (* (* x x) (* x x)))

simplify3.2s

Counts
155 → 155
Iterations
IterNodes
35333
21416
1466
0175

prune1.7s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize40.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* (* x x) (* x x)) -1/40320)
0.1b
(/ (* x x) 720)
0.1b
(* (* x x) (* x x))
16.6b
(+ (* (* (* x x) (* x x)) -1/40320) (/ (* x x) 720))

rewrite395.0ms

Algorithm
rewrite-expression-head
Rules
133×pow1
39×add-cbrt-cube add-exp-log
36×pow-prod-down pow-prod-up
22×prod-exp pow-sqr cbrt-unprod
18×pow-plus
13×pow2
add-sqr-sqrt
*-un-lft-identity add-cube-cbrt
add-log-exp
associate-*r* insert-posit16
associate-/r* times-frac
cbrt-undiv div-exp associate-*l* *-commutative unswap-sqr
+-commutative clear-num sum-log frac-2neg flip3-+ swap-sqr flip-+ div-inv associate-/l*
Counts
4 → 127
Calls
4 calls:
161.0ms
(* (* (* x x) (* x x)) -1/40320)
23.0ms
(/ (* x x) 720)
54.0ms
(* (* x x) (* x x))
153.0ms
(+ (* (* (* x x) (* x x)) -1/40320) (/ (* x x) 720))

series455.0ms

Counts
4 → 12
Calls
4 calls:
87.0ms
(* (* (* x x) (* x x)) -1/40320)
54.0ms
(/ (* x x) 720)
74.0ms
(* (* x x) (* x x))
240.0ms
(+ (* (* (* x x) (* x x)) -1/40320) (/ (* x x) 720))

simplify2.8s

Counts
139 → 139
Iterations
IterNodes
33314
2998
1384
0134

prune1.4s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

regimes63.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.4b against oracle of 0.4b and baseline of 31.6b

bsearch270.0ms

Steps
ItersRangePoint
11
6.39684937763006e-15
11427567992489.943
0.09809591180606583
9
-170.1724623506855
-7.250512869097592e-05
-0.12153203655906179

simplify9.0ms

Iterations
IterNodes
233
133
025

end0.0ms

sample8.9s

Algorithm
intervals
Results
3.9s1539×body5120valid
1.9s1242×body2560valid
913.0ms4071×body80valid
840.0ms134×body320valid
639.0ms619×body1280valid
382.0ms303×body640valid
34.0ms92×body160valid