Details

sample110.0ms

Algorithm

intervals

Results

56.0ms	59×	body	2560	valid
16.0ms	49×	body	640	valid
14.0ms	33×	body	1280	valid
9.0ms	36×	body	320	valid
5.0ms	66×	body	80	valid
2.0ms	13×	body	160	valid

simplify12.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	30
4	30
3	28
2	23
1	15
0	6

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.6b

localize23.0ms

Local error

Found 2 expressions with local error:

1.8b	(- 1 (cos x))
15.9b	(/ (- 1 (cos x)) (* x x))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `*-un-lft-identity`
7×	`add-cbrt-cube` `add-exp-log`
6×	`times-frac` `associate-/l*` `difference-of-squares`
4×	`add-cube-cbrt` `add-log-exp`
3×	`distribute-lft-out--`
2×	`pow1` `cbrt-undiv` `flip3--` `div-exp` `insert-posit16` `flip--` `associate-/l/`
1×	`clear-num` `associate-/r*` `sub-neg` `frac-2neg` `diff-log` `div-sub` `prod-exp` `cbrt-unprod` `div-inv`

Counts

2 → 47

Calls

2 calls:

18.0ms	(- 1 (cos x))
21.0ms	(/ (- 1 (cos x)) (* x x))

series89.0ms

Counts

2 → 6

Calls

2 calls:

20.0ms	(- 1 (cos x))
69.0ms	(/ (- 1 (cos x)) (* x x))

simplify865.0ms

Counts

53 → 53

Iterations

Iter	Nodes
done	5002
2	1354
1	260
0	93

prune220.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
0.3b	(+ 1 (cos x))
0.3b	(* (sin x) (sin x))
15.7b	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-cbrt-cube` `add-exp-log`
24×	`*-un-lft-identity`
22×	`times-frac`
16×	`add-sqr-sqrt`
14×	`add-cube-cbrt`
12×	`cbrt-undiv` `div-exp`
11×	`pow1` `associate-/l*`
7×	`prod-exp` `cbrt-unprod`
6×	`associate-/r/` `add-log-exp`
5×	`associate-/r*` `distribute-lft-out`
4×	`flip3-+` `flip-+` `insert-posit16` `div-inv`
3×	`div-sub` `swap-sqr` `associate-r` `associate-l` `sqr-sin`
2×	`clear-num` `frac-2neg` `sin-mult` `associate-/l/`
1×	`pow2` `+-commutative` `sum-log` `pow-plus` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up` `unswap-sqr`

Counts

4 → 115

Calls

4 calls:

37.0ms	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
12.0ms	(+ 1 (cos x))
20.0ms	(* (sin x) (sin x))
20.0ms	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))

series174.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
11.0ms	(+ 1 (cos x))
23.0ms	(* (sin x) (sin x))
92.0ms	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))

simplify3.1s

Counts

127 → 127

Iterations

Iter	Nodes
done	5000
2	4416
1	539
0	182

prune493.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize35.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (/ (sin x) x) (/ (tan (/ x 2)) x))
0.2b	(/ (tan (/ x 2)) x)
0.2b	(/ (sin x) x)

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-sqr-sqrt`
40×	`times-frac`
33×	`*-un-lft-identity` `add-cube-cbrt`
19×	`add-cbrt-cube` `add-exp-log`
13×	`associate-r` `associate-l`
6×	`cbrt-undiv` `associate-/r` `div-exp` `associate-/l`
5×	`pow1`
4×	`prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
3×	`insert-posit16` `add-log-exp`
2×	`clear-num` `frac-2neg`
1×	`frac-times` `pow-prod-down` `associate-l/` `tan-quot` `associate-r/` `*-commutative` `associate-/l/`

Counts

3 → 108

Calls

3 calls:

23.0ms	(* (/ (sin x) x) (/ (tan (/ x 2)) x))
12.0ms	(/ (tan (/ x 2)) x)
16.0ms	(/ (sin x) x)

series265.0ms

Counts

3 → 9

Calls

3 calls:

122.0ms	(* (/ (sin x) x) (/ (tan (/ x 2)) x))
94.0ms	(/ (tan (/ x 2)) x)
49.0ms	(/ (sin x) x)

simplify1.7s

Counts

117 → 117

Iterations

Iter	Nodes
done	5002
2	2677
1	448
0	166

prune503.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize27.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (* (/ (sin x) x) (tan (/ x 2))) x)
0.2b	(/ (sin x) x)
0.2b	(* (/ (sin x) x) (tan (/ x 2)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
22×	`times-frac`
21×	`*-un-lft-identity` `add-cube-cbrt`
19×	`add-cbrt-cube` `add-exp-log`
13×	`associate-l`
6×	`cbrt-undiv` `associate-/r*` `div-exp`
5×	`pow1`
4×	`prod-exp` `tan-quot` `cbrt-unprod` `associate-/l*`
3×	`associate-r` `insert-posit16` `div-inv` `add-log-exp` `associate-/l/`
2×	`frac-times` `clear-num` `frac-2neg` `associate-l/` `associate-r/` `unswap-sqr`
1×	`pow-prod-down` `*-commutative`

Counts

3 → 90

Calls

3 calls:

21.0ms	(/ (* (/ (sin x) x) (tan (/ x 2))) x)
10.0ms	(/ (sin x) x)
17.0ms	(* (/ (sin x) x) (tan (/ x 2)))

series244.0ms

Counts

3 → 9

Calls

3 calls:

105.0ms	(/ (* (/ (sin x) x) (tan (/ x 2))) x)
38.0ms	(/ (sin x) x)
100.0ms	(* (/ (sin x) x) (tan (/ x 2)))

simplify1.5s

Counts

99 → 99

Iterations

Iter	Nodes
done	5000
2	2275
1	382
0	154

prune372.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

regimes40.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	11
1	11
0	10

end0.0ms

sample4.9s

Algorithm

intervals

Results

1.7s	1535×	body	2560	valid
1.5s	1557×	body	640	valid
911.0ms	1240×	body	1280	valid
295.0ms	909×	body	320	valid
236.0ms	2260×	body	80	valid
144.0ms	499×	body	160	valid