Details

sample108.0ms

Algorithm

intervals

Results

57.0ms	63×	body	2560	valid
18.0ms	41×	body	1280	valid
13.0ms	46×	body	640	valid
4.0ms	74×	body	80	valid
3.0ms	17×	body	320	valid
2.0ms	15×	body	160	valid

simplify32.0ms

Counts

1 → 1

Iterations

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.6b

localize22.0ms

Local error

Found 2 expressions with local error:

0.9b	(- 1 (cos x))
19.2b	(/ (- 1 (cos x)) (* x x))

rewrite61.0ms

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:

9.0ms	(- 1 (cos x))
33.0ms	(/ (- 1 (cos x)) (* x x))

series123.0ms

Counts

2 → 6

Calls

2 calls:

26.0ms	(- 1 (cos x))
97.0ms	(/ (- 1 (cos x)) (* x x))

simplify2.1s

Counts

53 → 53

Iterations

Iter	Nodes
done	5139
3	3004
2	707
1	230
0	93

prune185.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize46.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
0.2b	(* (sin x) (sin x))
0.3b	(+ 1 (cos x))
18.9b	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))

rewrite108.0ms

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:

31.0ms	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
23.0ms	(* (sin x) (sin x))
10.0ms	(+ 1 (cos x))
42.0ms	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))

series156.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
24.0ms	(* (sin x) (sin x))
15.0ms	(+ 1 (cos x))
74.0ms	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))

simplify1.5s

Counts

127 → 127

Iterations

Iter	Nodes
done	5012
2	1801
1	507
0	182

prune458.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize18.0ms

Local error

Found 3 expressions with local error:

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

rewrite64.0ms

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:

35.0ms	(* (/ (sin x) x) (/ (tan (/ x 2)) x))
15.0ms	(/ (sin x) x)
11.0ms	(/ (tan (/ x 2)) x)

series644.0ms

Counts

3 → 9

Calls

3 calls:

518.0ms	(* (/ (sin x) x) (/ (tan (/ x 2)) x))
55.0ms	(/ (sin x) x)
71.0ms	(/ (tan (/ x 2)) x)

simplify1.5s

Counts

117 → 117

Iterations

Iter	Nodes
done	5000
2	1632
1	448
0	166

prune401.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize23.0ms

Local error

Found 2 expressions with local error:

0.4b	(/ (/ (sin x) 1) (/ (* x x) (tan (/ x 2))))
18.1b	(/ (* x x) (tan (/ x 2)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

230×	`times-frac`
95×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
37×	`add-exp-log`
28×	`add-cbrt-cube`
25×	`div-inv`
23×	`div-exp`
16×	`associate-/r/`
15×	`cbrt-undiv` `tan-quot`
14×	`associate-/l*`
11×	`associate-/r*`
4×	`prod-exp`
3×	`1-exp` `cbrt-unprod`
2×	`pow1` `clear-num` `frac-2neg` `insert-posit16` `add-log-exp`
1×	`associate-/l/`

Counts

2 → 176

Calls

2 calls:

16.0ms	(/ (/ (sin x) 1) (/ (* x x) (tan (/ x 2))))
10.0ms	(/ (* x x) (tan (/ x 2)))

series155.0ms

Counts

2 → 6

Calls

2 calls:

88.0ms	(/ (/ (sin x) 1) (/ (* x x) (tan (/ x 2))))
66.0ms	(/ (* x x) (tan (/ x 2)))

simplify1.7s

Counts

182 → 182

Iterations

Iter	Nodes
done	5016
2	3075
1	1030
0	350

prune632.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes54.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	9
1	9
0	8

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.5s	1584×	body	2560	valid
541.0ms	1487×	body	640	valid
517.0ms	1210×	body	1280	valid
166.0ms	910×	body	320	valid
159.0ms	2328×	body	80	valid
101.0ms	481×	body	160	valid