Details

sample165.0ms

Algorithm

intervals

Results

62.0ms	53×	body	2560	valid
33.0ms	39×	body	320	valid
26.0ms	38×	body	1280	valid
21.0ms	41×	body	640	valid
8.0ms	67×	body	80	valid
4.0ms	18×	body	160	valid

simplify16.0ms

Counts

1 → 1

Iterations

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.2b

localize11.0ms

Local error

Found 2 expressions with local error:

2.2b	(- 1 (cos x))
15.8b	(/ (- 1 (cos x)) (* x x))

rewrite57.0ms

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:

25.0ms	(- 1 (cos x))
30.0ms	(/ (- 1 (cos x)) (* x x))

series108.0ms

Counts

2 → 6

Calls

2 calls:

35.0ms	(- 1 (cos x))
74.0ms	(/ (- 1 (cos x)) (* x x))

simplify2.1s

Counts

53 → 53

Iterations

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

prune201.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
0.2b	(* (sin x) (sin x))
0.5b	(+ 1 (cos x))
15.8b	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))

rewrite55.0ms

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:

15.0ms	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
11.0ms	(* (sin x) (sin x))
5.0ms	(+ 1 (cos x))
22.0ms	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))

series191.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
29.0ms	(* (sin x) (sin x))
14.0ms	(+ 1 (cos x))
101.0ms	(/ (/ (* (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

prune473.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize17.0ms

Local error

Found 2 expressions with local error:

0.2b	(* (sin x) (tan (/ x 2)))
15.8b	(/ (* (sin x) (tan (/ x 2))) (* x x))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 43

Calls

2 calls:

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

series213.0ms

Counts

2 → 6

Calls

2 calls:

82.0ms	(* (sin x) (tan (/ x 2)))
130.0ms	(/ (* (sin x) (tan (/ x 2))) (* x x))

simplify1.1s

Counts

49 → 49

Iterations

Iter	Nodes
done	5008
2	1080
1	241
0	95

prune214.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize46.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (* (sin x) (sin x)) x) (/ (/ 1 (+ 1 (cos x))) x))
0.2b	(* (sin x) (sin x))
0.5b	(+ 1 (cos x))
15.0b	(/ (* (sin x) (sin x)) x)

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

110×	`times-frac`
81×	`add-sqr-sqrt`
77×	`*-un-lft-identity`
71×	`add-exp-log`
61×	`associate-r`
55×	`add-cube-cbrt`
47×	`add-cbrt-cube`
30×	`div-exp`
22×	`prod-exp`
17×	`cbrt-undiv`
14×	`cbrt-unprod`
13×	`pow1`
10×	`associate-l` `distribute-lft-out`
9×	`unswap-sqr`
6×	`associate-/r/` `div-inv` `add-log-exp`
4×	`flip3-+` `flip-+` `insert-posit16`
3×	`rec-exp` `associate-/r*` `1-exp` `swap-sqr`
2×	`pow-prod-down` `*-commutative` `sqr-sin` `sin-mult`
1×	`pow2` `frac-times` `+-commutative` `clear-num` `sum-log` `frac-2neg` `pow-plus` `div-sub` `associate-l/` `associate-r/` `pow-sqr` `pow-prod-up` `associate-/l*` `associate-/l/`

Counts

4 → 175

Calls

4 calls:

34.0ms	(* (/ (* (sin x) (sin x)) x) (/ (/ 1 (+ 1 (cos x))) x))
10.0ms	(* (sin x) (sin x))
5.0ms	(+ 1 (cos x))
28.0ms	(/ (* (sin x) (sin x)) x)

series220.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(* (/ (* (sin x) (sin x)) x) (/ (/ 1 (+ 1 (cos x))) x))
31.0ms	(* (sin x) (sin x))
17.0ms	(+ 1 (cos x))
80.0ms	(/ (* (sin x) (sin x)) x)

simplify2.3s

Counts

187 → 187

Iterations

Iter	Nodes
done	5054
2	3323
1	995
0	307

prune775.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes77.0ms

Accuracy

98.2% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 15.4b

bsearch94.0ms

Steps

Iters	Range		Point
8	0.006928851504795399	68.55102067575892	0.007030302033610333
9	-17438.246738609338	-0.0018335887134067947	-0.03474669209571521

simplify8.0ms

Iterations

Iter	Nodes
done	33
1	33
0	27

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.6s	1603×	body	2560	valid
1.0s	1229×	body	1280	valid
681.0ms	1455×	body	640	valid
360.0ms	953×	body	320	valid
224.0ms	2260×	body	80	valid
91.0ms	500×	body	160	valid