Details

sample84.0ms

Algorithm

intervals

Results

32.0ms	47×	body	2560	valid
18.0ms	44×	body	1280	valid
11.0ms	44×	body	640	valid
7.0ms	34×	body	320	valid
4.0ms	69×	body	80	valid
2.0ms	18×	body	160	valid

simplify43.0ms

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: 30.4b

localize12.0ms

Local error

Found 2 expressions with local error:

1.5b	(- 1 (cos x))
15.5b	(/ (- 1 (cos x)) (* x x))

rewrite44.0ms

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:

11.0ms	(- 1 (cos x))
29.0ms	(/ (- 1 (cos x)) (* x x))

series115.0ms

Counts

2 → 6

Calls

2 calls:

21.0ms	(- 1 (cos x))
94.0ms	(/ (- 1 (cos x)) (* x x))

simplify2.5s

Counts

53 → 53

Iterations

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

prune229.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize42.0ms

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))
15.5b	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))

rewrite145.0ms

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:

38.0ms	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
11.0ms	(+ 1 (cos x))
27.0ms	(* (sin x) (sin x))
62.0ms	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))

series203.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
10.0ms	(+ 1 (cos x))
25.0ms	(* (sin x) (sin x))
115.0ms	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))

simplify1.5s

Counts

127 → 127

Iterations

Iter	Nodes
done	5004
2	1801
1	508
0	182

prune470.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ (sin x) x) (/ (sin x) x))
0.1b	(/ (sin x) x)
0.1b	(/ (sin x) x)
0.3b	(+ (cos x) 1)

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

60×	`add-sqr-sqrt`
58×	`times-frac`
50×	`*-un-lft-identity`
48×	`add-cube-cbrt`
20×	`add-cbrt-cube` `add-exp-log`
13×	`swap-sqr` `associate-r` `associate-l`
11×	`pow1`
6×	`cbrt-undiv` `associate-/r` `div-exp` `div-inv` `associate-/l` `add-log-exp`
4×	`prod-exp` `cbrt-unprod` `insert-posit16` `unswap-sqr`
2×	`clear-num` `frac-2neg`
1×	`pow2` `frac-times` `+-commutative` `sum-log` `flip3-+` `pow-plus` `pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up` `flip-+` `distribute-lft-out`

Counts

4 → 137

Calls

4 calls:

44.0ms	(* (/ (sin x) x) (/ (sin x) x))
15.0ms	(/ (sin x) x)
20.0ms	(/ (sin x) x)
12.0ms	(+ (cos x) 1)

series162.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(* (/ (sin x) x) (/ (sin x) x))
32.0ms	(/ (sin x) x)
54.0ms	(/ (sin x) x)
18.0ms	(+ (cos x) 1)

simplify2.0s

Counts

149 → 149

Iterations

Iter	Nodes
done	5003
2	1925
1	505
0	162

prune630.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize46.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* (sin x) (/ (/ (sin x) x) x)) (+ (cos x) 1))
0.1b	(/ (sin x) x)
0.2b	(* (sin x) (/ (/ (sin x) x) x))
0.3b	(+ (cos x) 1)

rewrite135.0ms

Algorithm

rewrite-expression-head

Rules

82×	`times-frac`
59×	`add-sqr-sqrt`
56×	`*-un-lft-identity`
50×	`add-cube-cbrt`
43×	`associate-r`
29×	`add-cbrt-cube` `add-exp-log`
11×	`cbrt-undiv` `div-exp`
7×	`associate-/r*`
6×	`pow1` `prod-exp` `cbrt-unprod` `div-inv` `add-log-exp`
4×	`insert-posit16` `associate-/l*`
3×	`associate-l` `distribute-lft-out` `unswap-sqr`
2×	`clear-num` `frac-2neg` `flip3-+` `associate-*r/` `associate-/r/` `flip-+`
1×	`+-commutative` `sum-log` `pow-prod-down` `*-commutative` `associate-/l/`

Counts

4 → 138

Calls

4 calls:

49.0ms	(/ (* (sin x) (/ (/ (sin x) x) x)) (+ (cos x) 1))
10.0ms	(/ (sin x) x)
56.0ms	(* (sin x) (/ (/ (sin x) x) x))
13.0ms	(+ (cos x) 1)

series219.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(/ (* (sin x) (/ (/ (sin x) x) x)) (+ (cos x) 1))
36.0ms	(/ (sin x) x)
71.0ms	(* (sin x) (/ (/ (sin x) x) x))
18.0ms	(+ (cos x) 1)

simplify1.9s

Counts

150 → 150

Iterations

Iter	Nodes
done	5023
2	2419
1	673
0	245

prune662.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes65.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	13
1	13
0	9

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.6s	1624×	body	2560	valid
1.0s	1456×	body	640	valid
681.0ms	1258×	body	1280	valid
242.0ms	2192×	body	80	valid
233.0ms	958×	body	320	valid
125.0ms	512×	body	160	valid