Details

sample140.0ms

Algorithm

intervals

Results

77.0ms	54×	body	2560	valid
34.0ms	84×	body	1280	valid
16.0ms	69×	body	640	valid
4.0ms	29×	body	320	valid
1.0ms	13×	body	160	valid
0.0ms	7×	body	80	valid

simplify6.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	6	7
1	11	7
2	14	7
3	16	7
done	16	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.6b

localize7.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ (- 1.0 (cos x)) (sin x))
1.2b	(- 1.0 (cos x))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt` `*-un-lft-identity`
15×	`times-frac`
12×	`add-cube-cbrt`
5×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`associate-/r*`
2×	`pow1` `flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

2 → 52

Calls

2 calls:

8.0ms	(/ (- 1.0 (cos x)) (sin x))
3.0ms	(- 1.0 (cos x))

series60.0ms

Counts

2 → 6

Calls

2 calls:

41.0ms	(/ (- 1.0 (cos x)) (sin x))
20.0ms	(- 1.0 (cos x))

simplify2.1s

Counts

58 → 58

Iterations

Useful iterations: 4 (1.1s)

Iter	Nodes	Cost
0	106	665
1	235	645
2	525	609
3	1299	609
4	4031	608
done	5001	608

prune173.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 0.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (exp (log (- 1.0 (cos x)))) (sin x))
0.2b	(exp (log (- 1.0 (cos x))))
0.3b	(log (- 1.0 (cos x)))
1.2b	(- 1.0 (cos x))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt` `*-un-lft-identity`
30×	`log-prod`
25×	`exp-sum`
24×	`add-cube-cbrt` `times-frac`
8×	`associate-/l*`
7×	`distribute-lft-out--` `difference-of-squares`
6×	`pow1` `add-exp-log` `log-div` `add-cbrt-cube` `add-log-exp`
4×	`exp-prod` `flip3--` `exp-diff` `flip--`
3×	`associate-/r*`
2×	`log-pow` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `clear-num` `div-inv` `rem-exp-log`

Counts

4 → 98

Calls

4 calls:

11.0ms	(/ (exp (log (- 1.0 (cos x)))) (sin x))
3.0ms	(exp (log (- 1.0 (cos x))))
3.0ms	(log (- 1.0 (cos x)))
3.0ms	(- 1.0 (cos x))

series158.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(/ (exp (log (- 1.0 (cos x)))) (sin x))
20.0ms	(exp (log (- 1.0 (cos x))))
81.0ms	(log (- 1.0 (cos x)))
19.0ms	(- 1.0 (cos x))

simplify2.5s

Counts

110 → 110

Iterations

Useful iterations: 4 (1.5s)

Iter	Nodes	Cost
0	168	1421
1	290	1183
2	640	1121
3	1555	1107
4	4819	1088
done	5000	1088

prune238.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (+ (cos x) 1.0) (- 1.0 (cos x))) (+ (cos x) 1.0))
0.4b	(+ (cos x) 1.0)
0.4b	(+ (cos x) 1.0)
1.2b	(- 1.0 (cos x))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

16×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-sqr-sqrt` `associate-/l/`
6×	`add-cube-cbrt` `flip3-+` `flip-+`
4×	`pow1` `frac-times` `flip3--` `times-frac` `associate-/r*` `flip--` `distribute-lft-out`
2×	`cbrt-undiv` `+-commutative` `associate-r/` `div-exp` `associate-l/` `sum-log` `associate-/r/`
1×	`sub-neg` `frac-2neg` `diff-log` `prod-exp` `clear-num` `cbrt-unprod` `div-inv` `associate-/l*` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 71

Calls

4 calls:

14.0ms	(/ (* (+ (cos x) 1.0) (- 1.0 (cos x))) (+ (cos x) 1.0))
3.0ms	(+ (cos x) 1.0)
3.0ms	(+ (cos x) 1.0)
3.0ms	(- 1.0 (cos x))

series63.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(/ (* (+ (cos x) 1.0) (- 1.0 (cos x))) (+ (cos x) 1.0))
10.0ms	(+ (cos x) 1.0)
10.0ms	(+ (cos x) 1.0)
23.0ms	(- 1.0 (cos x))

simplify2.6s

Counts

83 → 83

Iterations

Useful iterations: 3 (1.4s)

Iter	Nodes	Cost
0	109	1033
1	305	997
2	1148	793
3	4855	745
done	5000	745

prune224.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.2b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- 1.0 (cos x)) (sin x))
0.2b	(exp (/ (- 1.0 (cos x)) (sin x)))
0.7b	(log (exp (/ (- 1.0 (cos x)) (sin x))))
1.2b	(- 1.0 (cos x))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-sqr-sqrt` `*-un-lft-identity`
45×	`times-frac`
38×	`exp-prod`
33×	`add-cube-cbrt`
20×	`log-pow`
11×	`distribute-lft-out--` `difference-of-squares`
7×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-/l*`
3×	`log-prod` `div-sub` `associate-/r*` `div-inv`
2×	`flip3--` `exp-diff` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `log-div` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `clear-num` `rem-exp-log`

Counts

4 → 112

Calls

4 calls:

8.0ms	(/ (- 1.0 (cos x)) (sin x))
12.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
13.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
3.0ms	(- 1.0 (cos x))

series147.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(/ (- 1.0 (cos x)) (sin x))
50.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
37.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
24.0ms	(- 1.0 (cos x))

simplify2.4s

Counts

124 → 124

Iterations

Useful iterations: 4 (1.5s)

Iter	Nodes	Cost
0	163	1406
1	305	1293
2	633	1220
3	1531	1218
4	4655	1217
done	5000	1217

prune287.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 0.1b

regimes198.0ms

Accuracy

99% (0.3b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 30.1b

bsearch81.0ms

Steps

Iters	Range		Point
10	3.2824798326487284e-15	0.08347146558812443	0.023267676544555443
9	-5.7596417613087905	-6.7357437175194845e-09	-0.019541465084207187

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	40
1	35	40
2	37	40
done	37	40

end0.0ms

sample4.1s

Algorithm

intervals

Results

2.1s	1566×	body	2560	valid
1.2s	2771×	body	1280	valid
451.0ms	1917×	body	640	valid
150.0ms	941×	body	320	valid
54.0ms	444×	body	160	valid
23.0ms	357×	body	80	valid
13.0ms	4×	body	5120	valid