Details

sample52.0ms

Algorithm

intervals

Results

18.0ms	41×	body	2560	valid
11.0ms	48×	body	1280	valid
9.0ms	47×	body	640	valid
3.0ms	28×	body	320	valid
2.0ms	70×	body	80	valid
2.0ms	22×	body	160	valid

simplify12.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	6	8
1	13	8
2	21	8
3	26	8
4	29	8
done	29	8

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.4b

localize6.0ms

Local error

Found 2 expressions with local error:

2.1b	(- 1.0 (cos x))
13.0b	(/ (- 1.0 (cos x)) (* x x))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 42

Calls

2 calls:

2.0ms	(- 1.0 (cos x))
9.0ms	(/ (- 1.0 (cos x)) (* x x))

series63.0ms

Counts

2 → 6

Calls

2 calls:

18.0ms	(- 1.0 (cos x))
45.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify1.7s

Counts

48 → 48

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	88	507
1	218	497
2	621	441
3	2141	441
done	5000	440

prune105.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize8.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sqrt (- 1.0 (cos x))) x)
0.2b	(/ (sqrt (- 1.0 (cos x))) x)
2.1b	(- 1.0 (cos x))
2.1b	(- 1.0 (cos x))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 126

Calls

4 calls:

8.0ms	(/ (sqrt (- 1.0 (cos x))) x)
8.0ms	(/ (sqrt (- 1.0 (cos x))) x)
2.0ms	(- 1.0 (cos x))
3.0ms	(- 1.0 (cos x))

series215.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(/ (sqrt (- 1.0 (cos x))) x)
88.0ms	(/ (sqrt (- 1.0 (cos x))) x)
17.0ms	(- 1.0 (cos x))
21.0ms	(- 1.0 (cos x))

simplify1.6s

Counts

138 → 138

Iterations

Useful iterations: 2 (81.0ms)

Iter	Nodes	Cost
0	132	1732
1	242	1618
2	550	1548
3	1678	1548
done	5001	1548

prune303.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sqrt (log (exp (- 1.0 (cos x))))) x)
2.1b	(- 1.0 (cos x))
2.1b	(- 1.0 (cos x))
2.2b	(log (exp (- 1.0 (cos x))))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 111

Calls

4 calls:

19.0ms	(/ (sqrt (log (exp (- 1.0 (cos x))))) x)
3.0ms	(- 1.0 (cos x))
3.0ms	(- 1.0 (cos x))
8.0ms	(log (exp (- 1.0 (cos x))))

series148.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(/ (sqrt (log (exp (- 1.0 (cos x))))) x)
18.0ms	(- 1.0 (cos x))
18.0ms	(- 1.0 (cos x))
23.0ms	(log (exp (- 1.0 (cos x))))

simplify1.6s

Counts

123 → 123

Iterations

Useful iterations: 3 (374.0ms)

Iter	Nodes	Cost
0	181	1589
1	304	1274
2	631	1242
3	1792	1218
done	5000	1218

prune282.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 4 expressions with local error:

2.1b	(- 1.0 (cos x))
2.1b	(- 1.0 (cos x))
2.2b	(log (exp (- 1.0 (cos x))))
2.2b	(log (exp (- 1.0 (cos x))))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt` `*-un-lft-identity`
12×	`log-pow`
10×	`log-prod` `exp-prod`
8×	`add-cube-cbrt` `add-log-exp`
6×	`pow1`
4×	`add-exp-log` `sub-neg` `exp-sum` `add-cbrt-cube` `distribute-lft-out--` `difference-of-squares`
2×	`log-div` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 68

Calls

4 calls:

3.0ms	(- 1.0 (cos x))
3.0ms	(- 1.0 (cos x))
7.0ms	(log (exp (- 1.0 (cos x))))
11.0ms	(log (exp (- 1.0 (cos x))))

series78.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(- 1.0 (cos x))
18.0ms	(- 1.0 (cos x))
18.0ms	(log (exp (- 1.0 (cos x))))
19.0ms	(log (exp (- 1.0 (cos x))))

simplify2.9s

Counts

80 → 80

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	72	678
1	128	576
2	235	534
3	437	534
4	1288	534
5	4440	534
done	5000	534

prune227.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.1b

regimes55.0ms

Accuracy

99.3% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 30.3b

bsearch77.0ms

Steps

Iters	Range		Point
9	0.00016167321766412214	1766.3470775505596	0.028078975194333212
10	-3752817.331716861	-5.670122129476186e-07	-0.03183261061140115

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	28	55
1	35	39
done	35	39

end0.0ms

sample1.8s

Algorithm

intervals

Results

927.0ms	1558×	body	2560	valid
297.0ms	1237×	body	1280	valid
233.0ms	1495×	body	640	valid
97.0ms	927×	body	320	valid
73.0ms	2286×	body	80	valid
44.0ms	497×	body	160	valid