Details

sample56.0ms

Algorithm

intervals

Results

24.0ms	54×	body	2560	valid
11.0ms	52×	body	640	valid
8.0ms	37×	body	1280	valid
3.0ms	29×	body	320	valid
2.0ms	71×	body	80	valid
1.0ms	13×	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: 29.8b

localize6.0ms

Local error

Found 2 expressions with local error:

1.2b	(- 1.0 (cos x))
16.0b	(/ (- 1.0 (cos x)) (* x x))

rewrite13.0ms

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:

3.0ms	(- 1.0 (cos x))
9.0ms	(/ (- 1.0 (cos x)) (* x x))

series64.0ms

Counts

2 → 6

Calls

2 calls:

18.0ms	(- 1.0 (cos x))
46.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify1.1s

Counts

48 → 48

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	88	507
1	218	489
2	652	441
3	2387	441
done	5000	440

prune114.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize7.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sqrt (- 1.0 (cos x))) x)
0.2b	(/ (sqrt (- 1.0 (cos x))) x)
1.2b	(- 1.0 (cos x))
1.2b	(- 1.0 (cos x))

rewrite26.0ms

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)
3.0ms	(- 1.0 (cos x))
3.0ms	(- 1.0 (cos x))

series218.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(/ (sqrt (- 1.0 (cos x))) x)
90.0ms	(/ (sqrt (- 1.0 (cos x))) x)
21.0ms	(- 1.0 (cos x))
19.0ms	(- 1.0 (cos x))

simplify1.2s

Counts

138 → 138

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	132	1732
1	242	1618
2	605	1548
3	2813	1548
done	5000	1548

prune308.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (- 1.0 (cos x)))
1.2b	(- 1.0 (cos x))
1.2b	(- 1.0 (cos x))
1.2b	(- 1.0 (cos x))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `*-un-lft-identity`
10×	`add-log-exp`
5×	`cbrt-prod` `add-cube-cbrt`
4×	`pow1` `add-exp-log` `flip3--` `add-cbrt-cube` `flip--` `distribute-lft-out--` `difference-of-squares`
3×	`sub-neg` `diff-log`
2×	`cbrt-div`
1×	`pow1/3`

Counts

4 → 57

Calls

4 calls:

2.0ms	(cbrt (- 1.0 (cos x)))
3.0ms	(- 1.0 (cos x))
3.0ms	(- 1.0 (cos x))
3.0ms	(- 1.0 (cos x))

series184.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(cbrt (- 1.0 (cos x)))
18.0ms	(- 1.0 (cos x))
23.0ms	(- 1.0 (cos x))
19.0ms	(- 1.0 (cos x))

simplify642.0ms

Counts

69 → 69

Iterations

Useful iterations: 3 (169.0ms)

Iter	Nodes	Cost
0	76	627
1	152	608
2	363	554
3	1183	534
done	5000	534

prune185.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 4 expressions with local error:

1.2b	(- 1.0 (cos x))
1.2b	(- 1.0 (cos x))
1.2b	(- 1.0 (cos x))
1.3b	(log (exp (- 1.0 (cos x))))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 62

Calls

4 calls:

3.0ms	(- 1.0 (cos x))
3.0ms	(- 1.0 (cos x))
3.0ms	(- 1.0 (cos x))
8.0ms	(log (exp (- 1.0 (cos x))))

series77.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify2.0s

Counts

74 → 74

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	72	615
1	128	556
2	262	519
3	683	519
4	3049	519
done	5001	519

prune202.0ms

Pruning

13 alts after pruning (10 fresh and 3 done)

Merged error: 0.1b

regimes65.0ms

Accuracy

99.1% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 30.6b

bsearch73.0ms

Steps

Iters	Range		Point
10	3.2824798326487284e-15	0.08347146558812443	0.03157722500580303
9	-5.7596417613087905	-6.7357437175194845e-09	-0.03315307006442389

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	46
1	31	46
done	31	46

end0.0ms

sample1.6s

Algorithm

intervals

Results

729.0ms	1570×	body	2560	valid
284.0ms	1251×	body	1280	valid
213.0ms	1507×	body	640	valid
108.0ms	935×	body	320	valid
70.0ms	2289×	body	80	valid
32.0ms	448×	body	160	valid