Details

sample247.0ms

Algorithm

intervals

Results

116.0ms	47×	body	2560	valid
69.0ms	87×	body	1280	valid
26.0ms	58×	body	640	valid
12.0ms	37×	body	320	valid
3.0ms	16×	body	160	valid
1.0ms	11×	body	80	valid

simplify14.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.3b

localize10.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ (- 1.0 (cos x)) (sin x))
1.5b	(- 1.0 (cos x))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt` `*-un-lft-identity`
19×	`add-cube-cbrt`
15×	`times-frac`
9×	`prod-diff`
5×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`fma-neg` `associate-/r*`
2×	`pow1` `expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

2 → 68

Calls

2 calls:

56.0ms	(/ (- 1.0 (cos x)) (sin x))
7.0ms	(- 1.0 (cos x))

series83.0ms

Counts

2 → 6

Calls

2 calls:

62.0ms	(/ (- 1.0 (cos x)) (sin x))
21.0ms	(- 1.0 (cos x))

simplify1.5s

Counts

74 → 74

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	134	964
1	309	834
2	1215	733
done	5001	692

prune344.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize24.0ms

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)))
1.5b	(- 1.0 (cos x))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-sqr-sqrt` `*-un-lft-identity`
31×	`add-cube-cbrt`
30×	`log-prod`
25×	`exp-sum`
24×	`times-frac`
9×	`prod-diff`
8×	`associate-/l*`
7×	`distribute-lft-out--` `difference-of-squares`
6×	`pow1` `add-exp-log` `log-div` `add-cbrt-cube` `add-log-exp`
4×	`expm1-log1p-u` `exp-prod` `flip3--` `exp-diff` `flip--` `log1p-expm1-u`
3×	`fma-neg` `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 → 118

Calls

4 calls:

29.0ms	(/ (exp (log (- 1.0 (cos x)))) (sin x))
9.0ms	(exp (log (- 1.0 (cos x))))
7.0ms	(log (- 1.0 (cos x)))
16.0ms	(- 1.0 (cos x))

series226.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(/ (exp (log (- 1.0 (cos x)))) (sin x))
41.0ms	(exp (log (- 1.0 (cos x))))
112.0ms	(log (- 1.0 (cos x)))
22.0ms	(- 1.0 (cos x))

simplify1.1s

Counts

130 → 130

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	200	1750
1	374	1389
2	1294	1247
done	5001	1206

prune513.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b	(exp (log1p (expm1 (log (- 1.0 (cos x))))))
0.3b	(log (- 1.0 (cos x)))
1.3b	(log1p (expm1 (log (- 1.0 (cos x)))))
1.5b	(- 1.0 (cos x))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt` `*-un-lft-identity`
13×	`add-cube-cbrt`
9×	`prod-diff`
7×	`add-log-exp`
5×	`pow1` `add-exp-log` `log-prod`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`exp-prod` `fma-neg`
2×	`log-div` `log1p-udef` `flip3--` `flip--` `rem-exp-log` `distribute-lft-out--` `difference-of-squares`
1×	`sub-neg` `diff-log` `log1p-expm1` `rem-log-exp` `log-pow`

Counts

4 → 71

Calls

4 calls:

2.0ms	(exp (log1p (expm1 (log (- 1.0 (cos x))))))
7.0ms	(log (- 1.0 (cos x)))
0.0ms	(log1p (expm1 (log (- 1.0 (cos x)))))
7.0ms	(- 1.0 (cos x))

series626.0ms

Counts

4 → 12

Calls

4 calls:

280.0ms	(exp (log1p (expm1 (log (- 1.0 (cos x))))))
92.0ms	(log (- 1.0 (cos x)))
228.0ms	(log1p (expm1 (log (- 1.0 (cos x)))))
27.0ms	(- 1.0 (cos x))

simplify935.0ms

Counts

83 → 83

Iterations

Useful iterations: done (933.0ms)

Iter	Nodes	Cost
0	133	940
1	265	733
2	880	611
done	5000	568

prune437.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.1b

localize12.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ (- 1 (cos x)) (sin x))
1.5b	(- 1 (cos x))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt` `*-un-lft-identity`
20×	`add-cube-cbrt`
18×	`times-frac`
10×	`difference-of-squares`
9×	`prod-diff`
6×	`associate-/l*`
5×	`distribute-lft-out--`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`fma-neg` `associate-/r*`
2×	`pow1` `expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u` `associate-/l/`
1×	`cbrt-undiv` `hang-p0-tan` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

2 → 74

Calls

2 calls:

25.0ms	(/ (- 1 (cos x)) (sin x))
8.0ms	(- 1 (cos x))

series78.0ms

Counts

2 → 6

Calls

2 calls:

49.0ms	(/ (- 1 (cos x)) (sin x))
28.0ms	(- 1 (cos x))

simplify1.2s

Counts

80 → 80

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	142	1040
1	336	809
2	1350	721
done	5000	693

prune232.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	4
done	4	4

end0.0ms

sample8.6s

Algorithm

intervals

Results

3.5s	1581×	body	2560	valid
3.4s	2726×	body	1280	valid
943.0ms	1918×	body	640	valid
333.0ms	955×	body	320	valid
96.0ms	454×	body	160	valid
45.0ms	362×	body	80	valid
23.0ms	4×	body	5120	valid