Details

analyze4.0s

Algorithm

sampling

Space saved by range analysis: 0.048828%

Space saved by search: 0.048828%

Guaranteed chance to sample good point: 0.219727%

sample246.0ms

Algorithm

intervals

Results

147.0ms	49×	body	2560	valid
64.0ms	90×	body	1280	valid
16.0ms	58×	body	640	valid
6.0ms	35×	body	320	valid
2.0ms	16×	body	160	valid
1.0ms	8×	body	80	valid

simplify388.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	5
1	17	5
2	19	5
3	19	5

prune5.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 33.1b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.9b	(- x (tan x))
1.9b	(- x (sin x))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 80

Calls

3 calls:

7.0ms	(/ (- x (sin x)) (- x (tan x)))
3.0ms	(- x (tan x))
5.0ms	(- x (sin x))

series37.0ms

Counts

3 → 9

Calls

3 calls:

13.0ms	(/ (- x (sin x)) (- x (tan x)))
11.0ms	(- x (tan x))
13.0ms	(- x (sin x))

simplify148.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	363	718
1	1148	684
2	4781	684
3	5001	684

prune96.0ms

Filtered

63 candidates to 89 candidates (-41.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	87	2	89
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	88	2	90

Merged error: 0b

Counts

90 → 2

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 27/2800 (pow x 4)) 1/2)
0.1b	(* 9/40 (pow x 2))
0.3b	(* 27/2800 (pow x 4))
14.8b	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
15×	`associate-r`
14×	`add-exp-log`
11×	`add-log-exp`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`unpow-prod-down` `add-cbrt-cube`
7×	`unswap-sqr`
6×	`associate-l` `prod-exp`
4×	`pow1` `sqr-pow`
2×	`pow-to-exp` `diff-log` `pow-exp` `sum-log` `*-commutative` `cbrt-unprod` `unpow2`
1×	`+-commutative` `sub-neg` `flip3--` `flip3-+` `flip--` `flip-+` `associate--r+`

Counts

4 → 77

Calls

4 calls:

4.0ms	(+ (* 27/2800 (pow x 4)) 1/2)
5.0ms	(* 9/40 (pow x 2))
5.0ms	(* 27/2800 (pow x 4))
7.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

series22.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(+ (* 27/2800 (pow x 4)) 1/2)
3.0ms	(* 9/40 (pow x 2))
4.0ms	(* 27/2800 (pow x 4))
5.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

simplify45.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	316	412
1	1299	379
2	5001	374

prune119.0ms

Filtered

56 candidates to 89 candidates (-58.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	89	0	89
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	89	2	91

Merged error: 0b

Counts

91 → 2

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (/ (sin x) (cos x))))
0.1b	(/ (sin x) (cos x))
1.9b	(- x (/ (sin x) (cos x)))
1.9b	(- x (sin x))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

76×	`add-sqr-sqrt`
55×	`*-un-lft-identity`
46×	`times-frac`
25×	`add-cube-cbrt`
22×	`difference-of-squares`
15×	`distribute-lft-out--`
9×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube` `associate-/l*` `add-log-exp`
4×	`pow1` `flip3--` `flip--`
2×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `clear-num` `associate-/r/` `div-inv` `associate-/l/`
1×	`quot-tan` `div-sub`

Counts

4 → 115

Calls

4 calls:

10.0ms	(/ (- x (sin x)) (- x (/ (sin x) (cos x))))
4.0ms	(/ (sin x) (cos x))
6.0ms	(- x (/ (sin x) (cos x)))
3.0ms	(- x (sin x))

series33.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(/ (- x (sin x)) (- x (/ (sin x) (cos x))))
6.0ms	(/ (sin x) (cos x))
9.0ms	(- x (/ (sin x) (cos x)))
5.0ms	(- x (sin x))

simplify48.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	458	1225
1	1565	1174
2	5001	1172

prune97.0ms

Filtered

91 candidates to 127 candidates (-39.6%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	127	0	127
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	127	2	129

Merged error: 0b

Counts

129 → 2

Details

analyze4.0s

sample246.0ms

simplify388.0ms

prune5.0ms

localize11.0ms

rewrite20.0ms

series37.0ms

simplify148.0ms

prune96.0ms

localize10.0ms

rewrite23.0ms

series22.0ms

simplify45.0ms

prune119.0ms

localize9.0ms

rewrite28.0ms

series33.0ms

simplify48.0ms

prune97.0ms

regimes37.0ms

bsearch1.0ms

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