Details

sample111.0ms

Algorithm

intervals

Results

56.0ms	114×	body	1280	valid
22.0ms	76×	body	640	valid
11.0ms	312×	body	80	nan
7.0ms	39×	body	320	valid
2.0ms	21×	body	160	valid
0.0ms	6×	body	80	valid

simplify14.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	6
1	25	6
2	40	6
3	61	6
4	88	6
5	104	6
6	113	6
7	113	6

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 58.7b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ 1.0 x) (- 1.0 x))
5.3b	(log (/ (+ 1.0 x) (- 1.0 x)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

63×	`*-un-lft-identity`
41×	`add-sqr-sqrt`
40×	`times-frac`
26×	`log-prod`
23×	`add-cube-cbrt`
11×	`distribute-lft-out`
9×	`distribute-lft-out--` `difference-of-squares`
7×	`add-exp-log`
5×	`associate-/r*`
4×	`associate-/r/` `add-cbrt-cube` `associate-/l*`
3×	`pow1`
2×	`flip3--` `div-exp` `rem-log-exp` `flip--` `div-inv` `associate-/l/` `add-log-exp`
1×	`cbrt-undiv` `log-div` `frac-2neg` `flip3-+` `clear-num` `log-pow` `flip-+`

Counts

2 → 82

Calls

2 calls:

11.0ms	(/ (+ 1.0 x) (- 1.0 x))
7.0ms	(log (/ (+ 1.0 x) (- 1.0 x)))

series159.0ms

Counts

2 → 6

Calls

2 calls:

36.0ms	(/ (+ 1.0 x) (- 1.0 x))
123.0ms	(log (/ (+ 1.0 x) (- 1.0 x)))

simplify120.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (25.0ms)

Iter	Nodes	Cost
0	318	660
1	1025	624
2	4261	602
3	5001	602

prune163.0ms

Filtered

88 candidates to 58 candidates (65.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	84	4	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	85	4	89

Merged error: 0.2b

Counts

89 → 4

localize12.0ms

Local error

Found 1 expressions with local error:

0.0b	(* 2.0 (/ (pow x 2) (pow 1.0 2)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

80×	`times-frac`
69×	`add-sqr-sqrt`
68×	`associate-r`
56×	`unpow-prod-down`
35×	`add-cube-cbrt` `*-un-lft-identity`
24×	`add-exp-log` `unpow2` `sqr-pow`
17×	`unswap-sqr`
10×	`prod-exp`
9×	`div-exp`
6×	`pow-to-exp` `pow-exp` `add-cbrt-cube`
3×	`pow1` `associate-l`
2×	`cbrt-unprod`
1×	`cbrt-undiv` `associate-r/` `pow-prod-down` `-commutative` `div-inv` `add-log-exp`

Counts

1 → 110

Calls

1 calls:

25.0ms

(* 2.0 (/ (pow x 2) (pow 1.0 2)))

series49.0ms

Counts

1 → 3

Calls

1 calls:

49.0ms

(* 2.0 (/ (pow x 2) (pow 1.0 2)))

simplify54.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	528	643
1	2205	526
2	5001	525

prune241.0ms

Filtered

113 candidates to 68 candidates (60.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	113	0	113
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	113	4	117

Merged error: 0.2b

Counts

117 → 4

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (log (+ 1.0 x)) (log (- 1.0 x)))
5.4b	(log (+ 1.0 x))
5.4b	(log (- 1.0 x))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
18×	`log-prod`
13×	`add-sqr-sqrt`
9×	`pow1`
8×	`log-div`
7×	`add-cube-cbrt`
6×	`log-pow` `distribute-lft-out--`
5×	`add-exp-log` `associate--r+`
4×	`associate--l+`
3×	`flip3--` `add-cbrt-cube` `flip--` `add-log-exp` `difference-of-squares`
2×	`associate--l-` `flip3-+` `rem-log-exp` `flip-+` `distribute-lft-out` `associate--r-`
1×	`sub-neg` `diff-log`

Counts

3 → 61

Calls

3 calls:

9.0ms	(- (log (+ 1.0 x)) (log (- 1.0 x)))
3.0ms	(log (+ 1.0 x))
3.0ms	(log (- 1.0 x))

series344.0ms

Counts

3 → 9

Calls

3 calls:

259.0ms	(- (log (+ 1.0 x)) (log (- 1.0 x)))
40.0ms	(log (+ 1.0 x))
46.0ms	(log (- 1.0 x))

simplify75.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (20.0ms)

Iter	Nodes	Cost
0	302	431
1	776	410
2	2776	393
3	5001	393

prune145.0ms

Filtered

70 candidates to 53 candidates (75.7%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	69	1	70
Fresh	2	0	2
Picked	1	0	1
Done	1	0	1
Total	73	1	74

Merged error: 0b

Counts

74 → 1

localize16.0ms

Local error

Found 2 expressions with local error:

0.1b	(* 2/5 (/ (pow x 5) (pow 1.0 5)))
0.1b	(* 2/3 (/ (pow x 3) (pow 1.0 3)))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

218×	`times-frac`
201×	`associate-r`
171×	`add-sqr-sqrt`
128×	`unpow-prod-down`
106×	`add-cube-cbrt` `*-un-lft-identity`
80×	`cube-prod`
52×	`sqr-pow`
48×	`add-exp-log`
27×	`unswap-sqr`
24×	`cube-mult` `unpow3`
20×	`prod-exp`
18×	`div-exp`
12×	`pow-to-exp` `pow-exp` `add-cbrt-cube`
6×	`pow1` `associate-l`
4×	`cbrt-unprod`
2×	`cbrt-undiv` `associate-r/` `pow-prod-down` `-commutative` `div-inv` `add-log-exp`

Counts

2 → 278

Calls

2 calls:

22.0ms	(* 2/5 (/ (pow x 5) (pow 1.0 5)))
40.0ms	(* 2/3 (/ (pow x 3) (pow 1.0 3)))

series368.0ms

Counts

2 → 6

Calls

2 calls:

289.0ms	(* 2/5 (/ (pow x 5) (pow 1.0 5)))
79.0ms	(* 2/3 (/ (pow x 3) (pow 1.0 3)))

simplify48.0ms

Algorithm

egg-herbie

Counts

284 → 284

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1050	1560
1	5001	1380

prune605.0ms

Filtered

284 candidates to 148 candidates (52.1%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	284	0	284
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	284	1	285

Merged error: 0b

Counts

285 → 1

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	13
1	26	13

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.7s	3460×	body	1280	valid
684.0ms	2422×	body	640	valid
293.0ms	8149×	body	80	nan
221.0ms	1283×	body	320	valid
70.0ms	658×	body	160	valid
9.0ms	177×	body	80	valid