Details

sample491.0ms

Algorithm

intervals

Results

140.0ms	57×	body	2560	valid
45.0ms	79×	body	1280	valid
14.0ms	53×	body	640	valid
4.0ms	26×	body	320	valid
3.0ms	23×	body	160	valid
1.0ms	18×	body	80	valid

simplify35.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (23.0ms)

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

prune4.0ms

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: 30.8b

Counts

2 → 1

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.7b	(- x (tan x))
1.7b	(- x (sin x))

rewrite23.0ms

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:

8.0ms	(/ (- x (sin x)) (- x (tan x)))
4.0ms	(- x (tan x))
6.0ms	(- x (sin x))

series176.0ms

Counts

3 → 9

Calls

3 calls:

77.0ms	(/ (- x (sin x)) (- x (tan x)))
58.0ms	(- x (tan x))
41.0ms	(- x (sin x))

simplify156.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 1 (9.0ms)

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

prune190.0ms

Filtered

89 candidates to 63 candidates (70.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	84	5	89
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	85	5	90

Merged error: 0.0b

Counts

90 → 5

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin x) (- x (tan x)))
1.5b	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
1.7b	(- x (tan x))
1.7b	(- x (tan x))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

54×	`*-un-lft-identity`
44×	`add-sqr-sqrt`
33×	`times-frac`
18×	`distribute-lft-out--`
16×	`add-cube-cbrt`
12×	`difference-of-squares`
10×	`add-log-exp`
6×	`add-exp-log` `flip3--` `associate-/r/` `add-cbrt-cube` `flip--`
5×	`associate-/r*`
4×	`pow1`
3×	`sub-neg` `distribute-rgt-out--` `diff-log` `div-inv` `associate-/l*`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `frac-sub` `sub-div`

Counts

4 → 94

Calls

4 calls:

6.0ms	(/ (sin x) (- x (tan x)))
28.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
3.0ms	(- x (tan x))
4.0ms	(- x (tan x))

series340.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(/ (sin x) (- x (tan x)))
173.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
52.0ms	(- x (tan x))
53.0ms	(- x (tan x))

simplify42.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	376	909
1	1205	870
2	5001	870

prune219.0ms

Filtered

106 candidates to 80 candidates (75.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	103	3	106
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	105	6	111

Merged error: 0.0b

Counts

111 → 6

localize21.0ms

Local error

Found 4 expressions with local error:

1.7b	(- x (tan x))
1.7b	(- x (tan x))
1.7b	(- x (tan x))
1.7b	(- x (tan x))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 56

Calls

4 calls:

3.0ms	(- x (tan x))
4.0ms	(- x (tan x))
4.0ms	(- x (tan x))
4.0ms	(- x (tan x))

series212.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(- x (tan x))
54.0ms	(- x (tan x))
49.0ms	(- x (tan x))
54.0ms	(- x (tan x))

simplify156.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	91	324
1	200	300
2	471	300
3	1247	300
4	4646	300
5	5001	300

prune218.0ms

Filtered

68 candidates to 52 candidates (76.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	68	0	68
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	68	6	74

Merged error: 0.0b

Counts

74 → 6

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))
0.2b	(* 27/2800 (pow x 4))
15.8b	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

rewrite26.0ms

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:

5.0ms	(+ (* 27/2800 (pow x 4)) 1/2)
6.0ms	(* 9/40 (pow x 2))
5.0ms	(* 27/2800 (pow x 4))
8.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

series197.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(+ (* 27/2800 (pow x 4)) 1/2)
25.0ms	(* 9/40 (pow x 2))
36.0ms	(* 27/2800 (pow x 4))
50.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

simplify56.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (42.0ms)

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

prune147.0ms

Filtered

89 candidates to 56 candidates (62.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	89	0	89
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	89	6	95

Merged error: 0.0b

Counts

95 → 6

Details

sample491.0ms

simplify35.0ms

prune4.0ms

localize12.0ms

rewrite23.0ms

series176.0ms

simplify156.0ms

prune190.0ms

localize10.0ms

rewrite45.0ms

series340.0ms

simplify42.0ms

prune219.0ms

localize21.0ms

rewrite16.0ms

series212.0ms

simplify156.0ms

prune218.0ms

localize10.0ms

rewrite26.0ms

series197.0ms

simplify56.0ms

prune147.0ms

regimes42.0ms

bsearch3.0ms

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