Details

sample4.5s

Algorithm

intervals

sampling

Space saved by range analysis: 0.048828%

Space saved by search: 0.048828%

Guaranteed chance to sample good point: 0%

Results

129.0ms	49×	body	2560	valid
65.0ms	100×	body	1280	valid
20.0ms	57×	body	640	valid
4.0ms	23×	body	320	valid
2.0ms	15×	body	160	valid
1.0ms	12×	body	80	valid

simplify374.0ms

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

prune4.0ms

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: 32.4b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.4b	(- x (tan x))
1.5b	(- 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))
6.0ms	(- x (sin x))

series38.0ms

Counts

3 → 9

Calls

3 calls:

13.0ms	(/ (- x (sin x)) (- x (tan x)))
12.0ms	(- x (tan x))
13.0ms	(- x (sin x))

simplify147.0ms

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

prune103.0ms

Filtered

63 candidates to 89 candidates (-41.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	85	4	89
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	86	4	90

Merged error: 0.1b

Counts

90 → 4

localize9.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 27/2800 (pow x 4))
0.1b	(* 9/40 (pow x 2))
18.1b	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 66

Calls

3 calls:

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

series15.0ms

Counts

3 → 9

Calls

3 calls:

3.0ms	(* 27/2800 (pow x 4))
5.0ms	(* 9/40 (pow x 2))
6.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

simplify41.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	273	349
1	1123	316
2	5001	313

prune116.0ms

Filtered

46 candidates to 75 candidates (-63.0%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	73	2	75
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	74	5	79

Merged error: 0.1b

Counts

79 → 5

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (- (* 9/40 (pow x 2)) (* 27/2800 (pow x 4))) 1/2)
0.1b	(* 27/2800 (pow x 4))
0.1b	(* 9/40 (pow x 2))
18.1b	(- (* 9/40 (pow x 2)) (* 27/2800 (pow x 4)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 82

Calls

4 calls:

6.0ms	(- (- (* 9/40 (pow x 2)) (* 27/2800 (pow x 4))) 1/2)
5.0ms	(* 27/2800 (pow x 4))
5.0ms	(* 9/40 (pow x 2))
4.0ms	(- (* 9/40 (pow x 2)) (* 27/2800 (pow x 4)))

series20.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(- (- (* 9/40 (pow x 2)) (* 27/2800 (pow x 4))) 1/2)
3.0ms	(* 27/2800 (pow x 4))
3.0ms	(* 9/40 (pow x 2))
9.0ms	(- (* 9/40 (pow x 2)) (* 27/2800 (pow x 4)))

simplify48.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	308	474
1	1219	442
2	5001	431

prune139.0ms

Filtered

59 candidates to 94 candidates (-59.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	94	0	94
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	94	5	99

Merged error: 0.1b

Counts

99 → 5

localize14.0ms

Local error

Found 4 expressions with local error:

14.4b	(cbrt (- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2)))
18.1b	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))
18.1b	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))
18.1b	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-log-exp`
6×	`diff-log`
5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `flip3--` `add-cbrt-cube` `flip--`
3×	`cbrt-prod` `sub-neg` `sum-log` `associate--r+`
2×	`cbrt-div`
1×	`pow1/3`

Counts

4 → 55

Calls

4 calls:

6.0ms	(cbrt (- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2)))
7.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))
7.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))
7.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

series32.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(cbrt (- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2)))
5.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))
5.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))
5.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

simplify98.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 2 (20.0ms)

Iter	Nodes	Cost
0	227	719
1	723	651
2	3160	649
3	5001	649

prune240.0ms

Filtered

48 candidates to 67 candidates (-39.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	67	0	67
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	67	5	72

Merged error: 0.1b

Counts

72 → 5

regimes93.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 32.1b

bsearch49.0ms

Steps

Iters	Range		Point
10	0.000975852108371138	15187447970.527506	0.028237605054750856
6	-0.12556691585268046	-0.019223410576720813	-0.02836701413477812

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	13
1	30	13

end0.0ms

sample10.6s

Algorithm

intervals

sampling

Space saved by range analysis: 0.048828%

Space saved by search: 0.048828%

Guaranteed chance to sample good point: 0%

Results

3.7s	1518×	body	2560	valid
1.7s	2775×	body	1280	valid
697.0ms	1921×	body	640	valid
172.0ms	927×	body	320	valid
69.0ms	505×	body	160	valid
32.0ms	354×	body	80	valid

Details

sample4.5s

simplify374.0ms

prune4.0ms

localize11.0ms

rewrite20.0ms

series38.0ms

simplify147.0ms

prune103.0ms

localize9.0ms

rewrite18.0ms

series15.0ms

simplify41.0ms

prune116.0ms

localize9.0ms

rewrite22.0ms

series20.0ms

simplify48.0ms

prune139.0ms

localize14.0ms

rewrite27.0ms

series32.0ms

simplify98.0ms

prune240.0ms

regimes93.0ms

bsearch49.0ms

simplify2.0ms

end0.0ms

sample10.6s

Profiling