Details

sample415.0ms

Algorithm

intervals

Results

85.0ms	48×	body	2560	valid
53.0ms	90×	body	1280	valid
17.0ms	66×	body	640	valid
4.0ms	26×	body	320	valid
2.0ms	18×	body	160	valid
2.0ms	8×	body	80	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 32.3b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.8b	(- x (tan x))
1.9b	(- x (sin x))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 110

Calls

3 calls:

9.0ms	(/ (- x (sin x)) (- x (tan x)))
4.0ms	(- x (tan x))
7.0ms	(- x (sin x))

series181.0ms

Counts

3 → 9

Calls

3 calls:

78.0ms	(/ (- x (sin x)) (- x (tan x)))
60.0ms	(- x (tan x))
42.0ms	(- x (sin x))

simplify56.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	472	1059
1	1737	854
2	5001	854

prune217.0ms

Filtered

119 candidates to 79 candidates (66.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	116	3	119
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	117	3	120

Merged error: 0.0b

Counts

120 → 3

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma 27/2800 (pow x 4) 1/2)
15.6b	(fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

2×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

2 → 20

Calls

2 calls:

1.0ms	(fma 27/2800 (pow x 4) 1/2)
1.0ms	(fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))

series136.0ms

Counts

2 → 6

Calls

2 calls:

89.0ms	(fma 27/2800 (pow x 4) 1/2)
47.0ms	(fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))

simplify144.0ms

Algorithm

egg-herbie

Counts

26 → 26

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	51	133
1	162	117
2	626	117
3	3552	117
4	5001	117

prune72.0ms

Filtered

26 candidates to 20 candidates (76.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	24	2	26
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	24	5	29

Merged error: 0.0b

Counts

29 → 5

localize14.0ms

Local error

Found 4 expressions with local error:

15.4b	(cbrt (fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2))))
15.6b	(fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))
15.6b	(fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))
15.6b	(fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `fma-udef`
1×	`pow1/3`

Counts

4 → 43

Calls

4 calls:

1.0ms	(cbrt (fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2))))
1.0ms	(fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))
1.0ms	(fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))
1.0ms	(fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))

series286.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(cbrt (fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2))))
48.0ms	(fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))
48.0ms	(fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))
46.0ms	(fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))

simplify55.0ms

Algorithm

egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 3 (48.0ms)

Iter	Nodes	Cost
0	155	462
1	435	416
2	1685	414
3	5003	411

prune183.0ms

Filtered

55 candidates to 45 candidates (81.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	54	1	55
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	55	5	60

Merged error: 0.0b

Counts

60 → 5

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (fma 27/2800 (pow x 4) 1/2) 3)
0.0b	(fma 27/2800 (pow x 4) 1/2)
6.2b	(cbrt (pow (fma 27/2800 (pow x 4) 1/2) 3))
15.6b	(fma 9/40 (pow x 2) (- (cbrt (pow (fma 27/2800 (pow x 4) 1/2) 3))))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`unpow-prod-down` `cube-prod`
5×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow`
2×	`cube-mult` `unpow3` `fma-udef` `sqr-pow`
1×	`pow-to-exp` `pow-pow` `pow1/3` `pow-exp` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 68

Calls

4 calls:

2.0ms	(pow (fma 27/2800 (pow x 4) 1/2) 3)
1.0ms	(fma 27/2800 (pow x 4) 1/2)
2.0ms	(cbrt (pow (fma 27/2800 (pow x 4) 1/2) 3))
1.0ms	(fma 9/40 (pow x 2) (- (cbrt (pow (fma 27/2800 (pow x 4) 1/2) 3))))

series326.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(pow (fma 27/2800 (pow x 4) 1/2) 3)
85.0ms	(fma 27/2800 (pow x 4) 1/2)
85.0ms	(cbrt (pow (fma 27/2800 (pow x 4) 1/2) 3))
49.0ms	(fma 9/40 (pow x 2) (- (cbrt (pow (fma 27/2800 (pow x 4) 1/2) 3))))

simplify188.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (24.0ms)

Iter	Nodes	Cost
0	170	394
1	637	363
2	4312	356
3	5001	356

prune166.0ms

Filtered

80 candidates to 48 candidates (60.0%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	80	0	80
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	80	5	85

Merged error: 0.0b

Counts

85 → 5

regimes65.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.9b

bsearch71.0ms

Steps

Iters	Range		Point
7	0.00999808388340962	0.475758948552502	0.029426069937885588
9	-164485.30314980465	-0.009598081335721272	-0.027401026806997613

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	12
1	28	12

end0.0ms

sample6.7s

Algorithm

intervals

Results

4.2s	1624×	body	2560	valid
1.6s	2730×	body	1280	valid
477.0ms	1911×	body	640	valid
155.0ms	940×	body	320	valid
50.0ms	440×	body	160	valid
25.0ms	355×	body	80	valid