Details

sample405.0ms

Algorithm

intervals

Results

85.0ms	45×	body	2560	valid
43.0ms	88×	body	1280	valid
14.0ms	59×	body	640	valid
7.0ms	31×	body	320	valid
2.0ms	18×	body	160	valid
1.0ms	15×	body	80	valid

simplify10.0ms

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

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: 31.4b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.5b	(- x (tan x))
1.5b	(- x (sin x))

rewrite22.0ms

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)))
3.0ms	(- x (tan x))
6.0ms	(- x (sin x))

series188.0ms

Counts

3 → 9

Calls

3 calls:

74.0ms	(/ (- x (sin x)) (- x (tan x)))
57.0ms	(- x (tan x))
57.0ms	(- x (sin x))

simplify151.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	363	718
1	1148	685
2	4795	685
3	5001	685

prune212.0ms

Filtered

89 candidates to 63 candidates (70.8%)

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: 0.0b

Counts

90 → 4

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (/ (- x (sin x)) (- x (tan x))) 3)
0.0b	(cbrt (pow (/ (- x (sin x)) (- x (tan x))) 3))
1.5b	(- x (tan x))
1.5b	(- x (sin x))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

134×	`add-sqr-sqrt` `*-un-lft-identity`
100×	`times-frac`
68×	`cbrt-prod`
62×	`unpow-prod-down` `cube-prod`
50×	`add-cube-cbrt`
42×	`distribute-lft-out--` `difference-of-squares`
8×	`associate-/r/` `add-log-exp`
7×	`add-exp-log` `add-cbrt-cube`
6×	`flip3--` `flip--`
5×	`pow1`
4×	`div-inv`
3×	`pow-unpow`
2×	`cube-div` `cube-mult` `sub-neg` `diff-log` `unpow3` `pow-exp` `rem-cube-cbrt` `sqr-pow`
1×	`cbrt-undiv` `pow-to-exp` `cbrt-div` `pow-pow` `pow1/3` `div-exp` `rem-cbrt-cube`

Counts

4 → 188

Calls

4 calls:

11.0ms	(pow (/ (- x (sin x)) (- x (tan x))) 3)
12.0ms	(cbrt (pow (/ (- x (sin x)) (- x (tan x))) 3))
3.0ms	(- x (tan x))
4.0ms	(- x (sin x))

series250.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(pow (/ (- x (sin x)) (- x (tan x))) 3)
76.0ms	(cbrt (pow (/ (- x (sin x)) (- x (tan x))) 3))
53.0ms	(- x (tan x))
31.0ms	(- x (sin x))

simplify80.0ms

Algorithm

egg-herbie

Counts

200 → 200

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	736	2195
1	3051	2083
2	5001	2069

prune302.0ms

Filtered

200 candidates to 85 candidates (42.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	200	0	200
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	200	4	204

Merged error: 0.0b

Counts

204 → 4

localize11.0ms

Local error

Found 4 expressions with local error:

1.5b	(- x (tan x))
1.5b	(- x (tan x))
1.5b	(- x (sin x))
1.5b	(- x (sin 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))
3.0ms	(- x (tan x))
4.0ms	(- x (sin x))
4.0ms	(- x (sin x))

series169.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(- x (tan x))
54.0ms	(- x (tan x))
30.0ms	(- x (sin x))
34.0ms	(- x (sin x))

simplify72.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	150	314
1	342	294
2	774	294
3	2023	294
4	5001	294

prune188.0ms

Filtered

68 candidates to 50 candidates (73.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	68	0	68
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	68	4	72

Merged error: 0.0b

Counts

72 → 4

localize10.0ms

Local error

Found 3 expressions with local error:

0.3b	(* 27/2800 (pow x 4))
0.4b	(* 9/40 (pow x 2))
13.1b	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

rewrite20.0ms

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))

series109.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(* 27/2800 (pow x 4))
29.0ms	(* 9/40 (pow x 2))
44.0ms	(- (* 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	318
2	5001	315

prune142.0ms

Filtered

75 candidates to 46 candidates (61.3%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	75	0	75
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	75	4	79

Merged error: 0.0b

Counts

79 → 4

regimes73.0ms

Accuracy

99.8% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.9b

bsearch77.0ms

Steps

Iters	Range		Point
8	2.0262054515877825e-05	0.3235305135594418	0.020919416033764127
10	-85019.06990604498	-4.503960361653909e-11	-1.5618953286310733

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	26
1	31	26

end0.0ms

sample6.4s

Algorithm

intervals

Results

4.1s	1655×	body	2560	valid
1.5s	2692×	body	1280	valid
448.0ms	1879×	body	640	valid
147.0ms	906×	body	320	valid
63.0ms	505×	body	160	valid
30.0ms	363×	body	80	valid