Details

sample10.8s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 0.219727%

Results

168.0ms	60×	body	2560	valid
51.0ms	84×	body	1280	valid
23.0ms	64×	body	640	valid
4.0ms	24×	body	320	valid
2.0ms	15×	body	160	valid
1.0ms	9×	body	80	valid

simplify487.0ms

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: 32.3b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.6b	(- x (tan x))
1.6b	(- x (sin x))

rewrite19.0ms

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))
5.0ms	(- x (sin x))

series37.0ms

Counts

3 → 9

Calls

3 calls:

12.0ms	(/ (- x (sin x)) (- x (tan x)))
11.0ms	(- x (tan x))
13.0ms	(- x (sin x))

simplify142.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 1 (8.0ms)

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

prune101.0ms

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: 0.0b

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))
15.1b	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

rewrite17.0ms

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

series15.0ms

Counts

3 → 9

Calls

3 calls:

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

simplify40.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 2 (34.0ms)

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

prune112.0ms

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: 0.0b

Counts

79 → 5

localize9.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 27/2800 (pow x 4))
0.1b	(* 9/40 (pow x 2))
15.1b	(- (* 9/40 (pow x 2)) (* 27/2800 (pow x 4)))

rewrite15.0ms

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`
7×	`add-cbrt-cube` `unswap-sqr`
6×	`associate-l` `prod-exp`
5×	`add-log-exp`
4×	`sqr-pow`
3×	`pow1`
2×	`pow-to-exp` `pow-exp` `*-commutative` `cbrt-unprod` `unpow2`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

3 → 64

Calls

3 calls:

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)))

series16.0ms

Counts

3 → 9

Calls

3 calls:

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)))

simplify40.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	249	308
1	1003	278
2	5001	273

prune104.0ms

Filtered

45 candidates to 73 candidates (-62.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	73	0	73
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	73	5	78

Merged error: 0.0b

Counts

78 → 5

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (exp (- (* 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))
15.1b	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 84

Calls

4 calls:

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

series18.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify43.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	304	534
1	1244	477
2	5001	474

prune148.0ms

Filtered

60 candidates to 96 candidates (-60.0%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	95	1	96
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	96	5	101

Merged error: 0.0b

Counts

101 → 5

regimes51.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.6b

bsearch66.0ms

Steps

Iters	Range		Point
10	9.769643162898516e-11	668520.6088970661	0.02893033204655101
9	-2361.549549310402	-0.011074949245274652	-0.02844530949916754

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	12
1	32	12

end0.0ms

sample17.5s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 0.219727%

Results

4.1s	1662×	body	2560	valid
1.9s	2736×	body	1280	valid
496.0ms	1888×	body	640	valid
163.0ms	936×	body	320	valid
56.0ms	450×	body	160	valid
25.0ms	328×	body	80	valid

Details

sample10.8s

simplify487.0ms

prune4.0ms

localize10.0ms

rewrite19.0ms

series37.0ms

simplify142.0ms

prune101.0ms

localize9.0ms

rewrite17.0ms

series15.0ms

simplify40.0ms

prune112.0ms

localize9.0ms

rewrite15.0ms

series16.0ms

simplify40.0ms

prune104.0ms

localize12.0ms

rewrite25.0ms

series18.0ms

simplify43.0ms

prune148.0ms

regimes51.0ms

bsearch66.0ms

simplify2.0ms

end0.0ms

sample17.5s

Profiling