Details

analyze1.4s

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
0%	100%	0%	4
0%	100%	0%	5
0%	100%	0%	6
0%	100%	0%	7
0%	100%	0%	8
0%	100%	0%	9
0%	100%	0%	10
0%	100%	0%	11
0%	100%	0%	12
0%	100%	0%	13
0.1%	99.9%	0%	14

sample222.0ms

Algorithm

intervals

Results

152.0ms	61×	body	2048	valid
38.0ms	97×	body	1024	valid
10.0ms	41×	body	512	valid
6.0ms	5×	body	4096	valid
4.0ms	28×	body	256	valid
2.0ms	24×	body	128	valid

simplify244.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	1005	14
1	1005	14

prune3.0ms

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: 30.6b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
0.7b	(-.f64 x (sin.f64 x))
0.7b	(-.f64 x (tan.f64 x))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

43×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
25×	`times-frac_binary64`
15×	`add-cube-cbrt_binary64`
14×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
7×	`add-log-exp_binary64`
5×	`associate-/r_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/l_binary64`
4×	`flip3--_binary64` `flip--_binary64`
3×	`pow1_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `diff-log_binary64` `associate-/r/_binary64`
1×	`cbrt-undiv_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

3 → 78

Calls

3 calls:

9.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
4.0ms	(-.f64 x (sin.f64 x))
5.0ms	(-.f64 x (tan.f64 x))

series283.0ms

Counts

3 → 9

Calls

3 calls:

120.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
41.0ms	(-.f64 x (sin.f64 x))
122.0ms	(-.f64 x (tan.f64 x))

simplify55.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	4906	1795
1	4906	1795

prune71.0ms

Filtered

63 candidates to 87 candidates (-38.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	83	4	87
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	84	4	88

Merged error: 0.0b

Counts

88 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

0.7b	(-.f64 x (sin.f64 x))
0.7b	(-.f64 x (tan.f64 x))
0.7b	(-.f64 x (tan.f64 x))
0.7b	(-.f64 x (tan.f64 x))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `add-sqr-sqrt_binary64`
4×	`sub-neg_binary64` `pow1_binary64` `flip3--_binary64` `diff-log_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `flip--_binary64`

Counts

4 → 52

Calls

4 calls:

4.0ms	(-.f64 x (sin.f64 x))
4.0ms	(-.f64 x (tan.f64 x))
4.0ms	(-.f64 x (tan.f64 x))
4.0ms	(-.f64 x (tan.f64 x))

series323.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(-.f64 x (sin.f64 x))
95.0ms	(-.f64 x (tan.f64 x))
93.0ms	(-.f64 x (tan.f64 x))
91.0ms	(-.f64 x (tan.f64 x))

simplify121.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (109.0ms)

Iter	Nodes	Cost
0	4886	798
1	4886	798

prune52.0ms

Filtered

51 candidates to 64 candidates (-25.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	64	0	64
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	64	4	68

Merged error: 0.0b

Counts

68 → 4

localize11.0ms

Local error

Found 4 expressions with local error:

0.7b	(-.f64 x (sin.f64 x))
0.7b	(-.f64 x (sin.f64 x))
0.7b	(-.f64 x (tan.f64 x))
0.7b	(-.f64 x (tan.f64 x))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `add-sqr-sqrt_binary64`
4×	`sub-neg_binary64` `pow1_binary64` `flip3--_binary64` `diff-log_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `flip--_binary64`

Counts

4 → 52

Calls

4 calls:

4.0ms	(-.f64 x (sin.f64 x))
4.0ms	(-.f64 x (sin.f64 x))
5.0ms	(-.f64 x (tan.f64 x))
4.0ms	(-.f64 x (tan.f64 x))

series263.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(-.f64 x (sin.f64 x))
44.0ms	(-.f64 x (sin.f64 x))
86.0ms	(-.f64 x (tan.f64 x))
93.0ms	(-.f64 x (tan.f64 x))

simplify120.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (107.0ms)

Iter	Nodes	Cost
0	4886	788
1	4886	788

prune51.0ms

Filtered

50 candidates to 64 candidates (-28.0%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	63	1	64
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	63	5	68

Merged error: 0.0b

Counts

68 → 5

localize9.0ms

Local error

Found 3 expressions with local error:

0.1b	(*.f64 27/2800 (pow.f64 x 4))
0.2b	(.f64 (.f64 x x) 9/40)
15.6b	(-.f64 (.f64 (.f64 x x) 9/40) (+.f64 1/2 (*.f64 27/2800 (pow.f64 x 4))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-exp-log_binary64` `add-sqr-sqrt_binary64`
10×	`associate-r_binary64` `add-cbrt-cube_binary64`
8×	`add-log-exp_binary64` `pow1_binary64`
7×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
6×	`prod-exp_binary64`
4×	`cbrt-unprod_binary64` `associate-l_binary64` `unswap-sqr_binary64` `unpow-prod-down_binary64`
3×	`pow-prod-down_binary64`
2×	`diff-log_binary64` `sqr-pow_binary64` `*-commutative_binary64`
1×	`pow-to-exp_binary64` `sub-neg_binary64` `associate--r+_binary64` `flip3--_binary64` `flip--_binary64` `pow-exp_binary64` `sum-log_binary64`

Counts

3 → 57

Calls

3 calls:

6.0ms	(*.f64 27/2800 (pow.f64 x 4))
6.0ms	(.f64 (.f64 x x) 9/40)
8.0ms	(-.f64 (.f64 (.f64 x x) 9/40) (+.f64 1/2 (*.f64 27/2800 (pow.f64 x 4))))

series157.0ms

Counts

3 → 9

Calls

3 calls:

58.0ms	(*.f64 27/2800 (pow.f64 x 4))
43.0ms	(.f64 (.f64 x x) 9/40)
55.0ms	(-.f64 (.f64 (.f64 x x) 9/40) (+.f64 1/2 (*.f64 27/2800 (pow.f64 x 4))))

simplify38.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5030	850

prune43.0ms

Filtered

40 candidates to 66 candidates (-65.0%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	66	5	71

Merged error: 0.0b

Counts

71 → 5

regimes47.0ms

Accuracy

99.8% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.8b

bsearch41.0ms

Steps

Iters	Range		Point
6	1.3135555284638416	9.891400668724321	1.5647396308575419
9	-65044.889277887894	-0.04862812317942692	-1.5635775292958538

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	90	67
1	90	67

end0.0ms

sample6.0s

Algorithm

intervals

Results

4.0s	1972×	body	2048	valid
1.2s	2958×	body	1024	valid
338.0ms	1590×	body	512	valid
123.0ms	95×	body	4096	valid
97.0ms	705×	body	256	valid
56.0ms	680×	body	128	valid

Details

analyze1.4s

sample222.0ms

simplify244.0ms

prune3.0ms

localize10.0ms

rewrite26.0ms

series283.0ms

simplify55.0ms

prune71.0ms

localize13.0ms

rewrite20.0ms

series323.0ms

simplify121.0ms

prune52.0ms

localize11.0ms

rewrite22.0ms

series263.0ms

simplify120.0ms

prune51.0ms

localize9.0ms

rewrite23.0ms

series157.0ms

simplify38.0ms

prune43.0ms

regimes47.0ms

bsearch41.0ms

simplify3.0ms

end0.0ms

sample6.0s

Profiling