Details

analyze233.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
75%	25%	0%	4
75%	25%	0%	5
75%	25%	0%	6
78.1%	21.9%	0%	7
78.1%	21.9%	0%	8
78.1%	21.9%	0%	9
78.1%	21.9%	0%	10
78.1%	21.9%	0%	11
78.1%	21.9%	0%	12
78.1%	21.9%	0%	13
78.1%	21.8%	0%	14

sample59.0ms

Algorithm

intervals

Results

25.0ms	49×	body	2560	valid
12.0ms	45×	body	1280	valid
9.0ms	52×	body	640	valid
4.0ms	31×	body	320	valid
2.0ms	68×	body	80	valid
1.0ms	11×	body	160	valid

simplify25.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	500	8
1	500	8

prune2.0ms

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: 31.2b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

1.2b	(-.f64 1.0 (cos.f64 x))
16.3b	(/.f64 (-.f64 1.0 (cos.f64 x)) (*.f64 x x))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
7×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`associate-/l*_binary64` `times-frac_binary64`
4×	`add-log-exp_binary64` `add-cube-cbrt_binary64`
3×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
2×	`associate-/l/_binary64` `pow1_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `div-exp_binary64` `flip--_binary64`
1×	`associate-/r*_binary64` `sub-neg_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `div-sub_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64`

Counts

2 → 41

Calls

2 calls:

4.0ms	(-.f64 1.0 (cos.f64 x))
8.0ms	(/.f64 (-.f64 1.0 (cos.f64 x)) (*.f64 x x))

series10.0ms

Counts

2 → 6

Calls

2 calls:

3.0ms	(-.f64 1.0 (cos.f64 x))
7.0ms	(/.f64 (-.f64 1.0 (cos.f64 x)) (*.f64 x x))

simplify58.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4894	437
1	4894	437

prune78.0ms

Filtered

34 candidates to 47 candidates (-38.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	36	11	47
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	37	11	48

Merged error: 0.2b

Counts

48 → 11

localize7.0ms

Local error

Found 3 expressions with local error:

0.1b	(*.f64 (/.f64 1 x) (/.f64 (-.f64 1.0 (cos.f64 x)) x))
0.1b	(/.f64 (-.f64 1.0 (cos.f64 x)) x)
1.2b	(-.f64 1.0 (cos.f64 x))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-sqr-sqrt_binary64`
47×	`*-un-lft-identity_binary64`
46×	`times-frac_binary64`
29×	`add-cube-cbrt_binary64`
27×	`add-exp-log_binary64`
19×	`associate-r_binary64`
17×	`add-cbrt-cube_binary64`
13×	`associate-l_binary64`
9×	`div-exp_binary64`
8×	`prod-exp_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64`
6×	`unswap-sqr_binary64`
5×	`add-log-exp_binary64` `pow1_binary64` `cbrt-undiv_binary64` `associate-/l*_binary64`
4×	`cbrt-unprod_binary64`
3×	`associate-/r*_binary64` `div-inv_binary64`
2×	`associate-/l/_binary64` `flip3--_binary64` `1-exp_binary64` `rec-exp_binary64` `flip--_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `diff-log_binary64` `associate-r/_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `frac-times_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

3 → 113

Calls

3 calls:

14.0ms	(*.f64 (/.f64 1 x) (/.f64 (-.f64 1.0 (cos.f64 x)) x))
6.0ms	(/.f64 (-.f64 1.0 (cos.f64 x)) x)
4.0ms	(-.f64 1.0 (cos.f64 x))

series16.0ms

Counts

3 → 9

Calls

3 calls:

7.0ms	(*.f64 (/.f64 1 x) (/.f64 (-.f64 1.0 (cos.f64 x)) x))
7.0ms	(/.f64 (-.f64 1.0 (cos.f64 x)) x)
3.0ms	(-.f64 1.0 (cos.f64 x))

simplify45.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5658	1207

prune115.0ms

Filtered

81 candidates to 122 candidates (-50.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	116	6	122
Fresh	4	6	10
Picked	1	0	1
Done	0	0	0
Total	121	12	133

Merged error: 0.2b

Counts

133 → 12

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (cos.f64 x) (+.f64 1.0 (cos.f64 x)))
0.3b	(pow.f64 (cos.f64 x) 3)
0.4b	(+.f64 1.0 (cos.f64 x))
1.0b	(-.f64 (pow.f64 1.0 3) (pow.f64 (cos.f64 x) 3))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt_binary64`
23×	`*-un-lft-identity_binary64`
16×	`difference-of-squares_binary64`
15×	`unpow-prod-down_binary64` `cube-prod_binary64`
9×	`add-cube-cbrt_binary64` `sqr-pow_binary64`
8×	`add-log-exp_binary64`
7×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`distribute-lft-out--_binary64`
4×	`associate-r_binary64`
3×	`pow-unpow_binary64` `associate-l_binary64`
2×	`flip3-+_binary64` `distribute-lft-out_binary64` `associate-*r/_binary64` `flip-+_binary64`
1×	`pow-to-exp_binary64` `pow-prod-down_binary64` `difference-cubes_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `pow-pow_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `rem-cube-cbrt_binary64` `prod-exp_binary64` `+-commutative_binary64` `flip--_binary64` `pow-exp_binary64` `unpow3_binary64` `sum-log_binary64` `*-commutative_binary64` `cube-mult_binary64`

Counts

4 → 91

Calls

4 calls:

8.0ms	(*.f64 (cos.f64 x) (+.f64 1.0 (cos.f64 x)))
3.0ms	(pow.f64 (cos.f64 x) 3)
6.0ms	(+.f64 1.0 (cos.f64 x))
12.0ms	(-.f64 (pow.f64 1.0 3) (pow.f64 (cos.f64 x) 3))

series24.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(*.f64 (cos.f64 x) (+.f64 1.0 (cos.f64 x)))
7.0ms	(pow.f64 (cos.f64 x) 3)
2.0ms	(+.f64 1.0 (cos.f64 x))
10.0ms	(-.f64 (pow.f64 1.0 3) (pow.f64 (cos.f64 x) 3))

simplify58.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5011	963

prune126.0ms

Filtered

61 candidates to 103 candidates (-68.9%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	98	5	103
Fresh	1	10	11
Picked	1	0	1
Done	0	0	0
Total	100	15	115

Merged error: 0.1b

Counts

115 → 15

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (pow.f64 (cos.f64 x) 3) 3)
0.3b	(cbrt.f64 (pow.f64 (pow.f64 (cos.f64 x) 3) 3))
0.4b	(+.f64 1.0 (cos.f64 x))
1.0b	(-.f64 (pow.f64 1.0 3) (cbrt.f64 (pow.f64 (pow.f64 (cos.f64 x) 3) 3)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

83×	`add-sqr-sqrt_binary64`
71×	`unpow-prod-down_binary64` `cube-prod_binary64`
70×	`cbrt-prod_binary64`
44×	`difference-of-squares_binary64`
29×	`sqr-pow_binary64`
22×	`*-un-lft-identity_binary64`
18×	`add-cube-cbrt_binary64`
8×	`add-log-exp_binary64`
6×	`add-exp-log_binary64` `unpow3_binary64` `cube-mult_binary64`
5×	`add-cbrt-cube_binary64`
4×	`pow1_binary64` `pow-exp_binary64`
3×	`pow-unpow_binary64`
2×	`pow-to-exp_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `rem-cbrt-cube_binary64` `flip3--_binary64` `diff-log_binary64` `distribute-lft-out_binary64` `pow1/3_binary64` `pow-pow_binary64` `rem-cube-cbrt_binary64` `distribute-lft-out--_binary64` `+-commutative_binary64` `flip--_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 150

Calls

4 calls:

5.0ms	(pow.f64 (pow.f64 (cos.f64 x) 3) 3)
5.0ms	(cbrt.f64 (pow.f64 (pow.f64 (cos.f64 x) 3) 3))
4.0ms	(+.f64 1.0 (cos.f64 x))
23.0ms	(-.f64 (pow.f64 1.0 3) (cbrt.f64 (pow.f64 (pow.f64 (cos.f64 x) 3) 3)))

series35.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(pow.f64 (pow.f64 (cos.f64 x) 3) 3)
7.0ms	(cbrt.f64 (pow.f64 (pow.f64 (cos.f64 x) 3) 3))
2.0ms	(+.f64 1.0 (cos.f64 x))
12.0ms	(-.f64 (pow.f64 1.0 3) (cbrt.f64 (pow.f64 (pow.f64 (cos.f64 x) 3) 3)))

simplify57.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4972	1780
1	4972	1780

prune96.0ms

Filtered

62 candidates to 162 candidates (-161.3%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	161	1	162
Fresh	1	13	14
Picked	0	1	1
Done	0	0	0
Total	162	15	177

Merged error: 0.1b

Counts

177 → 15

regimes138.0ms

Accuracy

98.9% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 31.0b

bsearch34.0ms

Steps

Iters	Range		Point
10	2.98076717192152e-15	30.40509460772629	0.03609453174808888
9	-0.051510977943339656	-4.761091517906183e-09	-0.03510726007850325

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	95	74
1	95	74

end0.0ms

sample1.8s

Algorithm

intervals

Results

789.0ms	1565×	body	2560	valid
347.0ms	1324×	body	1280	valid
249.0ms	1493×	body	640	valid
110.0ms	908×	body	320	valid
89.0ms	2278×	body	80	valid
35.0ms	432×	body	160	valid

Details

analyze233.0ms

sample59.0ms

simplify25.0ms

prune2.0ms

localize6.0ms

rewrite13.0ms

series10.0ms

simplify58.0ms

prune78.0ms

localize7.0ms

rewrite31.0ms

series16.0ms

simplify45.0ms

prune115.0ms

localize15.0ms

rewrite32.0ms

series24.0ms

simplify58.0ms

prune126.0ms

localize17.0ms

rewrite44.0ms

series35.0ms

simplify57.0ms

prune96.0ms

regimes138.0ms

bsearch34.0ms

simplify3.0ms

end0.0ms

sample1.8s

Profiling