Details

analyze532.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	50%	0%	4
50%	50%	0%	5
50%	50%	0%	6
50%	50%	0%	7
50%	50%	0%	8
50%	50%	0%	9
50%	50%	0%	10
50%	50%	0%	11
50%	50%	0%	12
50%	50%	0%	13
50%	49.9%	0%	14

sample37.0ms

Algorithm

intervals

Results

13.0ms	46×	body	1280	valid
7.0ms	156×	body	80	valid
7.0ms	35×	body	640	valid
2.0ms	14×	body	320	valid
0.0ms	5×	body	160	valid

simplify585.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (129.0ms)

Iter	Nodes	Cost
0	5726	15

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: 0.2b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))
0.1b	(/.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))
0.2b	(*.f64 (tan.f64 x) (tan.f64 x))
0.2b	(*.f64 (tan.f64 x) (tan.f64 x))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt_binary64`
27×	`*-un-lft-identity_binary64`
22×	`add-cube-cbrt_binary64`
18×	`pow1_binary64`
15×	`times-frac_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `difference-of-squares_binary64`
8×	`tan-quot_binary64`
6×	`add-log-exp_binary64` `swap-sqr_binary64` `associate-r_binary64` `associate-l_binary64`
5×	`associate-/l*_binary64`
3×	`associate-/r*_binary64`
2×	`pow-prod-down_binary64` `associate-/l/_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `pow-prod-up_binary64` `associate-r/_binary64` `associate-/r/_binary64` `pow-plus_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `pow-sqr_binary64` `flip--_binary64` `frac-times_binary64` `pow2_binary64` `associate-l/_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `flip-+_binary64`

Counts

4 → 109

Calls

4 calls:

3.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))
7.0ms	(/.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))
6.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
8.0ms	(*.f64 (tan.f64 x) (tan.f64 x))

series91.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))
49.0ms	(/.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))
9.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
22.0ms	(*.f64 (tan.f64 x) (tan.f64 x))

simplify58.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4967	1280
1	4967	1280

prune111.0ms

Filtered

83 candidates to 121 candidates (-45.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	113	8	121
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	114	8	122

Merged error: 0.0b

Counts

122 → 8

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(-.f64 1 (tan.f64 x))
0.2b	(/.f64 (+.f64 1 (pow.f64 (tan.f64 x) 2)) (-.f64 1 (tan.f64 x)))
0.2b	(/.f64 (+.f64 1 (tan.f64 x)) (/.f64 (+.f64 1 (pow.f64 (tan.f64 x) 2)) (-.f64 1 (tan.f64 x))))
0.2b	(pow.f64 (tan.f64 x) 2)

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

318×	`*-un-lft-identity_binary64`
264×	`times-frac_binary64`
182×	`add-sqr-sqrt_binary64`
104×	`add-cube-cbrt_binary64`
68×	`distribute-lft-out_binary64`
52×	`difference-of-squares_binary64`
36×	`associate-/r*_binary64`
26×	`distribute-lft-out--_binary64`
13×	`associate-/r/_binary64`
12×	`add-exp-log_binary64`
11×	`add-cbrt-cube_binary64`
8×	`associate-/l*_binary64`
7×	`flip3--_binary64` `div-inv_binary64` `flip--_binary64`
6×	`add-log-exp_binary64`
5×	`pow1_binary64`
4×	`associate-/l/_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
3×	`pow-unpow_binary64` `unpow-prod-down_binary64`
2×	`flip3-+_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip-+_binary64`
1×	`pow-to-exp_binary64` `sub-neg_binary64` `diff-log_binary64` `unpow2_binary64` `pow-pow_binary64` `sqr-pow_binary64` `pow-exp_binary64`

Counts

4 → 253

Calls

4 calls:

4.0ms	(-.f64 1 (tan.f64 x))
10.0ms	(/.f64 (+.f64 1 (pow.f64 (tan.f64 x) 2)) (-.f64 1 (tan.f64 x)))
18.0ms	(/.f64 (+.f64 1 (tan.f64 x)) (/.f64 (+.f64 1 (pow.f64 (tan.f64 x) 2)) (-.f64 1 (tan.f64 x))))
3.0ms	(pow.f64 (tan.f64 x) 2)

series83.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(-.f64 1 (tan.f64 x))
25.0ms	(/.f64 (+.f64 1 (pow.f64 (tan.f64 x) 2)) (-.f64 1 (tan.f64 x)))
42.0ms	(/.f64 (+.f64 1 (tan.f64 x)) (/.f64 (+.f64 1 (pow.f64 (tan.f64 x) 2)) (-.f64 1 (tan.f64 x))))
9.0ms	(pow.f64 (tan.f64 x) 2)

simplify93.0ms

Algorithm

egg-herbie

Counts

265 → 265

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4972	5877
1	4972	5877

prune172.0ms

Filtered

147 candidates to 265 candidates (-80.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	264	1	265
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	265	8	273

Merged error: 0.0b

Counts

273 → 8

localize9.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (tan.f64 x) 2)
0.2b	(pow.f64 (tan.f64 x) 2)
0.2b	(pow.f64 (tan.f64 x) 2)
0.3b	(-.f64 (/.f64 1 (+.f64 1 (pow.f64 (tan.f64 x) 2))) (/.f64 (pow.f64 (tan.f64 x) 2) (+.f64 1 (pow.f64 (tan.f64 x) 2))))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

53×	`add-sqr-sqrt_binary64`
48×	`*-un-lft-identity_binary64`
36×	`times-frac_binary64`
15×	`difference-of-squares_binary64`
12×	`add-cube-cbrt_binary64` `unpow-prod-down_binary64`
9×	`pow-unpow_binary64`
8×	`distribute-lft-out--_binary64`
7×	`pow1_binary64` `add-exp-log_binary64`
6×	`add-log-exp_binary64` `distribute-rgt-out--_binary64` `unpow2_binary64` `sqr-pow_binary64` `div-inv_binary64`
5×	`distribute-lft-out_binary64`
4×	`add-cbrt-cube_binary64` `associate-/r/_binary64`
3×	`pow-to-exp_binary64` `pow-pow_binary64` `pow-exp_binary64`
2×	`flip3-+_binary64` `flip-+_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `sub-div_binary64` `flip--_binary64` `frac-sub_binary64`

Counts

4 → 96

Calls

4 calls:

3.0ms	(pow.f64 (tan.f64 x) 2)
3.0ms	(pow.f64 (tan.f64 x) 2)
3.0ms	(pow.f64 (tan.f64 x) 2)
42.0ms	(-.f64 (/.f64 1 (+.f64 1 (pow.f64 (tan.f64 x) 2))) (/.f64 (pow.f64 (tan.f64 x) 2) (+.f64 1 (pow.f64 (tan.f64 x) 2))))

series89.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(pow.f64 (tan.f64 x) 2)
9.0ms	(pow.f64 (tan.f64 x) 2)
9.0ms	(pow.f64 (tan.f64 x) 2)
62.0ms	(-.f64 (/.f64 1 (+.f64 1 (pow.f64 (tan.f64 x) 2))) (/.f64 (pow.f64 (tan.f64 x) 2) (+.f64 1 (pow.f64 (tan.f64 x) 2))))

simplify59.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4914	1498
1	4914	1498

prune76.0ms

Filtered

66 candidates to 108 candidates (-63.6%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	107	1	108
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	107	9	116

Merged error: 0b

Counts

116 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2)) (+.f64 1 (pow.f64 (tan.f64 x) 2)))
0.2b	(pow.f64 (tan.f64 x) 2)
0.2b	(pow.f64 (tan.f64 x) 2)
0.2b	(log.f64 (exp.f64 (/.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2)) (+.f64 1 (pow.f64 (tan.f64 x) 2)))))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

148×	`*-un-lft-identity_binary64`
116×	`add-sqr-sqrt_binary64`
96×	`times-frac_binary64`
72×	`difference-of-squares_binary64`
55×	`log-pow_binary64`
54×	`exp-prod_binary64`
44×	`add-cube-cbrt_binary64`
25×	`distribute-lft-out_binary64`
24×	`unpow-prod-down_binary64`
20×	`unpow2_binary64` `sqr-pow_binary64`
12×	`associate-/l*_binary64`
9×	`distribute-lft-out--_binary64`
8×	`add-exp-log_binary64`
7×	`pow1_binary64`
6×	`pow-unpow_binary64` `add-cbrt-cube_binary64`
4×	`associate-/r*_binary64` `add-log-exp_binary64` `associate-/r/_binary64`
3×	`log-prod_binary64`
2×	`pow-to-exp_binary64` `flip3-+_binary64` `associate-/l/_binary64` `pow-pow_binary64` `div-sub_binary64` `div-inv_binary64` `flip-+_binary64` `pow-exp_binary64`
1×	`flip3--_binary64` `cbrt-undiv_binary64` `rem-log-exp_binary64` `exp-diff_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-exp_binary64` `log-div_binary64` `flip--_binary64`

Counts

4 → 184

Calls

4 calls:

13.0ms	(/.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2)) (+.f64 1 (pow.f64 (tan.f64 x) 2)))
3.0ms	(pow.f64 (tan.f64 x) 2)
3.0ms	(pow.f64 (tan.f64 x) 2)
19.0ms	(log.f64 (exp.f64 (/.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2)) (+.f64 1 (pow.f64 (tan.f64 x) 2)))))

series95.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(/.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2)) (+.f64 1 (pow.f64 (tan.f64 x) 2)))
9.0ms	(pow.f64 (tan.f64 x) 2)
9.0ms	(pow.f64 (tan.f64 x) 2)
37.0ms	(log.f64 (exp.f64 (/.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2)) (+.f64 1 (pow.f64 (tan.f64 x) 2)))))

simplify66.0ms

Algorithm

egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5166	2741

prune118.0ms

Filtered

119 candidates to 196 candidates (-64.7%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	196	0	196
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	196	9	205

Merged error: 0b

Counts

205 → 9

regimes77.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	16
1	22	16

end0.0ms

sample1.1s

Algorithm

intervals

Results

405.0ms	1506×	body	1280	valid
230.0ms	1276×	body	640	valid
171.0ms	4283×	body	80	valid
84.0ms	643×	body	320	valid
26.0ms	292×	body	160	valid

Details

analyze532.0ms

sample37.0ms

simplify585.0ms

prune3.0ms

localize10.0ms

rewrite29.0ms

series91.0ms

simplify58.0ms

prune111.0ms

localize10.0ms

rewrite53.0ms

series83.0ms

simplify93.0ms

prune172.0ms

localize9.0ms

rewrite56.0ms

series89.0ms

simplify59.0ms

prune76.0ms

localize11.0ms

rewrite51.0ms

series95.0ms

simplify66.0ms

prune118.0ms

regimes77.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.1s

Profiling