Details

analyze4.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0%	14

sample30.0ms

Algorithm

intervals

Results

7.0ms	49×	body	1280	valid
6.0ms	18×	body	320	valid
5.0ms	48×	body	640	valid
4.0ms	129×	body	80	valid
1.0ms	12×	body	160	valid

simplify101.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (99.0ms)

Iter	Nodes	Cost
0	1001	13
1	1001	13

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: 29.7b

Counts

2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(/.f64 x (+.f64 x 1.0))
0.0b	(/.f64 (+.f64 x 1.0) (-.f64 x 1.0))
2.6b	(-.f64 (/.f64 x (+.f64 x 1.0)) (/.f64 (+.f64 x 1.0) (-.f64 x 1.0)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

99×	`*-un-lft-identity_binary64`
52×	`times-frac_binary64`
45×	`add-sqr-sqrt_binary64`
23×	`add-cube-cbrt_binary64`
18×	`distribute-lft-out_binary64` `distribute-lft-out--_binary64`
9×	`associate-/r*_binary64` `difference-of-squares_binary64`
7×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/l*_binary64`
5×	`add-log-exp_binary64`
4×	`associate-/r/_binary64`
3×	`pow1_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `flip--_binary64` `flip-+_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `frac-sub_binary64`

Counts

3 → 103

Calls

3 calls:

5.0ms	(/.f64 x (+.f64 x 1.0))
8.0ms	(/.f64 (+.f64 x 1.0) (-.f64 x 1.0))
30.0ms	(-.f64 (/.f64 x (+.f64 x 1.0)) (/.f64 (+.f64 x 1.0) (-.f64 x 1.0)))

series19.0ms

Counts

3 → 9

Calls

3 calls:

3.0ms	(/.f64 x (+.f64 x 1.0))
3.0ms	(/.f64 (+.f64 x 1.0) (-.f64 x 1.0))
12.0ms	(-.f64 (/.f64 x (+.f64 x 1.0)) (/.f64 (+.f64 x 1.0) (-.f64 x 1.0)))

simplify60.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4955	1404
1	4955	1404

prune148.0ms

Filtered

76 candidates to 112 candidates (-47.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	106	6	112
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	107	6	113

Merged error: 0.3b

Counts

113 → 6

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 (/.f64 (+.f64 x 1.0) (-.f64 x 1.0)) 3)
0.0b	(*.f64 (/.f64 x (+.f64 x 1.0)) (/.f64 x (+.f64 x 1.0)))
0.1b	(pow.f64 (/.f64 x (+.f64 x 1.0)) 3)
2.5b	(-.f64 (pow.f64 (/.f64 x (+.f64 x 1.0)) 3) (pow.f64 (/.f64 (+.f64 x 1.0) (-.f64 x 1.0)) 3))

rewrite157.0ms

Algorithm

rewrite-expression-head

Rules

354×	`*-un-lft-identity_binary64`
216×	`times-frac_binary64`
190×	`add-sqr-sqrt_binary64`
104×	`unpow-prod-down_binary64` `cube-prod_binary64`
78×	`add-cube-cbrt_binary64`
66×	`distribute-lft-out_binary64`
61×	`distribute-lft-out--_binary64`
44×	`difference-of-squares_binary64`
24×	`swap-sqr_binary64`
22×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
18×	`associate-r_binary64` `associate-l_binary64`
16×	`associate-/r/_binary64`
14×	`sqr-pow_binary64`
13×	`pow1_binary64`
8×	`div-inv_binary64`
6×	`flip3-+_binary64` `pow-unpow_binary64` `add-log-exp_binary64` `cbrt-undiv_binary64` `div-exp_binary64` `flip-+_binary64`
4×	`cbrt-unprod_binary64` `cube-div_binary64` `unswap-sqr_binary64` `rem-cube-cbrt_binary64` `prod-exp_binary64` `pow-exp_binary64`
3×	`flip3--_binary64` `flip--_binary64`
2×	`pow-to-exp_binary64` `pow-pow_binary64` `unpow3_binary64` `cube-mult_binary64`
1×	`pow-prod-down_binary64` `difference-cubes_binary64` `sub-neg_binary64` `diff-log_binary64` `pow-prod-up_binary64` `associate-r/_binary64` `pow-plus_binary64` `pow-sqr_binary64` `frac-sub_binary64` `frac-times_binary64` `pow2_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

4 → 302

Calls

4 calls:

10.0ms	(pow.f64 (/.f64 (+.f64 x 1.0) (-.f64 x 1.0)) 3)
17.0ms	(*.f64 (/.f64 x (+.f64 x 1.0)) (/.f64 x (+.f64 x 1.0)))
7.0ms	(pow.f64 (/.f64 x (+.f64 x 1.0)) 3)
101.0ms	(-.f64 (pow.f64 (/.f64 x (+.f64 x 1.0)) 3) (pow.f64 (/.f64 (+.f64 x 1.0) (-.f64 x 1.0)) 3))

series30.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(pow.f64 (/.f64 (+.f64 x 1.0) (-.f64 x 1.0)) 3)
4.0ms	(*.f64 (/.f64 x (+.f64 x 1.0)) (/.f64 x (+.f64 x 1.0)))
4.0ms	(pow.f64 (/.f64 x (+.f64 x 1.0)) 3)
18.0ms	(-.f64 (pow.f64 (/.f64 x (+.f64 x 1.0)) 3) (pow.f64 (/.f64 (+.f64 x 1.0) (-.f64 x 1.0)) 3))

simplify74.0ms

Algorithm

egg-herbie

Counts

314 → 314

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5059	5149

prune382.0ms

Filtered

132 candidates to 314 candidates (-137.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	311	3	314
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	313	7	320

Merged error: 0.1b

Counts

320 → 7

localize28.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt.f64 x)
0.7b	(cbrt.f64 x)
0.7b	(cbrt.f64 x)
2.5b	(-.f64 (pow.f64 (/.f64 x (+.f64 x 1.0)) 3) (pow.f64 (/.f64 (+.f64 x 1.0) (-.f64 x 1.0)) 3))

rewrite300.0ms

Algorithm

rewrite-expression-head

Rules

193×	`*-un-lft-identity_binary64`
91×	`add-sqr-sqrt_binary64`
88×	`times-frac_binary64`
60×	`unpow-prod-down_binary64` `cube-prod_binary64`
53×	`distribute-lft-out--_binary64`
36×	`difference-of-squares_binary64`
32×	`distribute-lft-out_binary64`
12×	`sqr-pow_binary64`
9×	`cbrt-prod_binary64`
7×	`add-cube-cbrt_binary64`
6×	`add-log-exp_binary64`
4×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`pow1/3_binary64`
2×	`cube-div_binary64`
1×	`difference-cubes_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `flip--_binary64` `frac-sub_binary64`

Counts

4 → 119

Calls

4 calls:

1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)
100.0ms	(-.f64 (pow.f64 (/.f64 x (+.f64 x 1.0)) 3) (pow.f64 (/.f64 (+.f64 x 1.0) (-.f64 x 1.0)) 3))

series108.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(cbrt.f64 x)
32.0ms	(cbrt.f64 x)
29.0ms	(cbrt.f64 x)
18.0ms	(-.f64 (pow.f64 (/.f64 x (+.f64 x 1.0)) 3) (pow.f64 (/.f64 (+.f64 x 1.0) (-.f64 x 1.0)) 3))

simplify34.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (17.0ms)

Iter	Nodes	Cost
0	5072	2557

prune207.0ms

Filtered

68 candidates to 131 candidates (-92.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	130	1	131
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	131	7	138

Merged error: 0.1b

Counts

138 → 7

localize31.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt.f64 x)
0.7b	(cbrt.f64 x)
2.5b	(log.f64 (exp.f64 (-.f64 (pow.f64 (/.f64 x (+.f64 x 1.0)) 3) (pow.f64 (/.f64 (+.f64 x 1.0) (-.f64 x 1.0)) 3))))
2.5b	(-.f64 (pow.f64 (/.f64 x (+.f64 x 1.0)) 3) (pow.f64 (/.f64 (+.f64 x 1.0) (-.f64 x 1.0)) 3))

rewrite230.0ms

Algorithm

rewrite-expression-head

Rules

380×	`*-un-lft-identity_binary64`
176×	`add-sqr-sqrt_binary64` `times-frac_binary64`
120×	`unpow-prod-down_binary64` `cube-prod_binary64`
106×	`distribute-lft-out--_binary64`
78×	`log-pow_binary64`
77×	`exp-prod_binary64`
72×	`difference-of-squares_binary64`
64×	`distribute-lft-out_binary64`
24×	`sqr-pow_binary64`
8×	`add-cube-cbrt_binary64`
6×	`add-log-exp_binary64` `cbrt-prod_binary64`
5×	`pow1_binary64`
4×	`log-prod_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
2×	`difference-cubes_binary64` `sub-neg_binary64` `pow1/3_binary64` `cube-div_binary64`
1×	`flip3--_binary64` `diff-log_binary64` `rem-log-exp_binary64` `exp-diff_binary64` `exp-sum_binary64` `log-div_binary64` `flip--_binary64` `frac-sub_binary64`

Counts

4 → 199

Calls

4 calls:

1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)
107.0ms	(log.f64 (exp.f64 (-.f64 (pow.f64 (/.f64 x (+.f64 x 1.0)) 3) (pow.f64 (/.f64 (+.f64 x 1.0) (-.f64 x 1.0)) 3))))
102.0ms	(-.f64 (pow.f64 (/.f64 x (+.f64 x 1.0)) 3) (pow.f64 (/.f64 (+.f64 x 1.0) (-.f64 x 1.0)) 3))

series98.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(cbrt.f64 x)
34.0ms	(cbrt.f64 x)
17.0ms	(log.f64 (exp.f64 (-.f64 (pow.f64 (/.f64 x (+.f64 x 1.0)) 3) (pow.f64 (/.f64 (+.f64 x 1.0) (-.f64 x 1.0)) 3))))
18.0ms	(-.f64 (pow.f64 (/.f64 x (+.f64 x 1.0)) 3) (pow.f64 (/.f64 (+.f64 x 1.0) (-.f64 x 1.0)) 3))

simplify46.0ms

Algorithm

egg-herbie

Counts

211 → 211

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	5340	3664

prune302.0ms

Filtered

89 candidates to 211 candidates (-137.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	211	0	211
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	211	7	218

Merged error: 0.1b

Counts

218 → 7

regimes55.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 29.0b

bsearch23.0ms

Steps

Iters	Range		Point
6	6804.156044569223	82961.0911706557	14875.083937536368
8	-3761650.680535558	-5468.27390325817	-29361.18241715501

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	237	98
1	237	98

end0.0ms

sample704.0ms

Algorithm

intervals

Results

257.0ms	1706×	body	1280	valid
142.0ms	1233×	body	640	valid
130.0ms	4145×	body	80	valid
58.0ms	624×	body	320	valid
17.0ms	292×	body	160	valid

Details

analyze4.0ms

sample30.0ms

simplify101.0ms

prune2.0ms

localize6.0ms

rewrite47.0ms

series19.0ms

simplify60.0ms

prune148.0ms

localize16.0ms

rewrite157.0ms

series30.0ms

simplify74.0ms

prune382.0ms

localize28.0ms

rewrite300.0ms

series108.0ms

simplify34.0ms

prune207.0ms

localize31.0ms

rewrite230.0ms

series98.0ms

simplify46.0ms

prune302.0ms

regimes55.0ms

bsearch23.0ms

simplify4.0ms

end0.0ms

sample704.0ms

Profiling