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

sample25.0ms

Algorithm

intervals

Results

8.0ms	52×	body	1280	valid
5.0ms	40×	body	640	valid
5.0ms	139×	body	80	valid
2.0ms	18×	body	320	valid
0.0ms	7×	body	160	valid

simplify85.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	682	19
1	682	19

prune1.0ms

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: 27.8b

Counts

2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(/.f64 x (+.f64 x 1))
0.0b	(/.f64 (+.f64 x 1) (-.f64 x 1))
2.0b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

110×	`*-un-lft-identity_binary64`
60×	`times-frac_binary64`
57×	`add-sqr-sqrt_binary64`
25×	`add-cube-cbrt_binary64`
20×	`distribute-lft-out_binary64`
18×	`distribute-lft-out--_binary64`
14×	`difference-of-squares_binary64`
11×	`associate-/r*_binary64`
7×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/l*_binary64`
5×	`add-log-exp_binary64` `difference-of-sqr-1_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 → 113

Calls

3 calls:

5.0ms	(/.f64 x (+.f64 x 1))
9.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
39.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

series59.0ms

Counts

3 → 9

Calls

3 calls:

11.0ms	(/.f64 x (+.f64 x 1))
11.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
37.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

simplify94.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4950	2299
1	4950	2299

prune129.0ms

Filtered

77 candidates to 122 candidates (-58.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	119	3	122
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	120	3	123

Merged error: 0.0b

Counts

123 → 3

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (/.f64 x (sqrt.f64 (+.f64 x 1))) (sqrt.f64 (+.f64 x 1)))
0.0b	(/.f64 (+.f64 x 1) (-.f64 x 1))
0.1b	(/.f64 x (sqrt.f64 (+.f64 x 1)))
6.8b	(-.f64 (/.f64 (/.f64 x (sqrt.f64 (+.f64 x 1))) (sqrt.f64 (+.f64 x 1))) (/.f64 (+.f64 x 1) (-.f64 x 1)))

rewrite314.0ms

Algorithm

rewrite-expression-head

Rules

441×	`times-frac_binary64`
366×	`*-un-lft-identity_binary64`
276×	`add-sqr-sqrt_binary64`
234×	`sqrt-prod_binary64`
201×	`add-cube-cbrt_binary64`
66×	`distribute-lft-out_binary64`
34×	`associate-/l*_binary64`
24×	`difference-of-squares_binary64`
22×	`associate-/r/_binary64`
21×	`associate-/r*_binary64`
20×	`sqrt-div_binary64`
13×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
12×	`distribute-lft-out--_binary64`
11×	`flip3-+_binary64` `div-inv_binary64` `flip-+_binary64`
6×	`add-log-exp_binary64`
5×	`cbrt-undiv_binary64` `difference-of-sqr-1_binary64` `div-exp_binary64`
4×	`pow1_binary64`
3×	`associate-/l/_binary64` `clear-num_binary64` `frac-2neg_binary64`
2×	`flip3--_binary64` `flip--_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `frac-sub_binary64`

Counts

4 → 371

Calls

4 calls:

19.0ms	(/.f64 (/.f64 x (sqrt.f64 (+.f64 x 1))) (sqrt.f64 (+.f64 x 1)))
8.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
7.0ms	(/.f64 x (sqrt.f64 (+.f64 x 1)))
256.0ms	(-.f64 (/.f64 (/.f64 x (sqrt.f64 (+.f64 x 1))) (sqrt.f64 (+.f64 x 1))) (/.f64 (+.f64 x 1) (-.f64 x 1)))

series88.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(/.f64 (/.f64 x (sqrt.f64 (+.f64 x 1))) (sqrt.f64 (+.f64 x 1)))
11.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
26.0ms	(/.f64 x (sqrt.f64 (+.f64 x 1)))
38.0ms	(-.f64 (/.f64 (/.f64 x (sqrt.f64 (+.f64 x 1))) (sqrt.f64 (+.f64 x 1))) (/.f64 (+.f64 x 1) (-.f64 x 1)))

simplify159.0ms

Algorithm

egg-herbie

Counts

383 → 383

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4956	10112
1	4956	10112

prune273.0ms

Filtered

170 candidates to 383 candidates (-125.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	383	0	383
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	383	3	386

Merged error: 0.0b

Counts

386 → 3

localize4.0ms

Local error

Found 1 expressions with local error:

0.0b	(*.f64 x (+.f64 x 3))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

5×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
4×	`associate-r_binary64`
3×	`pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-l_binary64`
2×	`associate-*r/_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64` `distribute-lft-out_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `flip-+_binary64` `*-commutative_binary64`

Counts

1 → 23

Calls

1 calls:

6.0ms

(*.f64 x (+.f64 x 3))

series32.0ms

Counts

1 → 3

Calls

1 calls:

32.0ms

(*.f64 x (+.f64 x 3))

simplify78.0ms

Algorithm

egg-herbie

Counts

26 → 26

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4860	233
1	4860	233

prune15.0ms

Filtered

16 candidates to 26 candidates (-62.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	26	0	26
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	26	3	29

Merged error: 0.0b

Counts

29 → 3

localize9.0ms

Local error

Found 3 expressions with local error:

0.1b	(/.f64 3 (pow.f64 x 3))
0.5b	(/.f64 -1 (*.f64 x x))
6.0b	(-.f64 (/.f64 -1 (*.f64 x x)) (+.f64 (/.f64 3 x) (/.f64 3 (pow.f64 x 3))))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

40×	`times-frac_binary64`
35×	`*-un-lft-identity_binary64`
34×	`add-sqr-sqrt_binary64`
30×	`add-cube-cbrt_binary64`
13×	`associate-/r*_binary64` `add-exp-log_binary64`
12×	`unpow-prod-down_binary64` `cube-prod_binary64`
10×	`add-cbrt-cube_binary64`
8×	`add-log-exp_binary64`
6×	`associate-/l*_binary64`
5×	`div-exp_binary64`
4×	`sqr-pow_binary64` `unpow3_binary64` `cube-mult_binary64`
3×	`pow1_binary64` `cbrt-undiv_binary64` `frac-sub_binary64`
2×	`diff-log_binary64` `clear-num_binary64` `frac-2neg_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `div-inv_binary64`
1×	`pow-to-exp_binary64` `flip3-+_binary64` `sub-neg_binary64` `associate--r+_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `distribute-lft-out_binary64` `frac-add_binary64` `prod-exp_binary64` `flip--_binary64` `flip-+_binary64` `pow-exp_binary64` `sum-log_binary64`

Counts

3 → 106

Calls

3 calls:

6.0ms	(/.f64 3 (pow.f64 x 3))
5.0ms	(/.f64 -1 (*.f64 x x))
36.0ms	(-.f64 (/.f64 -1 (*.f64 x x)) (+.f64 (/.f64 3 x) (/.f64 3 (pow.f64 x 3))))

series67.0ms

Counts

3 → 9

Calls

3 calls:

28.0ms	(/.f64 3 (pow.f64 x 3))
20.0ms	(/.f64 -1 (*.f64 x x))
19.0ms	(-.f64 (/.f64 -1 (*.f64 x x)) (+.f64 (/.f64 3 x) (/.f64 3 (pow.f64 x 3))))

simplify58.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5251	1838

prune76.0ms

Filtered

68 candidates to 115 candidates (-69.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	115	0	115
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	115	3	118

Merged error: 0.0b

Counts

118 → 3

regimes20.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 30.0b

bsearch36.0ms

Steps

Iters	Range		Point
10	50.57574215350042	2.327231155695825e+16	8787.729879989492
9	-8420823.156456362	-0.02529614964935762	-1.0242786945796234

simplify5.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	91	65
1	91	65

end0.0ms

sample739.0ms

Algorithm

intervals

Results

270.0ms	1669×	body	1280	valid
154.0ms	1215×	body	640	valid
138.0ms	4203×	body	80	valid
56.0ms	596×	body	320	valid
20.0ms	317×	body	160	valid

Details

analyze4.0ms

sample25.0ms

simplify85.0ms

prune1.0ms

localize6.0ms

rewrite57.0ms

series59.0ms

simplify94.0ms

prune129.0ms

localize11.0ms

rewrite314.0ms

series88.0ms

simplify159.0ms

prune273.0ms

localize4.0ms

rewrite7.0ms

series32.0ms

simplify78.0ms

prune15.0ms

localize9.0ms

rewrite50.0ms

series67.0ms

simplify58.0ms

prune76.0ms

regimes20.0ms

bsearch36.0ms

simplify5.0ms

end0.0ms

sample739.0ms

Profiling