Details

analyze561.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
3.1%	90.5%	6.3%	6
4.7%	85.9%	9.5%	7
21.1%	64%	14.9%	8
23.4%	58.9%	17.7%	9
27.7%	51.3%	21%	10
28.9%	48.5%	22.6%	11
31.1%	44.4%	24.5%	12
31.7%	42.9%	25.4%	13
32.7%	41%	26.3%	14

sample58.0ms

Algorithm

intervals

Results

22.0ms	59×	body	1024	valid
8.0ms	140×	body	128	valid
7.0ms	31×	body	512	valid
5.0ms	6×	body	2048	valid
3.0ms	20×	body	256	valid
2.0ms	10×	body	512	invalid
1.0ms	4×	body	1024	invalid
1.0ms	9×	body	256	invalid
0.0ms	8×	body	128	invalid
0.0ms	7×	body	128	nan

simplify53.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4988	13
1	4988	13

prune3.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 10.6b

Counts

2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) x)
0.0b	(/.f64 x (+.f64 x y))
6.2b	(pow.f64 (/.f64 x (+.f64 x y)) x)

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac_binary64`
118×	`*-un-lft-identity_binary64`
90×	`unpow-prod-down_binary64`
80×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
25×	`associate-/l*_binary64`
19×	`distribute-lft-out_binary64`
16×	`add-exp-log_binary64`
12×	`associate-/r/_binary64`
7×	`associate-/r*_binary64` `add-cbrt-cube_binary64` `div-inv_binary64` `div-exp_binary64`
6×	`flip3-+_binary64` `flip-+_binary64`
5×	`sqr-pow_binary64`
4×	`pow1_binary64` `pow-exp_binary64`
3×	`pow-unpow_binary64` `add-log-exp_binary64`
2×	`pow-to-exp_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`pow-pow_binary64`

Counts

3 → 172

Calls

3 calls:

14.0ms	(/.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) x)
10.0ms	(/.f64 x (+.f64 x y))
8.0ms	(pow.f64 (/.f64 x (+.f64 x y)) x)

series699.0ms

Counts

3 → 9

Calls

3 calls:

264.0ms	(/.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) x)
60.0ms	(/.f64 x (+.f64 x y))
375.0ms	(pow.f64 (/.f64 x (+.f64 x y)) x)

simplify98.0ms

Algorithm

egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4976	4031
1	4976	4031

prune119.0ms

Filtered

131 candidates to 181 candidates (-38.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	176	5	181
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	177	5	182

Merged error: 0.3b

Counts

182 → 5

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)
1.6b	(pow.f64 (/.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 x y))) x)
3.3b	(pow.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 (+.f64 x y)) (cbrt.f64 (+.f64 x y)))) x)

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

61×	`unpow-prod-down_binary64`
51×	`cbrt-prod_binary64`
48×	`*-un-lft-identity_binary64`
43×	`times-frac_binary64`
36×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
20×	`add-exp-log_binary64`
14×	`cbrt-div_binary64`
10×	`associate-/r/_binary64`
7×	`flip3-+_binary64` `flip-+_binary64` `pow-exp_binary64`
6×	`pow-unpow_binary64` `pow1_binary64` `distribute-lft-out_binary64`
5×	`div-exp_binary64`
4×	`add-log-exp_binary64` `add-cbrt-cube_binary64` `prod-exp_binary64` `frac-times_binary64`
2×	`pow-to-exp_binary64` `associate-r/_binary64` `pow1/3_binary64` `pow-pow_binary64` `sqr-pow_binary64` `div-inv_binary64` `associate-l/_binary64`

Counts

4 → 116

Calls

4 calls:

1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)
13.0ms	(pow.f64 (/.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 x y))) x)
21.0ms	(pow.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 (+.f64 x y)) (cbrt.f64 (+.f64 x y)))) x)

series1.3s

Counts

4 → 12

Calls

4 calls:

161.0ms	(cbrt.f64 x)
165.0ms	(cbrt.f64 x)
443.0ms	(pow.f64 (/.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 x y))) x)
506.0ms	(pow.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 (+.f64 x y)) (cbrt.f64 (+.f64 x y)))) x)

simplify78.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5301	3064

prune118.0ms

Filtered

98 candidates to 128 candidates (-30.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	127	1	128
Fresh	2	2	4
Picked	1	0	1
Done	0	0	0
Total	130	3	133

Merged error: 0.0b

Counts

133 → 3

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)
1.6b	(pow.f64 (/.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 x y))) x)
5.1b	(log.f64 (/.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 x y))))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

96×	`cbrt-prod_binary64`
85×	`*-un-lft-identity_binary64`
84×	`times-frac_binary64`
61×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
48×	`log-prod_binary64` `unpow-prod-down_binary64`
12×	`distribute-lft-out_binary64`
10×	`add-exp-log_binary64`
6×	`pow1_binary64`
4×	`cbrt-div_binary64` `add-log-exp_binary64` `add-cbrt-cube_binary64` `associate-/r/_binary64`
3×	`pow-unpow_binary64`
2×	`flip3-+_binary64` `rem-log-exp_binary64` `pow1/3_binary64` `div-inv_binary64` `div-exp_binary64` `flip-+_binary64` `pow-exp_binary64`
1×	`pow-to-exp_binary64` `pow-pow_binary64` `log-pow_binary64` `sqr-pow_binary64` `log-div_binary64`

Counts

4 → 144

Calls

4 calls:

1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)
14.0ms	(pow.f64 (/.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 x y))) x)
9.0ms	(log.f64 (/.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 x y))))

series877.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(cbrt.f64 x)
137.0ms	(cbrt.f64 x)
446.0ms	(pow.f64 (/.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 x y))) x)
147.0ms	(log.f64 (/.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 x y))))

simplify134.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 0 (95.0ms)

Iter	Nodes	Cost
0	4990	3674
1	4990	3674

prune152.0ms

Filtered

124 candidates to 156 candidates (-25.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	156	0	156
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	156	3	159

Merged error: 0.0b

Counts

159 → 3

localize11.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)
6.2b	(pow.f64 (/.f64 x (+.f64 x y)) x)

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity_binary64`
18×	`unpow-prod-down_binary64`
16×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
12×	`times-frac_binary64`
9×	`cbrt-prod_binary64`
7×	`add-exp-log_binary64`
5×	`pow1_binary64`
4×	`add-log-exp_binary64` `add-cbrt-cube_binary64`
3×	`pow-unpow_binary64` `distribute-lft-out_binary64` `pow1/3_binary64`
2×	`associate-/r/_binary64` `pow-exp_binary64`
1×	`pow-to-exp_binary64` `flip3-+_binary64` `pow-pow_binary64` `sqr-pow_binary64` `div-inv_binary64` `div-exp_binary64` `flip-+_binary64`

Counts

4 → 66

Calls

4 calls:

1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)
8.0ms	(pow.f64 (/.f64 x (+.f64 x y)) x)

series822.0ms

Counts

4 → 12

Calls

4 calls:

151.0ms	(cbrt.f64 x)
153.0ms	(cbrt.f64 x)
161.0ms	(cbrt.f64 x)
356.0ms	(pow.f64 (/.f64 x (+.f64 x y)) x)

simplify66.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5175	932

prune57.0ms

Filtered

61 candidates to 78 candidates (-27.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	77	1	78
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	77	4	81

Merged error: 0.0b

Counts

81 → 4

regimes49.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 5.6b

bsearch79.0ms

Steps

Iters	Range		Point
10	0.011883268315695394	862742953.9619598	15626.173790724146
11	-1.6695384829602807e+22	-0.4880572903274403	-908952293.5860282

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	39	62
1	39	62

end0.0ms

sample1.7s

Algorithm

intervals

Results

676.0ms	1778×	body	1024	valid
257.0ms	4523×	body	128	valid
220.0ms	978×	body	512	valid
110.0ms	149×	body	2048	valid
77.0ms	572×	body	256	valid
64.0ms	188×	body	1024	invalid
49.0ms	230×	body	512	invalid
21.0ms	164×	body	256	invalid
14.0ms	224×	body	128	invalid
8.0ms	196×	body	128	nan

Details

analyze561.0ms

sample58.0ms

simplify53.0ms

prune3.0ms

localize6.0ms

rewrite52.0ms

series699.0ms

simplify98.0ms

prune119.0ms

localize16.0ms

rewrite55.0ms

series1.3s

simplify78.0ms

prune118.0ms

localize15.0ms

rewrite48.0ms

series877.0ms

simplify134.0ms

prune152.0ms

localize11.0ms

rewrite18.0ms

series822.0ms

simplify66.0ms

prune57.0ms

regimes49.0ms

bsearch79.0ms

simplify2.0ms

end0.0ms

sample1.7s

Profiling