Details

analyze581.0ms

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

sample67.0ms

Algorithm

intervals

Results

26.0ms	53×	body	1280	valid
13.0ms	42×	body	640	valid
7.0ms	131×	body	80	valid
4.0ms	19×	body	320	valid
3.0ms	9×	body	640	invalid
1.0ms	11×	body	160	valid
1.0ms	6×	body	320	invalid
1.0ms	6×	body	160	invalid
0.0ms	8×	body	80	invalid
0.0ms	1×	body	1280	invalid
0.0ms	5×	body	80	nan

simplify44.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4985	9
1	4985	9

prune9.0ms

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: 9.8b

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))
5.6b	(pow.f64 (/.f64 x (+.f64 x y)) x)

rewrite32.0ms

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:

11.0ms	(/.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) x)
5.0ms	(/.f64 x (+.f64 x y))
7.0ms	(pow.f64 (/.f64 x (+.f64 x y)) x)

series93.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(/.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) x)
7.0ms	(/.f64 x (+.f64 x y))
49.0ms	(pow.f64 (/.f64 x (+.f64 x y)) x)

simplify60.0ms

Algorithm

egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4951	2646
1	4951	2646

prune142.0ms

Filtered

131 candidates to 181 candidates (-38.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	178	3	181
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	179	3	182

Merged error: 0.3b

Counts

182 → 3

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)
1.2b	(pow.f64 (/.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 x y))) x)
1.7b	(pow.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 (+.f64 x y)) (cbrt.f64 (+.f64 x y)))) x)

rewrite38.0ms

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)
11.0ms	(pow.f64 (/.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 x y))) x)
19.0ms	(pow.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 (+.f64 x y)) (cbrt.f64 (+.f64 x y)))) x)

series169.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(cbrt.f64 x)
19.0ms	(cbrt.f64 x)
60.0ms	(pow.f64 (/.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 x y))) x)
70.0ms	(pow.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 (+.f64 x y)) (cbrt.f64 (+.f64 x y)))) x)

simplify53.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5562	1979

prune114.0ms

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	0	2	2
Picked	1	0	1
Done	0	0	0
Total	128	3	131

Merged error: 0b

Counts

131 → 3

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)
1.2b	(pow.f64 (/.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 x y))) x)
2.9b	(log.f64 (/.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 x y))))

rewrite31.0ms

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)
2.0ms	(cbrt.f64 x)
13.0ms	(pow.f64 (/.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 x y))) x)
8.0ms	(log.f64 (/.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 x y))))

series123.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(cbrt.f64 x)
19.0ms	(cbrt.f64 x)
64.0ms	(pow.f64 (/.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 x y))) x)
21.0ms	(log.f64 (/.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 x y))))

simplify65.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4900	2282
1	4900	2282

prune147.0ms

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: 0b

Counts

159 → 3

localize4.0ms

Local error

Found 1 expressions with local error:

0.0b	(/.f64 (exp.f64 (neg.f64 y)) x)

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `times-frac_binary64`
3×	`associate-/r_binary64` `add-cbrt-cube_binary64` `associate-/l_binary64`
2×	`associate-/l/_binary64` `add-exp-log_binary64`
1×	`add-log-exp_binary64` `pow1_binary64` `neg-sub0_binary64` `cbrt-undiv_binary64` `exp-diff_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `exp-neg_binary64`

Counts

1 → 29

Calls

1 calls:

5.0ms

(/.f64 (exp.f64 (neg.f64 y)) x)

series6.0ms

Counts

1 → 3

Calls

1 calls:

6.0ms

(/.f64 (exp.f64 (neg.f64 y)) x)

simplify63.0ms

Algorithm

egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4919	265
1	4919	265

prune23.0ms

Filtered

24 candidates to 32 candidates (-33.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	32	0	32
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	32	3	35

Merged error: 0b

Counts

35 → 3

regimes93.0ms

Accuracy

85.6% (0.8b remaining)

Error of 0.8b against oracle of 0.0b and baseline of 5.5b

bsearch63.0ms

Steps

Iters	Range		Point
8	1.2375278304228266e-14	2.758181384577642e-11	2.7264805425091357e-11
6	-1.0491272188570164e+134	-2.1518477105781146e+133	-2.1718994123994335e+133

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	37	39
1	37	39

end0.0ms

sample1.9s

Algorithm

intervals

Results

737.0ms	1484×	body	1280	valid
356.0ms	1200×	body	640	valid
230.0ms	4300×	body	80	valid
136.0ms	668×	body	320	valid
75.0ms	267×	body	640	invalid
45.0ms	348×	body	160	valid
35.0ms	80×	body	1280	invalid
34.0ms	171×	body	320	invalid
12.0ms	103×	body	160	invalid
9.0ms	154×	body	80	invalid
7.0ms	177×	body	80	nan

Details

analyze581.0ms

sample67.0ms

simplify44.0ms

prune9.0ms

localize6.0ms

rewrite32.0ms

series93.0ms

simplify60.0ms

prune142.0ms

localize17.0ms

rewrite38.0ms

series169.0ms

simplify53.0ms

prune114.0ms

localize15.0ms

rewrite31.0ms

series123.0ms

simplify65.0ms

prune147.0ms

localize4.0ms

rewrite6.0ms

series6.0ms

simplify63.0ms

prune23.0ms

regimes93.0ms

bsearch63.0ms

simplify3.0ms

end0.0ms

sample1.9s

Profiling