Details

analyze584.0ms

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

sample73.0ms

Algorithm

intervals

Results

25.0ms	47×	body	1280	valid
12.0ms	40×	body	640	valid
8.0ms	137×	body	80	valid
5.0ms	21×	body	320	valid
3.0ms	9×	body	640	invalid
2.0ms	5×	body	1280	invalid
1.0ms	11×	body	160	valid
1.0ms	5×	body	320	invalid
0.0ms	7×	body	80	nan
0.0ms	5×	body	80	invalid
0.0ms	1×	body	160	invalid

simplify207.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	5908	13

prune14.0ms

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: 10.1b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/.f64 x (+.f64 x y))
0.0b	(/.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) x)
3.9b	(pow.f64 (/.f64 x (+.f64 x y)) x)

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac_binary64_4421`
118×	`*-un-lft-identity_binary64_4426`
90×	`unpow-prod-down_binary64_4361`
80×	`add-sqr-sqrt_binary64_4411` `add-cube-cbrt_binary64_4397`
25×	`associate-/l*_binary64_4490`
19×	`distribute-lft-out_binary64_4470`
16×	`add-exp-log_binary64_4390`
12×	`associate-/r/_binary64_4491`
7×	`associate-/r*_binary64_4489` `div-inv_binary64_4427` `div-exp_binary64_4379` `add-cbrt-cube_binary64_4398`
6×	`flip-+_binary64_4451` `flip3-+_binary64_4424`
5×	`sqr-pow_binary64_4458`
4×	`pow1_binary64_4372` `pow-exp_binary64_4350`
3×	`pow-unpow_binary64_4359` `add-log-exp_binary64_4391`
2×	`frac-2neg_binary64_4419` `clear-num_binary64_4429` `cbrt-undiv_binary64_4396` `pow-to-exp_binary64_4351`
1×	`pow-pow_binary64_4354`

Counts

3 → 172

Calls

3 calls:

10.0ms	(/.f64 x (+.f64 x y))
12.0ms	(/.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) x)
8.0ms	(pow.f64 (/.f64 x (+.f64 x y)) x)

series351.0ms

Counts

3 → 9

Calls

3 calls:

29.0ms	(/.f64 x (+.f64 x y))
135.0ms	(/.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) x)
186.0ms	(pow.f64 (/.f64 x (+.f64 x y)) x)

simplify91.0ms

Algorithm

egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5041	4035

prune747.0ms

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: 0.5b

Counts

182 → 5

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/.f64 x (+.f64 x y))
0.0b	(*.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) (/.f64 1 x))
3.9b	(pow.f64 (/.f64 x (+.f64 x y)) x)

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

65×	`add-sqr-sqrt_binary64_4411`
61×	`*-un-lft-identity_binary64_4426`
56×	`times-frac_binary64_4421`
42×	`unpow-prod-down_binary64_4361`
37×	`add-cube-cbrt_binary64_4397`
36×	`add-exp-log_binary64_4390`
22×	`associate-l_binary64_4486`
13×	`associate-r_binary64_4485`
12×	`unswap-sqr_binary64_4454` `prod-exp_binary64_4377`
10×	`add-cbrt-cube_binary64_4398` `distribute-lft-out_binary64_4470`
9×	`div-exp_binary64_4379`
8×	`pow-exp_binary64_4350`
6×	`associate-/r/_binary64_4491`
5×	`sqr-pow_binary64_4458`
4×	`associate-/r*_binary64_4489` `pow1_binary64_4372` `div-inv_binary64_4427` `pow-to-exp_binary64_4351` `rec-exp_binary64_4378`
3×	`associate-/l*_binary64_4490` `flip-+_binary64_4451` `pow-unpow_binary64_4359` `flip3-+_binary64_4424` `add-log-exp_binary64_4391`
2×	`cbrt-undiv_binary64_4396` `cbrt-unprod_binary64_4395`
1×	`-commutative_binary64_4494` `frac-2neg_binary64_4419` `clear-num_binary64_4429` `associate-r/_binary64_4487` `un-div-inv_binary64_4428` `pow-pow_binary64_4354`

Counts

3 → 137

Calls

3 calls:

5.0ms	(/.f64 x (+.f64 x y))
22.0ms	(*.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) (/.f64 1 x))
7.0ms	(pow.f64 (/.f64 x (+.f64 x y)) x)

series344.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(/.f64 x (+.f64 x y))
137.0ms	(*.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) (/.f64 1 x))
181.0ms	(pow.f64 (/.f64 x (+.f64 x y)) x)

simplify98.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	5108	2553

prune406.0ms

Filtered

97 candidates to 146 candidates (-50.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	145	1	146
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	146	5	151

Merged error: 0.5b

Counts

151 → 5

localize26.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)
3.9b	(pow.f64 (/.f64 x (+.f64 x y)) x)

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity_binary64_4426`
18×	`unpow-prod-down_binary64_4361`
16×	`add-sqr-sqrt_binary64_4411` `add-cube-cbrt_binary64_4397`
12×	`times-frac_binary64_4421`
9×	`cbrt-prod_binary64_4393`
7×	`add-exp-log_binary64_4390`
5×	`pow1_binary64_4372`
4×	`add-cbrt-cube_binary64_4398` `add-log-exp_binary64_4391`
3×	`pow-unpow_binary64_4359` `distribute-lft-out_binary64_4470` `pow1/3_binary64_4364`
2×	`pow-exp_binary64_4350` `associate-/r/_binary64_4491`
1×	`flip-+_binary64_4451` `div-inv_binary64_4427` `div-exp_binary64_4379` `pow-pow_binary64_4354` `flip3-+_binary64_4424` `sqr-pow_binary64_4458` `pow-to-exp_binary64_4351`

Counts

4 → 66

Calls

4 calls:

1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)
7.0ms	(pow.f64 (/.f64 x (+.f64 x y)) x)

series451.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(cbrt.f64 x)
88.0ms	(cbrt.f64 x)
87.0ms	(cbrt.f64 x)
186.0ms	(pow.f64 (/.f64 x (+.f64 x y)) x)

simplify79.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4960	939
1	4960	939

prune265.0ms

Filtered

61 candidates to 78 candidates (-27.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	78	0	78
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	78	5	83

Merged error: 0.5b

Counts

83 → 5

localize9.0ms

Local error

Found 1 expressions with local error:

0.0b	(*.f64 (exp.f64 (neg.f64 y)) (/.f64 1 x))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64_4411`
13×	`associate-r_binary64_4485`
11×	`times-frac_binary64_4421`
10×	`*-un-lft-identity_binary64_4426`
9×	`add-cube-cbrt_binary64_4397`
6×	`add-cbrt-cube_binary64_4398`
5×	`add-exp-log_binary64_4390`
3×	`unswap-sqr_binary64_4454` `pow1_binary64_4372` `associate-l_binary64_4486` `prod-exp_binary64_4377`
2×	`frac-times_binary64_4418` `exp-neg_binary64_4386` `associate-*l/_binary64_4488` `exp-diff_binary64_4387` `neg-sub0_binary64_4432` `cbrt-unprod_binary64_4395`
1×	`-commutative_binary64_4494` `div-inv_binary64_4427` `div-exp_binary64_4379` `associate-r/_binary64_4487` `un-div-inv_binary64_4428` `cbrt-undiv_binary64_4396` `pow-prod-down_binary64_4353` `add-log-exp_binary64_4391` `rec-exp_binary64_4378`

Counts

1 → 39

Calls

1 calls:

11.0ms

(*.f64 (exp.f64 (neg.f64 y)) (/.f64 1 x))

series25.0ms

Counts

1 → 3

Calls

1 calls:

25.0ms

(*.f64 (exp.f64 (neg.f64 y)) (/.f64 1 x))

simplify72.0ms

Algorithm

egg-herbie

Counts

42 → 42

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5163	460

prune114.0ms

Filtered

28 candidates to 42 candidates (-50.0%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	41	1	42
Fresh	0	2	2
Picked	1	0	1
Done	0	2	2
Total	42	5	47

Merged error: 0.5b

Counts

47 → 5

regimes179.0ms

Accuracy

99.8% (0.0b remaining)

Error of 1.4b against oracle of 1.4b and baseline of 10.9b

bsearch90.0ms

Steps

Iters	Range		Point
11	7961586916263933/18014398509481984	74740141456892510208	6.240856440186883
9	-899452405546085/1099511627776	-246452102847557/36028797018963968	-9.58411435489314

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	60
1	29	60

end0.0ms

sample1.9s

Algorithm

intervals

Results

709.0ms	1423×	body	1280	valid
353.0ms	1168×	body	640	valid
253.0ms	4374×	body	80	valid
136.0ms	668×	body	320	valid
75.0ms	250×	body	640	invalid
47.0ms	367×	body	160	valid
47.0ms	107×	body	1280	invalid
32.0ms	151×	body	320	invalid
12.0ms	98×	body	160	invalid
10.0ms	174×	body	80	invalid
9.0ms	206×	body	80	nan

Details

analyze584.0ms

sample73.0ms

simplify207.0ms

prune14.0ms

localize9.0ms

rewrite39.0ms

series351.0ms

simplify91.0ms

prune747.0ms

localize11.0ms

rewrite41.0ms

series344.0ms

simplify98.0ms

prune406.0ms

localize26.0ms

rewrite12.0ms

series451.0ms

simplify79.0ms

prune265.0ms

localize9.0ms

rewrite13.0ms

series25.0ms

simplify72.0ms

prune114.0ms

regimes179.0ms

bsearch90.0ms

simplify3.0ms

end0.0ms

sample1.9s

Profiling