Details

analyze2.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	0%	50%	2

sample26.0ms

Algorithm

intervals

Results

8.0ms	58×	body	640	valid
5.0ms	137×	body	80	valid
4.0ms	24×	body	1280	valid
2.0ms	23×	body	320	valid
1.0ms	14×	body	160	valid

simplify16.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (7.0ms)

Iter	Nodes	Cost
0	76	17
1	76	17

prune3.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 19.1b

Counts

2 → 1

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1))
0.2b	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
0.3b	(/.f64 1 (sqrt.f64 x))
4.0b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

113×	`add-sqr-sqrt_binary64`
97×	`*-un-lft-identity_binary64` `times-frac_binary64`
64×	`sqrt-prod_binary64`
42×	`add-cube-cbrt_binary64`
25×	`difference-of-squares_binary64`
13×	`associate-/r*_binary64` `distribute-lft-out--_binary64`
12×	`add-exp-log_binary64`
9×	`pow1_binary64`
8×	`distribute-lft-out_binary64` `add-cbrt-cube_binary64`
6×	`add-log-exp_binary64` `associate-/l*_binary64` `div-inv_binary64` `pow-flip_binary64`
4×	`div-exp_binary64` `sqrt-div_binary64`
3×	`pow1/2_binary64` `sqrt-pow1_binary64`
2×	`flip3-+_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `rec-exp_binary64` `flip-+_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `rem-sqrt-square_binary64` `flip--_binary64` `frac-sub_binary64`

Counts

4 → 162

Calls

4 calls:

3.0ms	(sqrt.f64 (+.f64 x 1))
7.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
5.0ms	(/.f64 1 (sqrt.f64 x))
39.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

series97.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(sqrt.f64 (+.f64 x 1))
18.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
28.0ms	(/.f64 1 (sqrt.f64 x))
38.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

simplify92.0ms

Algorithm

egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4932	3393
1	4932	3393

prune146.0ms

Filtered

95 candidates to 174 candidates (-83.2%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	161	13	174
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	162	13	175

Merged error: 18.3b

Counts

175 → 13

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (sqrt.f64 (+.f64 1 x)))
0.3b	(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
0.3b	(/.f64 1 (sqrt.f64 x))
3.9b	(-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x)))

rewrite168.0ms

Algorithm

rewrite-expression-head

Rules

1318×	`*-un-lft-identity_binary64`
1237×	`times-frac_binary64`
717×	`add-sqr-sqrt_binary64`
426×	`distribute-lft-out_binary64`
304×	`sqrt-prod_binary64`
285×	`add-cube-cbrt_binary64`
180×	`distribute-lft-out--_binary64`
167×	`div-inv_binary64`
162×	`difference-of-squares_binary64`
29×	`associate-/r*_binary64`
28×	`associate-/l*_binary64`
14×	`add-exp-log_binary64`
10×	`add-cbrt-cube_binary64`
8×	`pow1_binary64`
6×	`add-log-exp_binary64` `pow-flip_binary64`
5×	`associate-/r/_binary64` `div-exp_binary64`
3×	`associate-/l/_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64`
2×	`flip3-+_binary64` `pow1/2_binary64` `flip3--_binary64` `1-exp_binary64` `sqrt-pow1_binary64` `inv-pow_binary64` `rec-exp_binary64` `flip--_binary64` `flip-+_binary64` `frac-sub_binary64` `sqrt-div_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `frac-add_binary64` `div-sub_binary64`

Counts

4 → 536

Calls

4 calls:

7.0ms	(/.f64 1 (sqrt.f64 (+.f64 1 x)))
63.0ms	(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
4.0ms	(/.f64 1 (sqrt.f64 x))
18.0ms	(-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x)))

series115.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(/.f64 1 (sqrt.f64 (+.f64 1 x)))
58.0ms	(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
27.0ms	(/.f64 1 (sqrt.f64 x))
13.0ms	(-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x)))

simplify213.0ms

Algorithm

egg-herbie

Counts

548 → 548

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5123	22047

prune314.0ms

Filtered

142 candidates to 548 candidates (-285.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	546	2	548
Fresh	10	2	12
Picked	0	1	1
Done	0	0	0
Total	556	5	561

Merged error: 3.1b

Counts

561 → 5

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (sqrt.f64 (+.f64 1 x)))
0.3b	(/.f64 1 (*.f64 x (+.f64 1 x)))
0.3b	(/.f64 1 (sqrt.f64 x))
3.3b	(/.f64 (/.f64 1 (*.f64 x (+.f64 1 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

417×	`times-frac_binary64`
399×	`*-un-lft-identity_binary64`
164×	`distribute-lft-out_binary64`
148×	`sqrt-prod_binary64`
141×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
61×	`div-inv_binary64`
42×	`add-exp-log_binary64`
41×	`associate-/r/_binary64`
36×	`associate-*r/_binary64`
30×	`associate-/r*_binary64`
22×	`add-cbrt-cube_binary64`
20×	`flip3-+_binary64` `flip-+_binary64`
19×	`div-exp_binary64`
18×	`associate-/l*_binary64`
11×	`pow1_binary64`
9×	`cbrt-undiv_binary64`
8×	`pow-flip_binary64`
6×	`1-exp_binary64` `prod-exp_binary64` `rec-exp_binary64`
4×	`add-log-exp_binary64` `clear-num_binary64` `frac-2neg_binary64`
3×	`inv-pow_binary64`
2×	`pow1/2_binary64` `cbrt-unprod_binary64` `sqrt-pow1_binary64` `sqrt-div_binary64`
1×	`pow-prod-down_binary64` `associate-/l/_binary64` `frac-add_binary64`

Counts

4 → 319

Calls

4 calls:

7.0ms	(/.f64 1 (sqrt.f64 (+.f64 1 x)))
7.0ms	(/.f64 1 (*.f64 x (+.f64 1 x)))
5.0ms	(/.f64 1 (sqrt.f64 x))
49.0ms	(/.f64 (/.f64 1 (*.f64 x (+.f64 1 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))

series143.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(/.f64 1 (sqrt.f64 (+.f64 1 x)))
10.0ms	(/.f64 1 (*.f64 x (+.f64 1 x)))
28.0ms	(/.f64 1 (sqrt.f64 x))
86.0ms	(/.f64 (/.f64 1 (*.f64 x (+.f64 1 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))

simplify130.0ms

Algorithm

egg-herbie

Counts

331 → 331

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5106	9598

prune272.0ms

Filtered

129 candidates to 331 candidates (-156.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	323	8	331
Fresh	2	1	3
Picked	1	0	1
Done	1	0	1
Total	327	9	336

Merged error: 0.0b

Counts

336 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (+.f64 x 1) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1)))))
0.2b	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
0.3b	(/.f64 1 (sqrt.f64 x))
0.3b	(/.f64 (/.f64 1 x) (*.f64 (+.f64 x 1) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))))

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

92×	`*-un-lft-identity_binary64`
88×	`times-frac_binary64`
59×	`add-sqr-sqrt_binary64`
57×	`add-cube-cbrt_binary64`
40×	`sqrt-prod_binary64`
36×	`add-exp-log_binary64`
22×	`add-cbrt-cube_binary64`
21×	`distribute-lft-out_binary64`
19×	`associate-/l*_binary64`
16×	`associate-r_binary64` `div-exp_binary64`
15×	`flip3-+_binary64` `flip-+_binary64`
14×	`associate-/r*_binary64`
13×	`associate-/r/_binary64`
12×	`frac-times_binary64`
10×	`pow1_binary64`
9×	`div-inv_binary64`
8×	`cbrt-undiv_binary64`
6×	`associate-*r/_binary64` `frac-add_binary64` `pow-flip_binary64`
5×	`prod-exp_binary64`
4×	`add-log-exp_binary64` `1-exp_binary64` `associate-l_binary64` `rec-exp_binary64` `associate-*l/_binary64`
3×	`cbrt-unprod_binary64` `clear-num_binary64` `frac-2neg_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `inv-pow_binary64` `sqrt-div_binary64`
1×	`pow-prod-down_binary64` `associate-/l/_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `*-commutative_binary64`

Counts

4 → 202

Calls

4 calls:

43.0ms	(*.f64 (+.f64 x 1) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1)))))
7.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
4.0ms	(/.f64 1 (sqrt.f64 x))
41.0ms	(/.f64 (/.f64 1 x) (*.f64 (+.f64 x 1) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))))

series153.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(*.f64 (+.f64 x 1) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1)))))
16.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
33.0ms	(/.f64 1 (sqrt.f64 x))
73.0ms	(/.f64 (/.f64 1 x) (*.f64 (+.f64 x 1) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))))

simplify138.0ms

Algorithm

egg-herbie

Counts

214 → 214

Iterations

Useful iterations: 0 (91.0ms)

Iter	Nodes	Cost
0	4958	4482
1	4958	4482

prune211.0ms

Filtered

128 candidates to 214 candidates (-67.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	210	4	214
Fresh	6	2	8
Picked	1	0	1
Done	0	0	0
Total	217	6	223

Merged error: 0b

Counts

223 → 6

regimes15.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	39
1	17	39

end0.0ms

sample882.0ms

Algorithm

intervals

Results

284.0ms	1841×	body	640	valid
229.0ms	1142×	body	1280	valid
170.0ms	4130×	body	80	valid
70.0ms	602×	body	320	valid
22.0ms	285×	body	160	valid

Details

analyze2.0ms

sample26.0ms

simplify16.0ms

prune3.0ms

localize9.0ms

rewrite62.0ms

series97.0ms

simplify92.0ms

prune146.0ms

localize13.0ms

rewrite168.0ms

series115.0ms

simplify213.0ms

prune314.0ms

localize12.0ms

rewrite91.0ms

series143.0ms

simplify130.0ms

prune272.0ms

localize13.0ms

rewrite104.0ms

series153.0ms

simplify138.0ms

prune211.0ms

regimes15.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample882.0ms

Profiling