Details

analyze2.0ms

Algorithm

Search

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

sample30.0ms

Algorithm

intervals

Results

15.0ms	90×	body	1024	valid
5.0ms	42×	body	512	valid
5.0ms	117×	body	128	valid
1.0ms	7×	body	256	valid

simplify10.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	75	17
1	75	17

prune2.0ms

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: 21.2b

Counts

2 → 1

localize8.0ms

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))
1.0b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

rewrite71.0ms

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`
10×	`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×	`sqrt-div_binary64`
3×	`pow1/2_binary64` `sqrt-pow1_binary64`
2×	`flip3-+_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `rec-exp_binary64` `div-exp_binary64` `flip-+_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `rem-sqrt-square_binary64` `flip--_binary64` `frac-sub_binary64`

Counts

4 → 160

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))
40.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

series177.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(sqrt.f64 (+.f64 x 1))
36.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
51.0ms	(/.f64 1 (sqrt.f64 x))
65.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

simplify92.0ms

Algorithm

egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4929	3368
1	4929	3368

prune136.0ms

Filtered

95 candidates to 172 candidates (-81.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	162	10	172
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	163	10	173

Merged error: 20.8b

Counts

173 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (sqrt.f64 (+.f64 1 x)))
0.2b	(/.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))
1.0b	(-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x)))

rewrite230.0ms

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`
12×	`add-exp-log_binary64`
10×	`add-cbrt-cube_binary64`
8×	`pow1_binary64`
6×	`add-log-exp_binary64` `pow-flip_binary64`
5×	`associate-/r/_binary64`
3×	`associate-/l/_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-exp_binary64`
2×	`flip3-+_binary64` `pow1/2_binary64` `flip3--_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 → 534

Calls

4 calls:

7.0ms	(/.f64 1 (sqrt.f64 (+.f64 1 x)))
69.0ms	(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
5.0ms	(/.f64 1 (sqrt.f64 x))
20.0ms	(-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x)))

series240.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(/.f64 1 (sqrt.f64 (+.f64 1 x)))
127.0ms	(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
52.0ms	(/.f64 1 (sqrt.f64 x))
29.0ms	(-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x)))

simplify198.0ms

Algorithm

egg-herbie

Counts

546 → 546

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5131	22030

prune276.0ms

Filtered

142 candidates to 546 candidates (-284.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	544	2	546
Fresh	8	1	9
Picked	1	0	1
Done	0	0	0
Total	553	3	556

Merged error: 6.8b

Counts

556 → 3

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (sqrt.f64 (+.f64 1 x)))
0.3b	(/.f64 1 (sqrt.f64 x))
0.8b	(/.f64 1 (*.f64 x (+.f64 1 x)))
7.0b	(/.f64 (/.f64 1 (*.f64 x (+.f64 1 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))

rewrite116.0ms

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`
41×	`associate-/r/_binary64`
36×	`associate-*r/_binary64`
32×	`add-exp-log_binary64`
30×	`associate-/r*_binary64`
22×	`add-cbrt-cube_binary64`
20×	`flip3-+_binary64` `flip-+_binary64`
18×	`associate-/l*_binary64`
11×	`pow1_binary64` `div-exp_binary64`
9×	`cbrt-undiv_binary64`
8×	`pow-flip_binary64`
6×	`rec-exp_binary64`
4×	`add-log-exp_binary64` `clear-num_binary64` `prod-exp_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 → 313

Calls

4 calls:

7.0ms	(/.f64 1 (sqrt.f64 (+.f64 1 x)))
5.0ms	(/.f64 1 (sqrt.f64 x))
7.0ms	(/.f64 1 (*.f64 x (+.f64 1 x)))
47.0ms	(/.f64 (/.f64 1 (*.f64 x (+.f64 1 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))

series260.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(/.f64 1 (sqrt.f64 (+.f64 1 x)))
48.0ms	(/.f64 1 (sqrt.f64 x))
22.0ms	(/.f64 1 (*.f64 x (+.f64 1 x)))
159.0ms	(/.f64 (/.f64 1 (*.f64 x (+.f64 1 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))

simplify121.0ms

Algorithm

egg-herbie

Counts

325 → 325

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5163	9479

prune237.0ms

Filtered

124 candidates to 325 candidates (-162.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	316	9	325
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	318	10	328

Merged error: 0.0b

Counts

328 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite128.0ms

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`
29×	`add-exp-log_binary64`
22×	`add-cbrt-cube_binary64`
21×	`distribute-lft-out_binary64`
19×	`associate-/l*_binary64`
16×	`associate-r_binary64`
15×	`flip3-+_binary64` `flip-+_binary64`
14×	`associate-/r*_binary64`
13×	`associate-/r/_binary64`
12×	`frac-times_binary64`
10×	`pow1_binary64` `div-exp_binary64`
9×	`div-inv_binary64`
8×	`cbrt-undiv_binary64`
6×	`associate-*r/_binary64` `frac-add_binary64` `pow-flip_binary64`
4×	`add-log-exp_binary64` `associate-l_binary64` `prod-exp_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 → 198

Calls

4 calls:

48.0ms	(*.f64 (+.f64 1 x) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
7.0ms	(/.f64 1 (sqrt.f64 (+.f64 1 x)))
5.0ms	(/.f64 1 (sqrt.f64 x))
45.0ms	(/.f64 (/.f64 1 x) (*.f64 (+.f64 1 x) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x))))))

series296.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(*.f64 (+.f64 1 x) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
30.0ms	(/.f64 1 (sqrt.f64 (+.f64 1 x)))
48.0ms	(/.f64 1 (sqrt.f64 x))
155.0ms	(/.f64 (/.f64 1 x) (*.f64 (+.f64 1 x) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x))))))

simplify108.0ms

Algorithm

egg-herbie

Counts

210 → 210

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4963	4437
1	4963	4437

prune204.0ms

Filtered

128 candidates to 210 candidates (-64.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	205	5	210
Fresh	8	1	9
Picked	1	0	1
Done	0	0	0
Total	214	6	220

Merged error: 0b

Counts

220 → 6

regimes15.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	39
1	15	39

end0.0ms

sample812.0ms

Algorithm

intervals

Results

374.0ms	2304×	body	1024	valid
176.0ms	4200×	body	128	valid
124.0ms	1027×	body	512	valid
37.0ms	469×	body	256	valid

Details

analyze2.0ms

sample30.0ms

simplify10.0ms

prune2.0ms

localize8.0ms

rewrite71.0ms

series177.0ms

simplify92.0ms

prune136.0ms

localize14.0ms

rewrite230.0ms

series240.0ms

simplify198.0ms

prune276.0ms

localize15.0ms

rewrite116.0ms

series260.0ms

simplify121.0ms

prune237.0ms

localize15.0ms

rewrite128.0ms

series296.0ms

simplify108.0ms

prune204.0ms

regimes15.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample812.0ms

Profiling