Details

analyze1.0ms

Algorithm

Search

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

sample25.0ms

Algorithm

intervals

Results

8.0ms	60×	body	640	valid
5.0ms	31×	body	1280	valid
5.0ms	146×	body	80	valid
1.0ms	10×	body	320	valid
1.0ms	9×	body	160	valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	74	11
1	74	11

prune7.0ms

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: 17.5b

Counts

2 → 1

localize7.0ms

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))
2.5b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

rewrite57.0ms

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))
34.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

series30.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(sqrt.f64 (+.f64 x 1))
5.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
8.0ms	(/.f64 1 (sqrt.f64 x))
14.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

simplify56.0ms

Algorithm

egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5299	2132

prune116.0ms

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: 16.9b

Counts

175 → 13

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (sqrt.f64 (+.f64 1 x)))
0.3b	(/.f64 1 (sqrt.f64 x))
0.3b	(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
2.5b	(-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x)))

rewrite162.0ms

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)))
5.0ms	(/.f64 1 (sqrt.f64 x))
64.0ms	(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
19.0ms	(-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x)))

series39.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(/.f64 1 (sqrt.f64 (+.f64 1 x)))
8.0ms	(/.f64 1 (sqrt.f64 x))
15.0ms	(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
3.0ms	(-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x)))

simplify118.0ms

Algorithm

egg-herbie

Counts

548 → 548

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	4998	14185
1	4998	14185

prune228.0ms

Filtered

142 candidates to 548 candidates (-285.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	545	3	548
Fresh	10	2	12
Picked	1	0	1
Done	0	0	0
Total	556	5	561

Merged error: 5.3b

Counts

561 → 5

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (sqrt.f64 (+.f64 1 x)))
0.2b	(/.f64 1 (*.f64 x (+.f64 1 x)))
0.3b	(/.f64 1 (sqrt.f64 x))
5.6b	(/.f64 (/.f64 1 (*.f64 x (+.f64 1 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))

rewrite88.0ms

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)))
9.0ms	(/.f64 1 (*.f64 x (+.f64 1 x)))
5.0ms	(/.f64 1 (sqrt.f64 x))
44.0ms	(/.f64 (/.f64 1 (*.f64 x (+.f64 1 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))

series36.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(/.f64 1 (sqrt.f64 (+.f64 1 x)))
3.0ms	(/.f64 1 (*.f64 x (+.f64 1 x)))
8.0ms	(/.f64 1 (sqrt.f64 x))
20.0ms	(/.f64 (/.f64 1 (*.f64 x (+.f64 1 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))

simplify71.0ms

Algorithm

egg-herbie

Counts

331 → 331

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	4994	6216
1	4994	6216

prune199.0ms

Filtered

129 candidates to 331 candidates (-156.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	322	9	331
Fresh	3	1	4
Picked	1	0	1
Done	0	0	0
Total	326	10	336

Merged error: 0.0b

Counts

336 → 10

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(*.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))
0.4b	(/.f64 (/.f64 1 x) (*.f64 (+.f64 x 1) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))))

rewrite109.0ms

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:

44.0ms	(*.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)))
5.0ms	(/.f64 1 (sqrt.f64 x))
44.0ms	(/.f64 (/.f64 1 x) (*.f64 (+.f64 x 1) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))))

series41.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(*.f64 (+.f64 x 1) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1)))))
5.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
8.0ms	(/.f64 1 (sqrt.f64 x))
20.0ms	(/.f64 (/.f64 1 x) (*.f64 (+.f64 x 1) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))))

simplify68.0ms

Algorithm

egg-herbie

Counts

214 → 214

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4947	2867
1	4947	2867

prune152.0ms

Filtered

128 candidates to 214 candidates (-67.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	211	3	214
Fresh	6	3	9
Picked	1	0	1
Done	0	0	0
Total	218	6	224

Merged error: 0b

Counts

224 → 6

regimes22.0ms

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 (1.0ms)

Iter	Nodes	Cost
0	15	25
1	15	25

end0.0ms

sample788.0ms

Algorithm

intervals

Results

262.0ms	1845×	body	640	valid
203.0ms	1129×	body	1280	valid
148.0ms	4112×	body	80	valid
64.0ms	634×	body	320	valid
19.0ms	280×	body	160	valid

Details

analyze1.0ms

sample25.0ms

simplify7.0ms

prune7.0ms

localize7.0ms

rewrite57.0ms

series30.0ms

simplify56.0ms

prune116.0ms

localize11.0ms

rewrite162.0ms

series39.0ms

simplify118.0ms

prune228.0ms

localize10.0ms

rewrite88.0ms

series36.0ms

simplify71.0ms

prune199.0ms

localize10.0ms

rewrite109.0ms

series41.0ms

simplify68.0ms

prune152.0ms

regimes22.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample788.0ms

Profiling