Details

analyze6.0ms

Algorithm

Search

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

sample28.0ms

Algorithm

intervals

Results

9.0ms	56×	body	640	valid
6.0ms	151×	body	80	valid
5.0ms	27×	body	1280	valid
2.0ms	15×	body	320	valid
1.0ms	7×	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

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: 15.6b

Counts

2 → 1

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1))
0.1b	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
0.3b	(/.f64 1 (sqrt.f64 x))
2.8b	(-.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))
35.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

series27.0ms

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))
11.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

simplify57.0ms

Algorithm

egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5299	2132

prune122.0ms

Filtered

95 candidates to 174 candidates (-83.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	163	11	174
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	164	11	175

Merged error: 15.1b

Counts

175 → 11

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.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)))))
2.7b	(-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x)))

rewrite161.0ms

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)))
9.0ms	(/.f64 1 (sqrt.f64 x))
61.0ms	(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x)))))
18.0ms	(-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x)))

series32.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(/.f64 1 (sqrt.f64 (+.f64 1 x)))
8.0ms	(/.f64 1 (sqrt.f64 x))
16.0ms	(/.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)))

simplify120.0ms

Algorithm

egg-herbie

Counts

548 → 548

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	4998	14185
1	4998	14185

prune232.0ms

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	8	2	10
Picked	1	0	1
Done	0	0	0
Total	554	5	559

Merged error: 3.6b

Counts

559 → 5

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 1 (sqrt.f64 (+.f64 1 x)))
0.3b	(/.f64 1 (*.f64 x (+.f64 1 x)))
0.3b	(/.f64 1 (sqrt.f64 x))
3.9b	(/.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)))
8.0ms	(/.f64 1 (*.f64 x (+.f64 1 x)))
5.0ms	(/.f64 1 (sqrt.f64 x))
46.0ms	(/.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)))))

simplify70.0ms

Algorithm

egg-herbie

Counts

331 → 331

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	4994	6216
1	4994	6216

prune198.0ms

Filtered

129 candidates to 331 candidates (-156.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	324	7	331
Fresh	3	1	4
Picked	1	0	1
Done	0	0	0
Total	328	8	336

Merged error: 0.0b

Counts

336 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite110.0ms

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:

7.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
46.0ms	(*.f64 (+.f64 x 1) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1)))))
5.0ms	(/.f64 1 (sqrt.f64 x))
43.0ms	(/.f64 (/.f64 1 x) (*.f64 (+.f64 x 1) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))))

series48.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
13.0ms	(*.f64 (+.f64 x 1) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1)))))
9.0ms	(/.f64 1 (sqrt.f64 x))
21.0ms	(/.f64 (/.f64 1 x) (*.f64 (+.f64 x 1) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))))

simplify74.0ms

Algorithm

egg-herbie

Counts

214 → 214

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4947	2867
1	4947	2867

prune157.0ms

Filtered

128 candidates to 214 candidates (-67.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	211	3	214
Fresh	4	3	7
Picked	0	1	1
Done	0	0	0
Total	215	7	222

Merged error: 0b

Counts

222 → 7

regimes31.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	25
1	17	25

end0.0ms

sample902.0ms

Algorithm

intervals

Results

294.0ms	1836×	body	640	valid
238.0ms	1147×	body	1280	valid
172.0ms	4093×	body	80	valid
72.0ms	616×	body	320	valid
24.0ms	308×	body	160	valid

Details

analyze6.0ms

sample28.0ms

simplify7.0ms

prune3.0ms

localize7.0ms

rewrite57.0ms

series27.0ms

simplify57.0ms

prune122.0ms

localize11.0ms

rewrite161.0ms

series32.0ms

simplify120.0ms

prune232.0ms

localize11.0ms

rewrite91.0ms

series36.0ms

simplify70.0ms

prune198.0ms

localize14.0ms

rewrite110.0ms

series48.0ms

simplify74.0ms

prune157.0ms

regimes31.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample902.0ms

Profiling