Details

analyze261.0ms

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
12.5%	87.4%	0.1%	6
28.1%	71.8%	0.1%	7
42.1%	57.7%	0.1%	8
43.7%	56.2%	0.1%	9
64.4%	35.5%	0.1%	10
71.6%	28.3%	0.1%	11
72.2%	27.7%	0.1%	12
81.6%	18.2%	0.2%	13
84.9%	14.9%	0.2%	14

sample22.0ms

Algorithm

intervals

Results

8.0ms	256×	body	80	valid
0.0ms	7×	body	80	invalid

simplify91.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (83.0ms)

Iter	Nodes	Cost
0	5157	16

prune20.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 1.1b

Counts

2 → 2

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(/.f64 v (+.f64 t1 u))
2.6b	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

223×	`times-frac_binary64`
181×	`add-sqr-sqrt_binary64`
174×	`*-un-lft-identity_binary64`
86×	`add-cube-cbrt_binary64`
38×	`difference-of-squares_binary64`
25×	`distribute-lft-out_binary64`
21×	`associate-/l*_binary64`
19×	`distribute-lft-out--_binary64`
18×	`associate-/r/_binary64`
10×	`associate-/r*_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `div-inv_binary64`
8×	`flip3-+_binary64` `flip-+_binary64`
4×	`cbrt-undiv_binary64` `div-exp_binary64`
2×	`add-log-exp_binary64` `pow1_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`associate-/l/_binary64` `flip3--_binary64` `flip--_binary64`

Counts

2 → 182

Calls

2 calls:

5.0ms	(/.f64 v (+.f64 t1 u))
21.0ms	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))

series88.0ms

Counts

2 → 6

Calls

2 calls:

25.0ms	(/.f64 v (+.f64 t1 u))
63.0ms	(/.f64 (/.f64 v (+.f64 t1 u)) (-.f64 -1 (/.f64 u t1)))

simplify102.0ms

Algorithm

egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5051	5524

prune476.0ms

Filtered

128 candidates to 188 candidates (-46.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	181	7	188
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	181	9	190

Merged error: 0.7b

Counts

190 → 9

localize29.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 (+.f64 u t1))
0.5b	(*.f64 (cbrt.f64 (+.f64 t1 u)) (cbrt.f64 (+.f64 t1 u)))
0.7b	(/.f64 (/.f64 1 (*.f64 (cbrt.f64 (+.f64 t1 u)) (cbrt.f64 (+.f64 t1 u)))) (/.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 v (cbrt.f64 (+.f64 u t1)))))
3.5b	(/.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 v (cbrt.f64 (+.f64 u t1))))

rewrite614.0ms

Algorithm

rewrite-expression-head

Rules

8386×	`times-frac_binary64`
4575×	`add-sqr-sqrt_binary64`
3821×	`*-un-lft-identity_binary64`
2267×	`add-cube-cbrt_binary64`
2236×	`cbrt-div_binary64`
1568×	`associate-/r/_binary64`
1264×	`cbrt-prod_binary64`
1118×	`flip3-+_binary64` `flip-+_binary64`
920×	`difference-of-squares_binary64`
676×	`frac-times_binary64`
460×	`distribute-lft-out--_binary64`
338×	`associate-r/_binary64` `associate-l/_binary64`
316×	`distribute-lft-out_binary64`
289×	`div-inv_binary64`
194×	`associate-/r*_binary64`
68×	`add-exp-log_binary64`
39×	`div-exp_binary64`
35×	`add-cbrt-cube_binary64`
27×	`cbrt-undiv_binary64`
21×	`associate-/l*_binary64`
11×	`pow1_binary64`
9×	`swap-sqr_binary64`
7×	`associate-r_binary64` `pow1/3_binary64` `associate-l_binary64` `prod-exp_binary64`
6×	`rec-exp_binary64`
4×	`add-log-exp_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64`
3×	`associate-/l/_binary64`
2×	`pow-prod-down_binary64` `pow-prod-up_binary64` `clear-num_binary64` `frac-2neg_binary64` `pow-sqr_binary64`
1×	`flip3--_binary64` `pow-plus_binary64` `div-sub_binary64` `flip--_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 3003

Calls

4 calls:

3.0ms	(cbrt.f64 (+.f64 u t1))
17.0ms	(*.f64 (cbrt.f64 (+.f64 t1 u)) (cbrt.f64 (+.f64 t1 u)))
93.0ms	(/.f64 (/.f64 1 (*.f64 (cbrt.f64 (+.f64 t1 u)) (cbrt.f64 (+.f64 t1 u)))) (/.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 v (cbrt.f64 (+.f64 u t1)))))
19.0ms	(/.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 v (cbrt.f64 (+.f64 u t1))))

series530.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(cbrt.f64 (+.f64 u t1))
157.0ms	(*.f64 (cbrt.f64 (+.f64 t1 u)) (cbrt.f64 (+.f64 t1 u)))
124.0ms	(/.f64 (/.f64 1 (*.f64 (cbrt.f64 (+.f64 t1 u)) (cbrt.f64 (+.f64 t1 u)))) (/.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 v (cbrt.f64 (+.f64 u t1)))))
131.0ms	(/.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 v (cbrt.f64 (+.f64 u t1))))

simplify1.8s

Algorithm

egg-herbie

Counts

3015 → 3015

Iterations

Useful iterations: 0 (110.0ms)

Iter	Nodes	Cost
0	4989	239793
1	4989	239793

prune7.7s

Filtered

1575 candidates to 3015 candidates (-91.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	3015	0	3015
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	3015	9	3024

Merged error: 0.7b

Counts

3024 → 9

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(/.f64 1 (+.f64 u t1))
0.2b	(*.f64 v (/.f64 1 (+.f64 u t1)))
2.6b	(/.f64 (*.f64 v (/.f64 1 (+.f64 u t1))) (-.f64 -1 (/.f64 u t1)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

42×	`*-un-lft-identity_binary64`
40×	`add-sqr-sqrt_binary64`
34×	`times-frac_binary64`
25×	`add-exp-log_binary64`
23×	`add-cube-cbrt_binary64`
19×	`add-cbrt-cube_binary64`
18×	`associate-r_binary64`
10×	`associate-/r*_binary64`
7×	`distribute-lft-out_binary64` `div-exp_binary64`
6×	`pow1_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64` `prod-exp_binary64`
4×	`cbrt-unprod_binary64` `difference-of-squares_binary64` `associate-/l*_binary64`
3×	`add-log-exp_binary64` `associate-l_binary64` `unswap-sqr_binary64` `rec-exp_binary64` `div-inv_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `associate-*r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `un-div-inv_binary64` `distribute-lft-out--_binary64` `flip-+_binary64`
1×	`pow-prod-down_binary64` `flip3--_binary64` `inv-pow_binary64` `flip--_binary64` `pow-flip_binary64` `*-commutative_binary64`

Counts

3 → 110

Calls

3 calls:

6.0ms	(/.f64 1 (+.f64 u t1))
10.0ms	(*.f64 v (/.f64 1 (+.f64 u t1)))
15.0ms	(/.f64 (*.f64 v (/.f64 1 (+.f64 u t1))) (-.f64 -1 (/.f64 u t1)))

series106.0ms

Counts

3 → 9

Calls

3 calls:

19.0ms	(/.f64 1 (+.f64 u t1))
26.0ms	(*.f64 v (/.f64 1 (+.f64 u t1)))
62.0ms	(/.f64 (*.f64 v (/.f64 1 (+.f64 u t1))) (-.f64 -1 (/.f64 u t1)))

simplify88.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	5203	1507

prune292.0ms

Filtered

69 candidates to 119 candidates (-72.5%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	119	0	119
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	119	9	128

Merged error: 0.7b

Counts

128 → 9

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(/.f64 v (+.f64 u t1))
0.5b	(/.f64 1 (/.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 v (+.f64 u t1))))
2.5b	(/.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 v (+.f64 u t1)))

rewrite120.0ms

Algorithm

rewrite-expression-head

Rules

1354×	`times-frac_binary64`
924×	`add-sqr-sqrt_binary64`
845×	`*-un-lft-identity_binary64`
469×	`add-cube-cbrt_binary64`
182×	`difference-of-squares_binary64`
135×	`associate-/r*_binary64`
97×	`distribute-lft-out_binary64`
91×	`distribute-lft-out--_binary64`
70×	`associate-/r/_binary64`
38×	`div-inv_binary64`
32×	`flip3-+_binary64` `flip-+_binary64`
25×	`add-exp-log_binary64`
19×	`add-cbrt-cube_binary64`
13×	`div-exp_binary64`
12×	`associate-/l*_binary64`
10×	`cbrt-undiv_binary64`
4×	`pow1_binary64`
3×	`add-log-exp_binary64` `clear-num_binary64` `frac-2neg_binary64` `rec-exp_binary64`
2×	`associate-/l/_binary64`
1×	`flip3--_binary64` `div-sub_binary64` `inv-pow_binary64` `flip--_binary64` `pow-flip_binary64`

Counts

3 → 660

Calls

3 calls:

6.0ms	(/.f64 v (+.f64 u t1))
30.0ms	(/.f64 1 (/.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 v (+.f64 u t1))))
21.0ms	(/.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 v (+.f64 u t1)))

series170.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(/.f64 v (+.f64 u t1))
109.0ms	(/.f64 1 (/.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 v (+.f64 u t1))))
34.0ms	(/.f64 (-.f64 -1 (/.f64 u t1)) (/.f64 v (+.f64 u t1)))

simplify246.0ms

Algorithm

egg-herbie

Counts

669 → 669

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4991	23944
1	4991	23944

prune1.3s

Filtered

362 candidates to 669 candidates (-84.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	668	1	669
Fresh	1	4	5
Picked	1	0	1
Done	1	2	3
Total	671	7	678

Merged error: 0.7b

Counts

678 → 7

regimes390.0ms

Accuracy

0% (1.9b remaining)

Error of 2.2b against oracle of 0.3b and baseline of 2.2b

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	19
1	30	19

end0.0ms

sample503.0ms

Algorithm

intervals

Results

273.0ms	8000×	body	80	valid
8.0ms	249×	body	80	invalid

Details

analyze261.0ms

sample22.0ms

simplify91.0ms

prune20.0ms

localize11.0ms

rewrite37.0ms

series88.0ms

simplify102.0ms

prune476.0ms

localize29.0ms

rewrite614.0ms

series530.0ms

simplify1.8s

prune7.7s

localize13.0ms

rewrite39.0ms

series106.0ms

simplify88.0ms

prune292.0ms

localize13.0ms

rewrite120.0ms

series170.0ms

simplify246.0ms

prune1.3s

regimes390.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample503.0ms

Profiling