Details

analyze2.2s

Algorithm: search

sample100.0ms

Algorithm

intervals

Results

37.0ms	394×	body	80	invalid
21.0ms	256×	body	80	valid

simplify91.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	43	14
1	96	14
2	291	14
3	825	14
4	2021	14
5	5001	14

prune7.0ms

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: 12.3b

Counts

2 → 1

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i))))
4.5b	(* j (- (* c a) (* y i)))
5.5b	(* x (- (* y z) (* t a)))
5.7b	(* b (- (* c z) (* t i)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
14×	`associate-*r/`
11×	`sub-neg`
10×	`pow1` `add-exp-log` `distribute-rgt-in` `add-cube-cbrt` `*-un-lft-identity` `distribute-lft-in` `add-cbrt-cube`
9×	`associate-r` `associate-l`
8×	`flip3--` `flip--`
6×	`add-log-exp`
4×	`associate--l+` `frac-sub` `associate--r+`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`diff-log`

Counts

4 → 96

Calls

4 calls:

9.0ms	(- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i))))
6.0ms	(* j (- (* c a) (* y i)))
6.0ms	(* x (- (* y z) (* t a)))
6.0ms	(* b (- (* c z) (* t i)))

series130.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i))))
22.0ms	(* j (- (* c a) (* y i)))
18.0ms	(* x (- (* y z) (* t a)))
19.0ms	(* b (- (* c z) (* t i)))

simplify94.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 1 (18.0ms)

Iter	Nodes	Cost
0	591	891
1	2752	825
2	5003	825

prune284.0ms

Filtered

71 candidates to 108 candidates (-52.1%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	87	21	108
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	88	21	109

Merged error: 4.2b

Counts

109 → 21

localize26.0ms

Local error

Found 4 expressions with local error:

5.7b	(* b (- (* c z) (* t i)))
7.6b	(cbrt (* x (- (* y z) (* t a))))
7.6b	(cbrt (* x (- (* y z) (* t a))))
7.6b	(cbrt (* x (- (* y z) (* t a))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `associate-*r/`
6×	`pow1` `add-exp-log` `add-cube-cbrt` `cbrt-div` `*-un-lft-identity` `add-cbrt-cube`
4×	`flip3--` `flip--` `add-log-exp`
3×	`cbrt-prod` `pow1/3` `associate-r` `associate-l`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 57

Calls

4 calls:

6.0ms	(* b (- (* c z) (* t i)))
5.0ms	(cbrt (* x (- (* y z) (* t a))))
4.0ms	(cbrt (* x (- (* y z) (* t a))))
6.0ms	(cbrt (* x (- (* y z) (* t a))))

series145.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(* b (- (* c z) (* t i)))
42.0ms	(cbrt (* x (- (* y z) (* t a))))
43.0ms	(cbrt (* x (- (* y z) (* t a))))
42.0ms	(cbrt (* x (- (* y z) (* t a))))

simplify122.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 3 (114.0ms)

Iter	Nodes	Cost
0	309	554
1	1108	501
2	4336	492
3	5002	480

prune239.0ms

Filtered

56 candidates to 69 candidates (-23.2%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	67	2	69
Fresh	0	20	20
Picked	1	0	1
Done	0	0	0
Total	68	22	90

Merged error: 4.2b

Counts

90 → 22

localize32.0ms

Local error

Found 4 expressions with local error:

5.7b	(* b (- (* c z) (* t i)))
7.1b	(cbrt (- (* y z) (* t a)))
7.6b	(cbrt (* x (- (* y z) (* t a))))
7.6b	(cbrt (* x (- (* y z) (* t a))))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `add-exp-log` `cbrt-div` `associate-*r/` `add-cbrt-cube`
5×	`cbrt-prod`
4×	`flip3--` `flip--` `add-log-exp`
3×	`pow1/3` `associate-r` `associate-l`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 59

Calls

4 calls:

6.0ms	(* b (- (* c z) (* t i)))
3.0ms	(cbrt (- (* y z) (* t a)))
4.0ms	(cbrt (* x (- (* y z) (* t a))))
5.0ms	(cbrt (* x (- (* y z) (* t a))))

series139.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(* b (- (* c z) (* t i)))
37.0ms	(cbrt (- (* y z) (* t a)))
43.0ms	(cbrt (* x (- (* y z) (* t a))))
41.0ms	(cbrt (* x (- (* y z) (* t a))))

simplify131.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	381	570
1	1300	519
2	4976	509
3	5001	509

prune236.0ms

Filtered

58 candidates to 71 candidates (-22.4%)

Pruning

22 alts after pruning (21 fresh and 1 done)

	Pruned	Kept	Total
New	71	0	71
Fresh	0	21	21
Picked	0	1	1
Done	0	0	0
Total	71	22	93

Merged error: 4.2b

Counts

93 → 22

localize25.0ms

Local error

Found 4 expressions with local error:

2.4b	(* (cbrt j) (- (* c a) (* y i)))
2.4b	(* (* (cbrt j) (cbrt j)) (* (cbrt j) (- (* c a) (* y i))))
5.5b	(* x (- (* y z) (* t a)))
5.7b	(* b (- (* c z) (* t i)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

22×	`pow1` `add-exp-log`
19×	`add-sqr-sqrt`
15×	`add-cbrt-cube`
14×	`distribute-rgt-in` `distribute-lft-in`
13×	`associate-l`
11×	`add-cube-cbrt` `*-un-lft-identity` `pow-prod-down` `prod-exp` `cbrt-unprod`
10×	`sub-neg` `associate-r/` `associate-r*`
4×	`cbrt-prod` `flip3--` `*-commutative` `flip--` `add-log-exp` `unswap-sqr`

Counts

4 → 108

Calls

4 calls:

6.0ms	(* (cbrt j) (- (* c a) (* y i)))
13.0ms	(* (* (cbrt j) (cbrt j)) (* (cbrt j) (- (* c a) (* y i))))
6.0ms	(* x (- (* y z) (* t a)))
6.0ms	(* b (- (* c z) (* t i)))

series128.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(* (cbrt j) (- (* c a) (* y i)))
23.0ms	(* (* (cbrt j) (cbrt j)) (* (cbrt j) (- (* c a) (* y i))))
18.0ms	(* x (- (* y z) (* t a)))
18.0ms	(* b (- (* c z) (* t i)))

simplify77.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	593	987
1	2490	787
2	5001	724

prune110.0ms

Filtered

71 candidates to 120 candidates (-69.0%)

Pruning

25 alts after pruning (24 fresh and 1 done)

	Pruned	Kept	Total
New	115	5	120
Fresh	1	19	20
Picked	1	0	1
Done	0	1	1
Total	117	25	142

Merged error: 3.5b

Counts

142 → 25

regimes2.7s

Accuracy

19.2% (7.2b remaining)

Error of 10.8b against oracle of 3.6b and baseline of 12.5b

bsearch6.0s

Steps

Iters	Range		Point
5	1.4125587426785253e-118	3.1166770836517706e-118	1.4658632737417495e-118
6	-1.0651312826624269e-95	-9.367979458668637e-97	-3.2546039134189075e-96

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	76	48
1	80	48
2	87	48
3	87	48

end0.0ms

analyze2.0s

Algorithm: search

sample2.6s

Algorithm

intervals

Results

940.0ms	11067×	body	80	invalid
679.0ms	8000×	body	80	valid

Details

analyze2.2s

sample100.0ms

simplify91.0ms

prune7.0ms

localize27.0ms

rewrite29.0ms

series130.0ms

simplify94.0ms

prune284.0ms

localize26.0ms

rewrite23.0ms

series145.0ms

simplify122.0ms

prune239.0ms

localize32.0ms

rewrite20.0ms

series139.0ms

simplify131.0ms

prune236.0ms

localize25.0ms

rewrite35.0ms

series128.0ms

simplify77.0ms

prune110.0ms

regimes2.7s

bsearch6.0s

simplify3.0ms

end0.0ms

analyze2.0s

sample2.6s

Profiling