Details

analyze2.1s

Algorithm: search

sample101.0ms

Algorithm

intervals

Results

38.0ms	377×	body	80	invalid
22.0ms	256×	body	80	valid

simplify82.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune6.0ms

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: 11.0b

Counts

2 → 1

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a))))
4.4b	(* x (- (* y z) (* t a)))
4.5b	(* j (- (* c t) (* i y)))
4.8b	(* b (- (* c z) (* i a)))

rewrite28.0ms

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

series130.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a))))
18.0ms	(* x (- (* y z) (* t a)))
18.0ms	(* j (- (* c t) (* i y)))
20.0ms	(* b (- (* c z) (* i a)))

simplify80.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	593	891
1	2760	825
2	5001	825

prune275.0ms

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: 4.6b

Counts

109 → 21

localize25.0ms

Local error

Found 4 expressions with local error:

4.5b	(* j (- (* c t) (* i y)))
5.9b	(cbrt (- (* c z) (* i a)))
5.9b	(cbrt (- (* c z) (* i a)))
5.9b	(cbrt (- (* c z) (* i a)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 63

Calls

4 calls:

6.0ms	(* j (- (* c t) (* i y)))
3.0ms	(cbrt (- (* c z) (* i a)))
3.0ms	(cbrt (- (* c z) (* i a)))
3.0ms	(cbrt (- (* c z) (* i a)))

series131.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* j (- (* c t) (* i y)))
36.0ms	(cbrt (- (* c z) (* i a)))
39.0ms	(cbrt (- (* c z) (* i a)))
37.0ms	(cbrt (- (* c z) (* i a)))

simplify102.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 3 (95.0ms)

Iter	Nodes	Cost
0	311	605
1	1070	558
2	3852	546
3	5001	537

prune223.0ms

Filtered

59 candidates to 75 candidates (-27.1%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	74	1	75
Fresh	0	20	20
Picked	1	0	1
Done	0	0	0
Total	75	21	96

Merged error: 4.6b

Counts

96 → 21

localize25.0ms

Local error

Found 4 expressions with local error:

2.4b	(* (cbrt b) (- (* c z) (* i a)))
2.6b	(* (* (cbrt b) (cbrt b)) (* (cbrt b) (- (* c z) (* i a))))
4.4b	(* x (- (* y z) (* t a)))
4.5b	(* j (- (* c t) (* i y)))

rewrite32.0ms

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 b) (- (* c z) (* i a)))
12.0ms	(* (* (cbrt b) (cbrt b)) (* (cbrt b) (- (* c z) (* i a))))
6.0ms	(* x (- (* y z) (* t a)))
6.0ms	(* j (- (* c t) (* i y)))

series126.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(* (cbrt b) (- (* c z) (* i a)))
25.0ms	(* (* (cbrt b) (cbrt b)) (* (cbrt b) (- (* c z) (* i a))))
18.0ms	(* x (- (* y z) (* t a)))
17.0ms	(* j (- (* c t) (* i y)))

simplify69.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	591	987
1	2501	780
2	5002	717

prune230.0ms

Filtered

71 candidates to 120 candidates (-69.0%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	119	1	120
Fresh	0	20	20
Picked	1	0	1
Done	0	0	0
Total	120	21	141

Merged error: 4.6b

Counts

141 → 21

localize29.0ms

Local error

Found 4 expressions with local error:

4.8b	(* b (- (* c z) (* i a)))
6.8b	(cbrt (* j (- (* c t) (* i y))))
6.8b	(cbrt (* j (- (* c t) (* i y))))
6.8b	(cbrt (* j (- (* c t) (* i y))))

rewrite20.0ms

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) (* i a)))
4.0ms	(cbrt (* j (- (* c t) (* i y))))
4.0ms	(cbrt (* j (- (* c t) (* i y))))
5.0ms	(cbrt (* j (- (* c t) (* i y))))

series144.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(* b (- (* c z) (* i a)))
41.0ms	(cbrt (* j (- (* c t) (* i y))))
43.0ms	(cbrt (* j (- (* c t) (* i y))))
42.0ms	(cbrt (* j (- (* c t) (* i y))))

simplify108.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 3 (99.0ms)

Iter	Nodes	Cost
0	310	554
1	1110	501
2	4336	492
3	5002	486

prune86.0ms

Filtered

56 candidates to 69 candidates (-23.2%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	67	2	69
Fresh	1	19	20
Picked	1	0	1
Done	0	0	0
Total	69	21	90

Merged error: 4.6b

Counts

90 → 21

regimes2.2s

Accuracy

29.1% (5.5b remaining)

Error of 10.3b against oracle of 4.8b and baseline of 12.6b

bsearch9.5s

Steps

Iters	Range		Point
8	9.124131826538034e+49	2.262679049320267e+53	2.166170184509982e+51
8	-1.8886284166294082e+64	-4.8049095230796695e+60	-1.310884934271574e+64

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	63	38
1	63	38

end0.0ms

analyze2.1s

Algorithm: search

sample2.7s

Algorithm

intervals

Results

996.0ms	11125×	body	80	invalid
706.0ms	8000×	body	80	valid

Details

analyze2.1s

sample101.0ms

simplify82.0ms

prune6.0ms

localize20.0ms

rewrite28.0ms

series130.0ms

simplify80.0ms

prune275.0ms

localize25.0ms

rewrite17.0ms

series131.0ms

simplify102.0ms

prune223.0ms

localize25.0ms

rewrite32.0ms

series126.0ms

simplify69.0ms

prune230.0ms

localize29.0ms

rewrite20.0ms

series144.0ms

simplify108.0ms

prune86.0ms

regimes2.2s

bsearch9.5s

simplify2.0ms

end0.0ms

analyze2.1s

sample2.7s

Profiling