Details

sample30.0ms

Algorithm

intervals

Results

9.0ms	256×	body	80	valid
2.0ms	17×	body	640	valid
1.0ms	14×	body	320	valid
1.0ms	7×	body	1280	valid
0.0ms	1×	body	2560	valid
0.0ms	3×	body	160	valid

simplify105.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (8.0ms)

Iter	Nodes	Cost
0	20	6
1	45	6
2	116	5
3	324	5
4	861	5
5	1912	5
6	4581	5
7	5001	5

prune12.0ms

Filtered

1 candidates to 1 candidates (100.0%)

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: 10.1b

Counts

2 → 2

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- y z) (- a z))
1.9b	(fma (/ (- y z) (- a z)) (- t x) x)

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt` `*-un-lft-identity`
25×	`times-frac`
14×	`add-cube-cbrt`
12×	`distribute-lft-out--` `difference-of-squares`
5×	`associate-/r` `associate-/l`
4×	`add-exp-log` `add-cbrt-cube`
2×	`pow1` `expm1-log1p-u` `flip3--` `associate-/r/` `flip--` `log1p-expm1-u` `associate-/l/` `add-log-exp`
1×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `clear-num` `fma-udef` `div-inv`

Counts

2 → 64

Calls

2 calls:

9.0ms	(/ (- y z) (- a z))
1.0ms	(fma (/ (- y z) (- a z)) (- t x) x)

series198.0ms

Counts

2 → 6

Calls

2 calls:

62.0ms	(/ (- y z) (- a z))
136.0ms	(fma (/ (- y z) (- a z)) (- t x) x)

simplify82.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (74.0ms)

Iter	Nodes	Cost
0	263	450
1	726	425
2	2550	423
3	5003	421

prune172.0ms

Filtered

70 candidates to 51 candidates (72.9%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	58	12	70
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	59	13	72

Merged error: 3.4b

Counts

72 → 13

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ y (- a z)) (/ z (- a z)))
0.0b	(/ z (- a z))
0.0b	(/ y (- a z))
1.9b	(fma (- (/ y (- a z)) (/ z (- a z))) (- t x) x)

rewrite132.0ms

Algorithm

rewrite-expression-head

Rules

819×	`*-un-lft-identity`
797×	`add-sqr-sqrt`
693×	`times-frac`
459×	`add-cube-cbrt`
441×	`prod-diff`
177×	`distribute-lft-out--`
167×	`difference-of-squares`
138×	`associate-/r*`
121×	`frac-sub`
94×	`associate-/r/`
72×	`associate-/l*`
48×	`flip3--` `flip--`
47×	`div-inv`
26×	`frac-2neg`
24×	`clear-num`
21×	`fma-neg`
13×	`sub-div`
8×	`add-exp-log` `add-cbrt-cube`
6×	`add-log-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-rgt-out--`
2×	`cbrt-undiv` `div-exp`
1×	`sub-neg` `diff-log` `fma-udef`

Counts

4 → 713

Calls

4 calls:

53.0ms	(- (/ y (- a z)) (/ z (- a z)))
6.0ms	(/ z (- a z))
6.0ms	(/ y (- a z))
1.0ms	(fma (- (/ y (- a z)) (/ z (- a z))) (- t x) x)

series302.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(- (/ y (- a z)) (/ z (- a z)))
51.0ms	(/ z (- a z))
39.0ms	(/ y (- a z))
133.0ms	(fma (- (/ y (- a z)) (/ z (- a z))) (- t x) x)

simplify208.0ms

Algorithm

egg-herbie

Counts

725 → 725

Iterations

Useful iterations: 1 (62.0ms)

Iter	Nodes	Cost
0	2170	17581
1	5001	13794

prune1.4s

Filtered

725 candidates to 344 candidates (47.4%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	717	8	725
Fresh	6	6	12
Picked	1	0	1
Done	0	0	0
Total	724	14	738

Merged error: 3.4b

Counts

738 → 14

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ y (- a z))
0.0b	(/ 1 (- a z))
0.1b	(* z (/ 1 (- a z)))
4.6b	(fma (- (/ y (- a z)) (* z (/ 1 (- a z)))) (- t x) x)

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

67×	`add-sqr-sqrt`
62×	`*-un-lft-identity`
47×	`times-frac`
36×	`add-cube-cbrt`
21×	`associate-r`
19×	`add-exp-log`
15×	`associate-/r*`
13×	`add-cbrt-cube`
12×	`distribute-lft-out--` `difference-of-squares`
11×	`associate-*r/`
10×	`associate-/l*`
7×	`pow1`
6×	`associate-/r/`
5×	`div-exp`
4×	`expm1-log1p-u` `prod-exp` `clear-num` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `flip3--` `frac-2neg` `associate-l` `un-div-inv` `flip--` `div-inv` `unswap-sqr`
2×	`rec-exp` `1-exp` `cbrt-unprod`
1×	`pow-flip` `pow-prod-down` `*-commutative` `fma-udef` `inv-pow`

Counts

4 → 150

Calls

4 calls:

6.0ms	(/ y (- a z))
6.0ms	(/ 1 (- a z))
13.0ms	(* z (/ 1 (- a z)))
1.0ms	(fma (- (/ y (- a z)) (* z (/ 1 (- a z)))) (- t x) x)

series261.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(/ y (- a z))
47.0ms	(/ 1 (- a z))
50.0ms	(* z (/ 1 (- a z)))
132.0ms	(fma (- (/ y (- a z)) (* z (/ 1 (- a z)))) (- t x) x)

simplify118.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	376	754
1	1470	671
2	4940	619
3	5001	619

prune328.0ms

Filtered

162 candidates to 103 candidates (63.6%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	154	8	162
Fresh	7	6	13
Picked	1	0	1
Done	0	0	0
Total	162	14	176

Merged error: 3.4b

Counts

176 → 14

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- a z) (- y z))
0.2b	(/ 1 (/ (- a z) (- y z)))
1.9b	(fma (/ 1 (/ (- a z) (- y z))) (- t x) x)

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

218×	`times-frac`
204×	`*-un-lft-identity`
201×	`add-sqr-sqrt`
93×	`add-cube-cbrt`
55×	`distribute-lft-out--`
54×	`difference-of-squares`
41×	`associate-/r*`
25×	`associate-/r/`
16×	`add-exp-log`
15×	`associate-/l*`
10×	`add-cbrt-cube`
8×	`div-exp`
7×	`flip3--` `flip--`
6×	`div-inv`
4×	`pow1` `cbrt-undiv` `clear-num` `associate-/l/`
3×	`expm1-log1p-u` `frac-2neg` `log1p-expm1-u` `remove-double-div` `add-log-exp`
2×	`rec-exp` `1-exp`
1×	`pow-flip` `div-sub` `fma-udef` `inv-pow`

Counts

3 → 231

Calls

3 calls:

15.0ms	(/ (- a z) (- y z))
15.0ms	(/ 1 (/ (- a z) (- y z)))
1.0ms	(fma (/ 1 (/ (- a z) (- y z))) (- t x) x)

series369.0ms

Counts

3 → 9

Calls

3 calls:

63.0ms	(/ (- a z) (- y z))
160.0ms	(/ 1 (/ (- a z) (- y z)))
145.0ms	(fma (/ 1 (/ (- a z) (- y z))) (- t x) x)

simplify94.0ms

Algorithm

egg-herbie

Counts

240 → 240

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	648	1956
1	2878	1768
2	5002	1591

prune306.0ms

Filtered

240 candidates to 113 candidates (47.1%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	237	3	240
Fresh	3	10	13
Picked	1	0	1
Done	0	0	0
Total	241	13	254

Merged error: 3.4b

Counts

254 → 13

regimes421.0ms

Accuracy

17.5% (6.6b remaining)

Error of 10.2b against oracle of 3.7b and baseline of 11.6b

bsearch97.0ms

Steps

Iters	Range		Point
8	1.1822453681052812e+79	2.6715655829828853e+82	1.0190187249698245e+82
7	-2.029412116266154e+183	-6.516182338417874e+181	-2.0807436000900952e+182

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	10
1	25	10

end0.0ms

sample769.0ms

Algorithm

intervals

Results

291.0ms	7733×	body	80	valid
70.0ms	480×	body	640	valid
44.0ms	273×	body	1280	valid
43.0ms	433×	body	320	valid
16.0ms	246×	body	160	valid
4.0ms	18×	body	2560	valid