Details

sample25.0ms

Algorithm

intervals

Results

8.0ms	248×	body	80	valid
2.0ms	17×	body	640	valid
1.0ms	13×	body	320	valid
1.0ms	6×	body	1280	valid
1.0ms	12×	body	160	valid

simplify72.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	6
1	44	6
2	122	6
3	327	6
4	868	6
5	1727	6
6	3544	6
7	5001	6

prune5.0ms

Filtered

1 candidates to 0 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: 14.6b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- t x) (- a z))
4.1b	(+ x (* (- y z) (/ (- t x) (- a z))))
5.7b	(* (- y z) (/ (- t x) (- a z)))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

101×	`*-un-lft-identity`
96×	`add-sqr-sqrt`
51×	`times-frac`
33×	`add-cube-cbrt`
31×	`associate-r` `distribute-lft-out--`
30×	`frac-times`
29×	`difference-of-squares`
22×	`flip3--` `flip--` `associate-/l*`
20×	`associate-/r*`
15×	`associate-*r/`
10×	`add-exp-log` `add-cbrt-cube`
8×	`associate-/l/`
7×	`associate-l`
5×	`pow1` `clear-num` `add-log-exp`
4×	`frac-2neg` `associate-/r/`
3×	`un-div-inv` `distribute-lft-out`
2×	`cbrt-undiv` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`+-commutative` `flip3-+` `div-sub` `pow-prod-down` `sum-log` `*-commutative` `flip-+`

Counts

3 → 167

Calls

3 calls:

8.0ms	(/ (- t x) (- a z))
22.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
21.0ms	(* (- y z) (/ (- t x) (- a z)))

series351.0ms

Counts

3 → 9

Calls

3 calls:

55.0ms	(/ (- t x) (- a z))
159.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
137.0ms	(* (- y z) (/ (- t x) (- a z)))

simplify80.0ms

Algorithm

egg-herbie

Counts

176 → 176

Iterations

Useful iterations: 1 (16.0ms)

Iter	Nodes	Cost
0	631	1308
1	3257	1259
2	5002	1259

prune307.0ms

Filtered

176 candidates to 118 candidates (33.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	166	10	176
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	167	10	177

Merged error: 4.2b

Counts

177 → 10

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- a z) (- t x))
4.1b	(+ x (/ (- y z) (/ (- a z) (- t x))))
5.6b	(/ (- y z) (/ (- a z) (- t x)))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

330×	`times-frac`
329×	`*-un-lft-identity`
327×	`add-sqr-sqrt`
115×	`add-cube-cbrt`
106×	`distribute-lft-out--` `difference-of-squares`
41×	`associate-/r*`
29×	`associate-/r/`
15×	`associate-/l*`
10×	`add-exp-log` `flip3--` `add-cbrt-cube` `flip--`
8×	`div-inv`
6×	`associate-/l/`
5×	`add-log-exp`
4×	`cbrt-undiv` `div-exp`
3×	`pow1` `frac-2neg` `div-sub` `clear-num`
1×	`+-commutative` `associate-+r-` `flip3-+` `sum-log` `flip-+` `distribute-lft-out`

Counts

3 → 288

Calls

3 calls:

10.0ms	(/ (- a z) (- t x))
44.0ms	(+ x (/ (- y z) (/ (- a z) (- t x))))
18.0ms	(/ (- y z) (/ (- a z) (- t x)))

series536.0ms

Counts

3 → 9

Calls

3 calls:

52.0ms	(/ (- a z) (- t x))
163.0ms	(+ x (/ (- y z) (/ (- a z) (- t x))))
321.0ms	(/ (- y z) (/ (- a z) (- t x)))

simplify114.0ms

Algorithm

egg-herbie

Counts

297 → 297

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	1068	3103
1	4405	3034
2	5001	3034

prune454.0ms

Filtered

297 candidates to 179 candidates (39.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	291	6	297
Fresh	6	3	9
Picked	0	1	1
Done	0	0	0
Total	297	10	307

Merged error: 4.2b

Counts

307 → 10

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- y z) (- (- a z)))
2.2b	(* (/ (- y z) (- (- a z))) (- (- t x)))
2.7b	(+ x (* (/ (- y z) (- (- a z))) (- (- t x))))

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

210×	`add-sqr-sqrt`
209×	`*-un-lft-identity`
141×	`times-frac`
81×	`add-cube-cbrt`
77×	`associate-l`
75×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
62×	`distribute-lft-out--` `difference-of-squares`
56×	`associate-/r*`
54×	`distribute-neg-frac`
48×	`frac-times`
31×	`flip3--` `flip--`
24×	`associate-*l/`
20×	`associate-/l*`
15×	`neg-mul-1`
14×	`associate-r`
10×	`add-exp-log` `add-cbrt-cube`
8×	`distribute-neg-in` `associate-/l/`
5×	`pow1` `add-log-exp`
4×	`distribute-rgt-in` `sub-neg` `associate-+r+` `frac-2neg` `distribute-lft-in` `clear-num` `associate-/r/`
3×	`distribute-rgt-neg-out`
2×	`cbrt-undiv` `associate-*r/` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `distribute-lft-out` `unswap-sqr`
1×	`+-commutative` `flip3-+` `div-sub` `unsub-neg` `pow-prod-down` `sum-log` `*-commutative` `flip-+`

Counts

3 → 309

Calls

3 calls:

10.0ms	(/ (- y z) (- (- a z)))
38.0ms	(* (/ (- y z) (- (- a z))) (- (- t x)))
49.0ms	(+ x (* (/ (- y z) (- (- a z))) (- (- t x))))

series519.0ms

Counts

3 → 9

Calls

3 calls:

52.0ms	(/ (- y z) (- (- a z)))
305.0ms	(* (/ (- y z) (- (- a z))) (- (- t x)))
161.0ms	(+ x (* (/ (- y z) (- (- a z))) (- (- t x))))

simplify56.0ms

Algorithm

egg-herbie

Counts

318 → 318

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1436	2916
1	5001	2861

prune751.0ms

Filtered

318 candidates to 214 candidates (32.7%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	317	1	318
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	317	11	328

Merged error: 4.2b

Counts

328 → 11

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- t x) (- a z))
0.4b	(/ 1 (/ (- t x) (- a z)))
5.6b	(/ (- y z) (/ 1 (/ (- t x) (- a z))))
6.3b	(+ x (/ (- y z) (/ 1 (/ (- t x) (- a z)))))

rewrite295.0ms

Algorithm

rewrite-expression-head

Rules

1811×	`times-frac`
1364×	`*-un-lft-identity`
1359×	`add-sqr-sqrt`
621×	`add-cube-cbrt`
370×	`distribute-lft-out--`
369×	`difference-of-squares`
214×	`associate-/r*`
190×	`associate-/r/`
53×	`associate-/l*`
36×	`add-exp-log`
33×	`flip3--` `flip--`
32×	`div-inv`
22×	`div-exp`
20×	`add-cbrt-cube`
18×	`associate-/l/`
12×	`clear-num`
11×	`frac-2neg`
10×	`cbrt-undiv`
6×	`add-log-exp`
5×	`pow1`
4×	`rec-exp` `1-exp`
3×	`div-sub` `remove-double-div`
1×	`+-commutative` `associate-+r-` `pow-flip` `flip3-+` `sum-log` `flip-+` `distribute-lft-out` `inv-pow`

Counts

4 → 967

Calls

4 calls:

8.0ms	(/ (- t x) (- a z))
14.0ms	(/ 1 (/ (- t x) (- a z)))
44.0ms	(/ (- y z) (/ 1 (/ (- t x) (- a z))))
137.0ms	(+ x (/ (- y z) (/ 1 (/ (- t x) (- a z)))))

series557.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(/ (- t x) (- a z))
212.0ms	(/ 1 (/ (- t x) (- a z)))
131.0ms	(/ (- y z) (/ 1 (/ (- t x) (- a z))))
162.0ms	(+ x (/ (- y z) (/ 1 (/ (- t x) (- a z)))))

simplify185.0ms

Algorithm

egg-herbie

Counts

979 → 979

Iterations

Useful iterations: 1 (55.0ms)

Iter	Nodes	Cost
0	3003	12630
1	5002	11738

prune1.3s

Filtered

979 candidates to 464 candidates (52.6%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	977	2	979
Fresh	2	6	8
Picked	0	1	1
Done	0	2	2
Total	979	11	990

Merged error: 4.2b

Counts

990 → 11

regimes233.0ms

Accuracy

-3.6% (7.8b remaining)

Error of 12.1b against oracle of 4.3b and baseline of 11.8b

bsearch89.0ms

Steps

Iters	Range		Point
6	6.205046733010805e-06	3.0981377036179784e-05	6.276232023584138e-06
9	-5.075255642507074e-86	-2.48737230382698e-95	-1.128219015475836e-90

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	14
1	39	14
2	42	14
3	42	14

end0.0ms

sample711.0ms

Algorithm

intervals

Results

259.0ms	7786×	body	80	valid
69.0ms	518×	body	640	valid
40.0ms	258×	body	1280	valid
36.0ms	376×	body	320	valid
20.0ms	321×	body	160	valid
4.0ms	21×	body	2560	valid