Details

sample25.0ms

Algorithm

intervals

Results

8.0ms	62×	body	1280	valid
5.0ms	48×	body	640	valid
4.0ms	122×	body	80	valid
1.0ms	19×	body	320	valid
0.0ms	5×	body	160	valid

simplify20.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	6
1	16	6
2	19	6
3	21	6
4	27	6
5	39	6
6	58	6
7	79	6
8	107	6
9	160	6
10	277	6
11	303	6
12	303	6

prune2.0ms

Filtered

1 candidates to 0 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: 31.7b

Counts

2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (+ x 1.0) (- x 1.0))
0.0b	(/ x (+ x 1.0))
2.1b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

99×	`*-un-lft-identity`
52×	`times-frac`
45×	`add-sqr-sqrt`
23×	`add-cube-cbrt`
18×	`distribute-lft-out` `distribute-lft-out--`
9×	`associate-/r*` `difference-of-squares`
7×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
5×	`add-log-exp`
4×	`associate-/r/`
3×	`pow1`
2×	`cbrt-undiv` `flip3--` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip--` `flip-+` `div-inv` `associate-/l/`
1×	`sub-neg` `diff-log` `frac-sub`

Counts

3 → 104

Calls

3 calls:

7.0ms	(/ (+ x 1.0) (- x 1.0))
5.0ms	(/ x (+ x 1.0))
33.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series204.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(/ (+ x 1.0) (- x 1.0))
38.0ms	(/ x (+ x 1.0))
128.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify48.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	392	760
1	1379	726
2	5001	716

prune188.0ms

Filtered

113 candidates to 76 candidates (67.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	106	7	113
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	107	7	114

Merged error: 0.1b

Counts

114 → 7

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ (neg 1.0) (pow x 2)) (/ 3.0 x))
0.1b	(/ 3.0 (pow x 3))
0.2b	(/ (neg 1.0) (pow x 2))
5.6b	(- (- (/ (neg 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

rewrite161.0ms

Algorithm

rewrite-expression-head

Rules

143×	`times-frac`
120×	`add-sqr-sqrt`
105×	`*-un-lft-identity`
78×	`add-cube-cbrt`
48×	`unpow-prod-down`
29×	`distribute-rgt-neg-in`
27×	`distribute-lft-neg-in`
20×	`associate-/r*`
18×	`sqr-pow`
15×	`difference-of-squares`
14×	`add-exp-log`
13×	`cube-prod` `associate-/l*` `unpow2`
11×	`add-log-exp`
10×	`distribute-lft-out--`
9×	`neg-mul-1`
8×	`add-cbrt-cube`
6×	`div-exp`
5×	`frac-sub`
4×	`pow1` `cube-mult` `diff-log` `unpow3`
3×	`sub-neg` `flip3--` `flip--`
2×	`cbrt-undiv` `associate--l-` `neg-sub0` `pow-to-exp` `frac-2neg` `div-sub` `pow-exp` `associate--l+` `clear-num` `div-inv`
1×	`distribute-frac-neg`

Counts

4 → 234

Calls

4 calls:

56.0ms	(- (/ (neg 1.0) (pow x 2)) (/ 3.0 x))
5.0ms	(/ 3.0 (pow x 3))
7.0ms	(/ (neg 1.0) (pow x 2))
83.0ms	(- (- (/ (neg 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

series165.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(- (/ (neg 1.0) (pow x 2)) (/ 3.0 x))
40.0ms	(/ 3.0 (pow x 3))
25.0ms	(/ (neg 1.0) (pow x 2))
37.0ms	(- (- (/ (neg 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

simplify103.0ms

Algorithm

egg-herbie

Counts

246 → 246

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	738	1746
1	3417	1585
2	5001	1567

prune352.0ms

Filtered

246 candidates to 129 candidates (52.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	245	1	246
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	245	8	253

Merged error: 0.1b

Counts

253 → 8

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ x 1.0) (- x 1.0))
0.0b	(/ x (+ x 1.0))
2.1b	(log (exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
2.1b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

148×	`*-un-lft-identity`
72×	`times-frac`
60×	`add-sqr-sqrt`
31×	`distribute-lft-out--`
26×	`add-cube-cbrt` `distribute-lft-out`
17×	`log-pow`
16×	`exp-prod`
13×	`difference-of-squares`
9×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube`
7×	`associate-/l*`
6×	`add-log-exp`
5×	`pow1` `log-prod`
4×	`associate-/r/`
2×	`cbrt-undiv` `sub-neg` `flip3--` `frac-2neg` `flip3-+` `div-exp` `exp-sum` `clear-num` `flip--` `flip-+` `div-inv` `associate-/l/`
1×	`log-div` `exp-diff` `diff-log` `rem-log-exp` `frac-sub`

Counts

4 → 135

Calls

4 calls:

7.0ms	(/ (+ x 1.0) (- x 1.0))
5.0ms	(/ x (+ x 1.0))
34.0ms	(log (exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
29.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series339.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(/ (+ x 1.0) (- x 1.0))
40.0ms	(/ x (+ x 1.0))
128.0ms	(log (exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
134.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify46.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	441	990
1	1497	930
2	5001	917

prune239.0ms

Filtered

147 candidates to 95 candidates (64.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	147	0	147
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	147	8	155

Merged error: 0.1b

Counts

155 → 8

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ x 1.0) (- x 1.0))
0.0b	(/ 1 (+ x 1.0))
0.1b	(* x (/ 1 (+ x 1.0)))
5.3b	(- (* x (/ 1 (+ x 1.0))) (/ (+ x 1.0) (- x 1.0)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

70×	`*-un-lft-identity`
50×	`add-sqr-sqrt`
46×	`times-frac`
33×	`add-cube-cbrt`
19×	`add-exp-log`
18×	`associate-r`
13×	`add-cbrt-cube` `distribute-lft-out`
9×	`associate-/r*`
7×	`pow1` `associate-/l*`
6×	`associate-/r/` `add-log-exp`
5×	`div-exp` `distribute-lft-out--` `difference-of-squares`
4×	`prod-exp`
3×	`cbrt-undiv` `flip3-+` `associate-l` `flip-+` `div-inv` `unswap-sqr`
2×	`rec-exp` `flip3--` `frac-2neg` `1-exp` `associate-*r/` `clear-num` `un-div-inv` `frac-sub` `flip--` `cbrt-unprod` `associate-/l/`
1×	`sub-neg` `pow-flip` `diff-log` `pow-prod-down` `*-commutative` `inv-pow`

Counts

4 → 137

Calls

4 calls:

8.0ms	(/ (+ x 1.0) (- x 1.0))
5.0ms	(/ 1 (+ x 1.0))
10.0ms	(* x (/ 1 (+ x 1.0)))
14.0ms	(- (* x (/ 1 (+ x 1.0))) (/ (+ x 1.0) (- x 1.0)))

series229.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(/ (+ x 1.0) (- x 1.0))
28.0ms	(/ 1 (+ x 1.0))
33.0ms	(* x (/ 1 (+ x 1.0)))
131.0ms	(- (* x (/ 1 (+ x 1.0))) (/ (+ x 1.0) (- x 1.0)))

simplify60.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	507	873
1	2099	791
2	5002	752

prune175.0ms

Filtered

149 candidates to 92 candidates (61.7%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	147	2	149
Fresh	3	2	5
Picked	0	1	1
Done	0	2	2
Total	150	7	157

Merged error: 0.0b

Counts

157 → 7

regimes61.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.9b

bsearch91.0ms

Steps

Iters	Range		Point
8	2456.611191262651	40897918.92904403	12060.12268311564
10	-1.2424803593581326e+20	-9627.362198738589	-13694.02034117937

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	30
1	50	30
2	53	30
3	53	30

end0.0ms

sample643.0ms

Algorithm

intervals

Results

223.0ms	1660×	body	1280	valid
135.0ms	1305×	body	640	valid
124.0ms	4109×	body	80	valid
48.0ms	614×	body	320	valid
17.0ms	312×	body	160	valid

Iter	Nodes	Cost
0	12	6
1	16	6
2	19	6
3	21	6
4	27	6
5	39	6
6	58	6
7	79	6
8	107	6
9	160	6
10	277	6
11	303	6
12	303	6

Iter	Nodes	Cost
0	12	6
1	16	6
2	19	6
3	21	6
4	27	6
5	39	6
6	58	6
7	79	6
8	107	6
9	160	6
10	277	6
11	303	6
12	303	6

Details

sample25.0ms

simplify20.0ms

prune2.0ms

localize6.0ms

rewrite49.0ms

series204.0ms

simplify48.0ms

prune188.0ms

localize11.0ms

rewrite161.0ms

series165.0ms

simplify103.0ms

prune352.0ms

localize9.0ms

rewrite83.0ms

series339.0ms

simplify46.0ms

prune239.0ms

localize7.0ms

rewrite42.0ms

series229.0ms

simplify60.0ms

prune175.0ms

regimes61.0ms

bsearch91.0ms

simplify2.0ms

end0.0ms

sample643.0ms

Profiling

Iter	Nodes	Cost
0	12	6
1	16	6
2	19	6
3	21	6
4	27	6
5	39	6
6	58	6
7	79	6
8	107	6
9	160	6
10	277	6
11	303	6
12	303	6