Details

sample22.0ms

Algorithm

intervals

Results

6.0ms	51×	body	1280	valid
4.0ms	44×	body	640	valid
4.0ms	145×	body	80	valid
1.0ms	11×	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: 26.5b

Counts

2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
1.5b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite50.0ms

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:

5.0ms	(/ x (+ x 1.0))
8.0ms	(/ (+ x 1.0) (- x 1.0))
33.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series204.0ms

Counts

3 → 9

Calls

3 calls:

33.0ms	(/ x (+ x 1.0))
41.0ms	(/ (+ x 1.0) (- x 1.0))
129.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify42.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (32.0ms)

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

prune198.0ms

Filtered

113 candidates to 76 candidates (67.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	109	4	113
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	110	4	114

Merged error: 0.0b

Counts

114 → 4

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (- x 1.0))
0.0b	(/ x (+ x 1.0))
0.1b	(* (+ x 1.0) (/ 1 (- x 1.0)))
4.6b	(- (/ x (+ x 1.0)) (* (+ x 1.0) (/ 1 (- x 1.0))))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 141

Calls

4 calls:

6.0ms	(/ 1 (- x 1.0))
5.0ms	(/ x (+ x 1.0))
13.0ms	(* (+ x 1.0) (/ 1 (- x 1.0)))
10.0ms	(- (/ x (+ x 1.0)) (* (+ x 1.0) (/ 1 (- x 1.0))))

series235.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(/ 1 (- x 1.0))
38.0ms	(/ x (+ x 1.0))
37.0ms	(* (+ x 1.0) (/ 1 (- x 1.0)))
134.0ms	(- (/ x (+ x 1.0)) (* (+ x 1.0) (/ 1 (- x 1.0))))

simplify73.0ms

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	576	950
1	2837	862
2	5001	820

prune193.0ms

Filtered

153 candidates to 100 candidates (65.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	153	0	153
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	153	4	157

Merged error: 0.0b

Counts

157 → 4

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ x 1.0) (- x 1.0))
0.0b	(* (sqrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (sqrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
1.5b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
1.5b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite175.0ms

Algorithm

rewrite-expression-head

Rules

943×	`*-un-lft-identity`
364×	`times-frac`
253×	`distribute-lft-out--`
186×	`sqrt-prod`
166×	`distribute-lft-out`
117×	`add-sqr-sqrt`
79×	`swap-sqr`
29×	`difference-of-squares`
24×	`sqrt-div`
23×	`add-cube-cbrt`
19×	`pow1` `associate-r` `associate-l`
11×	`flip3--` `flip--`
10×	`frac-sub`
9×	`frac-times`
8×	`add-exp-log` `sqrt-pow1` `pow1/2` `add-cbrt-cube` `add-log-exp`
5×	`associate-/r*` `pow-prod-up`
4×	`associate-/l*` `unswap-sqr`
3×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `pow2` `frac-2neg` `flip3-+` `pow-plus` `sqrt-unprod` `div-exp` `prod-exp` `clear-num` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `flip-+` `div-inv`

Counts

4 → 258

Calls

4 calls:

8.0ms	(/ (+ x 1.0) (- x 1.0))
73.0ms	(* (sqrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (sqrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
30.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
34.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series438.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(/ (+ x 1.0) (- x 1.0))
135.0ms	(* (sqrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (sqrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
135.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
130.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify85.0ms

Algorithm

egg-herbie

Counts

270 → 270

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	457	2586
1	1773	2448
2	5001	2412

prune303.0ms

Filtered

270 candidates to 113 candidates (41.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	270	0	270
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	270	4	274

Merged error: 0.0b

Counts

274 → 4

localize5.0ms

Local error

Found 1 expressions with local error:

0.0b	(* x (+ 3.0 (* x 1.0)))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 22

Calls

1 calls:

5.0ms

(* x (+ 3.0 (* x 1.0)))

series66.0ms

Counts

1 → 3

Calls

1 calls:

66.0ms

(* x (+ 3.0 (* x 1.0)))

simplify102.0ms

Algorithm

egg-herbie

Counts

25 → 25

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	144	117
1	680	103
2	3770	103
3	5002	103

prune26.0ms

Filtered

25 candidates to 16 candidates (64.0%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	25	0	25
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	25	4	29

Merged error: 0.0b

Counts

29 → 4

regimes45.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.8b

bsearch68.0ms

Steps

Iters	Range		Point
8	1.3894494120209264	29774.780359327975	10382.874295286307
9	-3141188.981794727	-6.238959787773506	-10689.65836839195

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	15
1	35	15

end0.0ms

sample621.0ms

Algorithm

intervals

Results

221.0ms	1739×	body	1280	valid
129.0ms	1289×	body	640	valid
119.0ms	4045×	body	80	valid
45.0ms	600×	body	320	valid
17.0ms	327×	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

sample22.0ms

simplify20.0ms

prune2.0ms

localize6.0ms

rewrite50.0ms

series204.0ms

simplify42.0ms

prune198.0ms

localize7.0ms

rewrite38.0ms

series235.0ms

simplify73.0ms

prune193.0ms

localize8.0ms

rewrite175.0ms

series438.0ms

simplify85.0ms

prune303.0ms

localize5.0ms

rewrite6.0ms

series66.0ms

simplify102.0ms

prune26.0ms

regimes45.0ms

bsearch68.0ms

simplify1.0ms

end0.0ms

sample621.0ms

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