Details

sample20.0ms

Algorithm

intervals

Results

5.0ms	53×	body	1280	valid
3.0ms	131×	body	80	valid
3.0ms	33×	body	640	valid
2.0ms	28×	body	320	valid
0.0ms	11×	body	160	valid

simplify23.0ms

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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.6b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
4.0b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite129.0ms

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:

11.0ms	(/ x (+ x 1.0))
26.0ms	(/ (+ x 1.0) (- x 1.0))
88.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series181.0ms

Counts

3 → 9

Calls

3 calls:

30.0ms	(/ x (+ x 1.0))
36.0ms	(/ (+ x 1.0) (- x 1.0))
114.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify43.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (34.0ms)

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

prune202.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
4.0b	(log (exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
4.0b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite381.0ms

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:

11.0ms	(/ x (+ x 1.0))
24.0ms	(/ (+ x 1.0) (- x 1.0))
251.0ms	(log (exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
88.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series298.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(/ x (+ x 1.0))
34.0ms	(/ (+ x 1.0) (- x 1.0))
117.0ms	(log (exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
114.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify47.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 2 (35.0ms)

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

prune268.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
4.0b	(+ (/ x (+ x 1.0)) (- (/ (+ x 1.0) (- x 1.0))))

rewrite161.0ms

Algorithm

rewrite-expression-head

Rules

101×	`*-un-lft-identity`
48×	`times-frac`
33×	`add-sqr-sqrt`
28×	`distribute-lft-out`
23×	`add-cube-cbrt`
9×	`distribute-rgt-neg-in` `associate-/r*` `distribute-lft-out--`
7×	`add-exp-log` `add-cbrt-cube` `associate-/l*` `add-log-exp`
5×	`difference-of-squares`
4×	`associate-/r/`
3×	`pow1` `flip3-+` `flip-+`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv` `associate-/l/`
1×	`+-commutative` `neg-sub0` `associate-+r-` `flip3--` `unsub-neg` `neg-log` `frac-add` `flip--` `distribute-neg-frac`

Counts

3 → 104

Calls

3 calls:

11.0ms	(/ x (+ x 1.0))
24.0ms	(/ (+ x 1.0) (- x 1.0))
120.0ms	(+ (/ x (+ x 1.0)) (- (/ (+ x 1.0) (- x 1.0))))

series188.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(/ x (+ x 1.0))
35.0ms	(/ (+ x 1.0) (- x 1.0))
117.0ms	(+ (/ x (+ x 1.0)) (- (/ (+ x 1.0) (- x 1.0))))

simplify48.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	408	720
1	1650	672
2	5002	658

prune171.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
4.0b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
4.0b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
4.0b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite324.0ms

Algorithm

rewrite-expression-head

Rules

189×	`*-un-lft-identity`
80×	`times-frac`
53×	`add-sqr-sqrt`
52×	`distribute-lft-out--`
32×	`distribute-lft-out`
16×	`cbrt-prod` `difference-of-squares`
10×	`add-log-exp`
5×	`add-cube-cbrt`
4×	`pow1` `add-exp-log` `flip3--` `frac-sub` `add-cbrt-cube` `flip--`
3×	`sub-neg` `cbrt-div` `diff-log`
1×	`pow1/3`

Counts

4 → 105

Calls

4 calls:

59.0ms	(cbrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
86.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
85.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
89.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series603.0ms

Counts

4 → 12

Calls

4 calls:

251.0ms	(cbrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
115.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
120.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
116.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify135.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 3 (116.0ms)

Iter	Nodes	Cost
0	344	1307
1	1031	1239
2	4296	1200
3	5001	1190

prune232.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes27.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.4b

bsearch80.0ms

Steps

Iters	Range		Point
10	26.826342714152005	1.350953981158519e+19	11258.21718550442
8	-5184857.938787598	-4116.604674393256	-14610.347047709978

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	20
1	37	20

end0.0ms

sample547.0ms

Algorithm

intervals

Results

182.0ms	1716×	body	1280	valid
101.0ms	1241×	body	640	valid
92.0ms	4094×	body	80	valid
40.0ms	665×	body	320	valid
12.0ms	284×	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

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