Details

sample39.0ms

Algorithm

intervals

Results

13.0ms	46×	body	1280	valid
8.0ms	46×	body	640	valid
8.0ms	138×	body	80	valid
2.0ms	16×	body	320	valid
1.0ms	10×	body	160	valid

simplify21.0ms

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: 27.4b

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
2.3b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite74.0ms

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))
11.0ms	(/ (+ x 1.0) (- x 1.0))
54.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series205.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(/ x (+ x 1.0))
41.0ms	(/ (+ x 1.0) (- x 1.0))
129.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify47.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (35.0ms)

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

prune212.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
0.0b	(* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
0.0b	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
2.2b	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))

rewrite220.0ms

Algorithm

rewrite-expression-head

Rules

544×	`*-un-lft-identity`
320×	`times-frac`
170×	`add-sqr-sqrt`
141×	`distribute-lft-out`
106×	`add-cube-cbrt`
72×	`swap-sqr`
52×	`distribute-lft-out--`
44×	`associate-r` `associate-l`
34×	`difference-of-squares`
30×	`add-exp-log` `add-cbrt-cube`
19×	`associate-/r/`
18×	`pow1` `frac-sub`
14×	`frac-times` `associate-r/` `associate-l/`
12×	`associate-/r*`
11×	`associate-/l/`
9×	`cbrt-undiv` `div-exp` `div-inv`
8×	`prod-exp` `cbrt-unprod` `unswap-sqr`
6×	`flip3--` `flip--` `add-log-exp`
5×	`flip3-+` `flip-+`
4×	`associate-/l*`
2×	`pow2` `pow-plus` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up`
1×	`sub-neg` `frac-2neg` `diff-log` `div-sub` `frac-add` `clear-num`

Counts

4 → 329

Calls

4 calls:

109.0ms	(/ (- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
50.0ms	(* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
29.0ms	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
10.0ms	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))

series668.0ms

Counts

4 → 12

Calls

4 calls:

353.0ms	(/ (- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
58.0ms	(* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
44.0ms	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
212.0ms	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))

simplify77.0ms

Algorithm

egg-herbie

Counts

341 → 341

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1294	4957
1	5002	4719

prune499.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (/ (+ x 1.0) (- x 1.0)) 4)
0.1b	(pow (/ x (+ x 1.0)) 4)
0.1b	(pow (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) 3)
2.2b	(- (pow (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) 3) (pow (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))) 3))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

53×	`unpow-prod-down`
51×	`*-un-lft-identity`
41×	`add-sqr-sqrt`
32×	`times-frac`
25×	`add-cube-cbrt`
23×	`add-exp-log`
21×	`cube-div`
20×	`difference-of-squares`
17×	`add-cbrt-cube`
14×	`pow1`
11×	`sqr-pow`
9×	`pow-unpow` `cube-prod` `pow-exp` `frac-sub`
8×	`pow-pow` `distribute-lft-out`
7×	`frac-times` `associate-r/` `associate-l/`
6×	`div-exp` `add-log-exp`
5×	`distribute-lft-out--` `rem-cube-cbrt`
4×	`cbrt-undiv` `prod-exp` `associate-/r/` `cbrt-unprod`
3×	`pow-to-exp`
2×	`flip3--` `flip--` `div-inv`
1×	`difference-cubes` `pow2` `cube-mult` `sub-neg` `flip3-+` `pow-plus` `diff-log` `unpow3` `pow-prod-down` `pow-sqr` `pow-prod-up` `flip-+`

Counts

4 → 148

Calls

4 calls:

14.0ms	(pow (/ (+ x 1.0) (- x 1.0)) 4)
7.0ms	(pow (/ x (+ x 1.0)) 4)
10.0ms	(pow (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) 3)
10.0ms	(- (pow (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) 3) (pow (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))) 3))

series622.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(pow (/ (+ x 1.0) (- x 1.0)) 4)
55.0ms	(pow (/ x (+ x 1.0)) 4)
70.0ms	(pow (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) 3)
435.0ms	(- (pow (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) 3) (pow (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))) 3))

simplify117.0ms

Algorithm

egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 2 (99.0ms)

Iter	Nodes	Cost
0	890	1688
1	3660	1598
2	5001	1581

prune531.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
0.5b	(cbrt (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
0.5b	(cbrt (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
2.2b	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))

rewrite138.0ms

Algorithm

rewrite-expression-head

Rules

145×	`*-un-lft-identity`
51×	`distribute-lft-out`
48×	`times-frac`
36×	`cbrt-prod`
12×	`distribute-lft-out--`
9×	`cbrt-div` `frac-sub`
7×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`frac-times` `associate-r/` `associate-l/` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`flip3-+` `pow1/3` `frac-add` `flip-+`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `difference-of-squares`

Counts

4 → 91

Calls

4 calls:

40.0ms	(cbrt (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
41.0ms	(cbrt (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
39.0ms	(cbrt (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
14.0ms	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))

series834.0ms

Counts

4 → 12

Calls

4 calls:

212.0ms	(cbrt (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
203.0ms	(cbrt (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
210.0ms	(cbrt (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
208.0ms	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))

simplify49.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	353	1323
1	1263	1222
2	5002	1208

prune218.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes50.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 28.9b

bsearch142.0ms

Steps

Iters	Range		Point
9	1654.2658435481542	671819857.7007226	13257.47252325277
9	-27324391.726681516	-29.541817090935037	-9606.770732012134

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	61	63
1	61	63

end0.0ms

sample1.1s

Algorithm

intervals

Results

382.0ms	1670×	body	1280	valid
257.0ms	4159×	body	80	valid
237.0ms	1261×	body	640	valid
88.0ms	603×	body	320	valid
31.0ms	307×	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