Details

sample24.0ms

Algorithm

intervals

Results

7.0ms	53×	body	1280	valid
4.0ms	41×	body	640	valid
4.0ms	128×	body	80	valid
2.0ms	26×	body	320	valid
0.0ms	8×	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

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: 30.3b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ x (+ x 1.0))
3.2b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

65×	`*-un-lft-identity`
32×	`times-frac`
23×	`add-sqr-sqrt`
13×	`distribute-lft-out--`
12×	`distribute-lft-out`
11×	`add-cube-cbrt`
4×	`add-exp-log` `associate-/r*` `add-cbrt-cube` `add-log-exp` `difference-of-squares`
3×	`associate-/l*`
2×	`pow1` `associate-/r/`
1×	`cbrt-undiv` `sub-neg` `flip3--` `frac-2neg` `flip3-+` `diff-log` `div-exp` `clear-num` `frac-sub` `flip--` `flip-+` `div-inv`

Counts

2 → 59

Calls

2 calls:

5.0ms	(/ x (+ x 1.0))
34.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series366.0ms

Counts

2 → 6

Calls

2 calls:

226.0ms	(/ x (+ x 1.0))
140.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify118.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 2 (23.0ms)

Iter	Nodes	Cost
0	266	459
1	872	434
2	3587	429
3	5001	429

prune119.0ms

Filtered

65 candidates to 44 candidates (67.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	60	5	65
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	61	5	66

Merged error: 0.0b

Counts

66 → 5

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
0.0b	(/ x (+ x 1.0))
3.2b	(log (exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
3.2b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

162×	`*-un-lft-identity`
72×	`times-frac`
52×	`add-sqr-sqrt`
39×	`distribute-lft-out--`
32×	`exp-prod`
28×	`distribute-lft-out`
17×	`log-pow`
16×	`add-cube-cbrt`
12×	`difference-of-squares`
9×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `log-prod`
4×	`exp-sum` `associate-/r*`
3×	`sub-neg` `associate-/l*`
2×	`exp-diff` `diff-log` `associate-/r/` `rem-exp-log`
1×	`cbrt-undiv` `log-div` `flip3--` `frac-2neg` `flip3-+` `div-exp` `rem-log-exp` `clear-num` `frac-sub` `flip--` `flip-+` `div-inv`

Counts

4 → 118

Calls

4 calls:

32.0ms	(exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
5.0ms	(/ x (+ x 1.0))
36.0ms	(log (exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
31.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series468.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
35.0ms	(/ x (+ x 1.0))
134.0ms	(log (exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
145.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify142.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	353	877
1	1123	810
2	4298	799
3	5003	799

prune201.0ms

Filtered

130 candidates to 79 candidates (60.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	129	1	130
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	130	5	135

Merged error: 0.0b

Counts

135 → 5

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ x 1.0))
0.3b	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
19.2b	(log (exp (- (* (/ 1 (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (/ x (cbrt (+ x 1.0)))) (/ (+ x 1.0) (- x 1.0)))))
19.2b	(- (* (/ 1 (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (/ x (cbrt (+ x 1.0)))) (/ (+ x 1.0) (- x 1.0)))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

31×	`*-un-lft-identity`
28×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
14×	`cbrt-div`
12×	`pow1`
9×	`swap-sqr`
7×	`flip3-+` `pow1/3` `associate-r` `associate-l` `flip-+` `distribute-lft-out`
6×	`add-exp-log` `add-log-exp`
5×	`frac-times` `log-prod`
4×	`log-pow` `add-cbrt-cube` `unswap-sqr`
3×	`exp-prod` `associate-r/` `associate-l/` `frac-sub`
2×	`sub-neg` `exp-sum` `pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `log-div` `flip3--` `pow-plus` `exp-diff` `diff-log` `rem-log-exp` `prod-exp` `*-commutative` `flip--` `cbrt-unprod`

Counts

4 → 100

Calls

4 calls:

3.0ms	(cbrt (+ x 1.0))
13.0ms	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
29.0ms	(log (exp (- (* (/ 1 (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (/ x (cbrt (+ x 1.0)))) (/ (+ x 1.0) (- x 1.0)))))
26.0ms	(- (* (/ 1 (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (/ x (cbrt (+ x 1.0)))) (/ (+ x 1.0) (- x 1.0)))

series470.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(cbrt (+ x 1.0))
106.0ms	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
137.0ms	(log (exp (- (* (/ 1 (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (/ x (cbrt (+ x 1.0)))) (/ (+ x 1.0) (- x 1.0)))))
136.0ms	(- (* (/ 1 (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (/ x (cbrt (+ x 1.0)))) (/ (+ x 1.0) (- x 1.0)))

simplify68.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	512	1287
1	2045	1134
2	5001	1058

prune278.0ms

Filtered

112 candidates to 80 candidates (71.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	111	1	112
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	111	6	117

Merged error: 0.0b

Counts

117 → 6

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ (- 1.0) (pow x 2)) (/ 3.0 x))
0.3b	(/ 3.0 (pow x 3))
1.1b	(/ (- 1.0) (pow x 2))
6.6b	(- (- (/ (- 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

rewrite168.0ms

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:

57.0ms	(- (/ (- 1.0) (pow x 2)) (/ 3.0 x))
5.0ms	(/ 3.0 (pow x 3))
7.0ms	(/ (- 1.0) (pow x 2))
89.0ms	(- (- (/ (- 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

series176.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(- (/ (- 1.0) (pow x 2)) (/ 3.0 x))
38.0ms	(/ 3.0 (pow x 3))
31.0ms	(/ (- 1.0) (pow x 2))
34.0ms	(- (- (/ (- 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3)))

simplify96.0ms

Algorithm

egg-herbie

Counts

246 → 246

Iterations

Useful iterations: 2 (74.0ms)

Iter	Nodes	Cost
0	738	1754
1	3448	1596
2	5001	1578

prune369.0ms

Filtered

246 candidates to 133 candidates (54.1%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	246	0	246
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	246	6	252

Merged error: 0.0b

Counts

252 → 6

regimes59.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 29.2b

bsearch3.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	22
1	26	22

end0.0ms

sample639.0ms

Algorithm

intervals

Results

232.0ms	1718×	body	1280	valid
131.0ms	1226×	body	640	valid
115.0ms	4109×	body	80	valid
50.0ms	636×	body	320	valid
17.0ms	311×	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