Details

sample25.0ms

Algorithm

intervals

Results

4.0ms	256×	body	80	valid
4.0ms	272×	pre	80	false
4.0ms	256×	pre	80	true

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	10	3
1	12	3
2	12	3

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: 8.2b

Counts

2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

1.0b	(/ x0 (- 1.0 x1))
7.3b	(- (/ x0 (- 1.0 x1)) x0)

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
16×	`times-frac`
12×	`add-cube-cbrt`
6×	`difference-of-squares`
5×	`associate-/r*` `distribute-lft-out--`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`associate-/l*`
2×	`pow1` `flip3--` `associate-/r/` `flip--`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `clear-num` `div-inv`

Counts

2 → 52

Calls

2 calls:

5.0ms	(/ x0 (- 1.0 x1))
12.0ms	(- (/ x0 (- 1.0 x1)) x0)

series88.0ms

Counts

2 → 6

Calls

2 calls:

37.0ms	(/ x0 (- 1.0 x1))
51.0ms	(- (/ x0 (- 1.0 x1)) x0)

simplify93.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	240	328
1	779	315
2	3025	310
3	5001	310

prune59.0ms

Filtered

58 candidates to 44 candidates (75.9%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	56	2	58
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	57	2	59

Merged error: 7.1b

Counts

59 → 2

localize9.0ms

Local error

Found 4 expressions with local error:

1.0b	(/ x0 (- 1.0 x1))
1.0b	(/ x0 (- 1.0 x1))
1.0b	(/ x0 (- 1.0 x1))
6.6b	(- (* (/ x0 (- 1.0 x1)) (/ x0 (- 1.0 x1))) (* x0 x0))

rewrite302.0ms

Algorithm

rewrite-expression-head

Rules

198×	`add-sqr-sqrt`
75×	`times-frac`
70×	`*-un-lft-identity`
57×	`difference-of-squares`
34×	`add-cube-cbrt`
29×	`unswap-sqr`
21×	`swap-sqr`
19×	`distribute-lft-out--`
15×	`associate-/r` `-commutative`
10×	`add-exp-log` `add-cbrt-cube`
9×	`associate-/l*`
6×	`associate-l` `associate-/r/` `add-log-exp`
5×	`div-inv`
4×	`pow1` `flip3--` `flip--`
3×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num`
1×	`sub-neg` `diff-log`

Counts

4 → 175

Calls

4 calls:

5.0ms	(/ x0 (- 1.0 x1))
5.0ms	(/ x0 (- 1.0 x1))
5.0ms	(/ x0 (- 1.0 x1))
278.0ms	(- (* (/ x0 (- 1.0 x1)) (/ x0 (- 1.0 x1))) (* x0 x0))

series186.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(/ x0 (- 1.0 x1))
34.0ms	(/ x0 (- 1.0 x1))
37.0ms	(/ x0 (- 1.0 x1))
78.0ms	(- (* (/ x0 (- 1.0 x1)) (/ x0 (- 1.0 x1))) (* x0 x0))

simplify56.0ms

Algorithm

egg-herbie

Counts

187 → 187

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	381	1440
1	1361	1387
2	5001	1376

prune186.0ms

Filtered

187 candidates to 112 candidates (59.9%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	185	2	187
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	187	2	189

Merged error: 6.2b

Counts

189 → 2

localize10.0ms

Local error

Found 4 expressions with local error:

0.5b	(+ (/ x0 (- 1.0 x1)) x0)
1.0b	(/ x0 (- 1.0 x1))
1.0b	(/ x0 (- 1.0 x1))
5.8b	(- (* (/ 1 (- 1.0 x1)) (/ x0 (- 1.0 x1))) x0)

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

65×	`add-sqr-sqrt`
49×	`*-un-lft-identity`
37×	`times-frac`
24×	`add-cube-cbrt`
15×	`difference-of-squares`
11×	`distribute-lft-out--`
10×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
6×	`associate-/l*` `unswap-sqr`
4×	`pow1` `associate-/r/`
3×	`flip3--` `flip--` `div-inv`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `associate-l` `clear-num`
1×	`+-commutative` `sub-neg` `flip3-+` `diff-log` `sum-log` `flip-+` `distribute-lft-out`

Counts

4 → 108

Calls

4 calls:

11.0ms	(+ (/ x0 (- 1.0 x1)) x0)
5.0ms	(/ x0 (- 1.0 x1))
5.0ms	(/ x0 (- 1.0 x1))
51.0ms	(- (* (/ 1 (- 1.0 x1)) (/ x0 (- 1.0 x1))) x0)

series152.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(+ (/ x0 (- 1.0 x1)) x0)
35.0ms	(/ x0 (- 1.0 x1))
34.0ms	(/ x0 (- 1.0 x1))
44.0ms	(- (* (/ 1 (- 1.0 x1)) (/ x0 (- 1.0 x1))) x0)

simplify44.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	377	811
1	1240	779
2	5002	767

prune197.0ms

Filtered

120 candidates to 89 candidates (74.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	118	2	120
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	120	2	122

Merged error: 5.1b

Counts

122 → 2

localize12.0ms

Local error

Found 4 expressions with local error:

1.0b	(/ x0 (- 1.0 x1))
1.0b	(/ x0 (- 1.0 x1))
1.0b	(/ x0 (- 1.0 x1))
5.8b	(- (* (/ 1 (- 1.0 x1)) (* (sqrt (/ x0 (- 1.0 x1))) (sqrt (/ x0 (- 1.0 x1))))) x0)

rewrite315.0ms

Algorithm

rewrite-expression-head

Rules

290×	`add-sqr-sqrt`
103×	`times-frac`
80×	`*-un-lft-identity`
78×	`unswap-sqr`
64×	`difference-of-squares`
54×	`sqrt-prod`
34×	`add-cube-cbrt`
15×	`swap-sqr` `associate-/r*` `distribute-lft-out--`
10×	`add-exp-log` `add-cbrt-cube`
9×	`associate-/l*`
6×	`associate-/r/` `add-log-exp`
4×	`pow1` `flip3--` `flip--` `div-inv`
3×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `*-commutative`
2×	`associate-l`
1×	`sub-neg` `diff-log`

Counts

4 → 178

Calls

4 calls:

9.0ms	(/ x0 (- 1.0 x1))
5.0ms	(/ x0 (- 1.0 x1))
5.0ms	(/ x0 (- 1.0 x1))
285.0ms	(- (* (/ 1 (- 1.0 x1)) (* (sqrt (/ x0 (- 1.0 x1))) (sqrt (/ x0 (- 1.0 x1))))) x0)

series154.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(/ x0 (- 1.0 x1))
34.0ms	(/ x0 (- 1.0 x1))
39.0ms	(/ x0 (- 1.0 x1))
43.0ms	(- (* (/ 1 (- 1.0 x1)) (* (sqrt (/ x0 (- 1.0 x1))) (sqrt (/ x0 (- 1.0 x1))))) x0)

simplify58.0ms

Algorithm

egg-herbie

Counts

190 → 190

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	435	2063
1	1288	1923
2	5002	1855

prune255.0ms

Filtered

190 candidates to 111 candidates (58.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	189	1	190
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	190	2	192

Merged error: 4.9b

Counts

192 → 2

regimes40.0ms

Accuracy

100% (0.0b remaining)

Error of 5.1b against oracle of 5.1b and baseline of 6.6b

bsearch30.0ms

Steps

Iters	Range		Point
7	0.000209	0.0186	0.018204597656249998

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	40
1	33	40

end0.0ms

sample619.0ms

Algorithm

intervals

Results

135.0ms	8000×	body	80	valid
125.0ms	8193×	pre	80	false
119.0ms	8000×	pre	80	true