Details

sample35.0ms

Algorithm

intervals

Results

9.0ms	246×	body	80	nan
9.0ms	70×	body	1280	valid
5.0ms	49×	body	640	valid
3.0ms	118×	body	80	valid
1.0ms	15×	body	320	valid
0.0ms	4×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	4
1	10	4
2	10	4

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: 33.2b

Counts

2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1.0))
2.1b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity` `sqrt-prod`
4×	`add-log-exp` `difference-of-squares`
3×	`pow1` `add-cube-cbrt` `distribute-lft-out--`
2×	`add-exp-log` `sqrt-div` `add-cbrt-cube` `distribute-lft-out`
1×	`sub-neg` `rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip--` `flip-+`

Counts

2 → 35

Calls

2 calls:

3.0ms	(sqrt (+ x 1.0))
8.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series238.0ms

Counts

2 → 6

Calls

2 calls:

55.0ms	(sqrt (+ x 1.0))
183.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify33.0ms

Algorithm

egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	282	318
1	1037	308
2	5001	297

prune86.0ms

Filtered

41 candidates to 31 candidates (75.6%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	39	2	41
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	40	2	42

Merged error: 0.1b

Counts

42 → 2

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.2b	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

66×	`*-un-lft-identity`
28×	`distribute-lft-out`
24×	`times-frac` `sqrt-prod`
16×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
6×	`associate-/r*`
4×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
3×	`pow1` `flip3-+` `flip-+`
2×	`sqrt-div` `associate-/r/` `associate-/l/` `add-log-exp`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv`

Counts

2 → 66

Calls

2 calls:

3.0ms	(sqrt (+ x 1.0))
12.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

series263.0ms

Counts

2 → 6

Calls

2 calls:

57.0ms	(sqrt (+ x 1.0))
206.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify65.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	461	668
1	2026	631
2	5002	595

prune148.0ms

Filtered

72 candidates to 45 candidates (62.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	64	8	72
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	64	10	74

Merged error: 0.0b

Counts

74 → 10

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (sqrt (+ x 1.0)))
0.1b	(sqrt (sqrt (+ x 1.0)))
0.2b	(/ (+ 1.0 0) (+ (* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0)))) (sqrt x)))
0.3b	(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

106×	`sqrt-prod`
63×	`add-sqr-sqrt`
55×	`*-un-lft-identity`
40×	`sqrt-pow1`
32×	`sqrt-div`
31×	`pow1`
29×	`add-cube-cbrt`
20×	`pow1/2`
18×	`swap-sqr`
12×	`times-frac` `distribute-lft-out`
10×	`flip3-+` `associate-r` `associate-l` `flip-+`
9×	`pow-prod-up` `unswap-sqr`
8×	`add-exp-log` `add-cbrt-cube`
5×	`pow-prod-down` `pow-sqr`
4×	`frac-times` `rem-sqrt-square` `associate-/l*` `add-log-exp`
3×	`associate-/r*`
2×	`associate-r/` `associate-l/` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `pow2` `frac-2neg` `pow-plus` `sqrt-unprod` `div-exp` `prod-exp` `clear-num` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 167

Calls

4 calls:

4.0ms	(sqrt (sqrt (+ x 1.0)))
4.0ms	(sqrt (sqrt (+ x 1.0)))
23.0ms	(/ (+ 1.0 0) (+ (* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0)))) (sqrt x)))
15.0ms	(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))

series440.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(sqrt (sqrt (+ x 1.0)))
88.0ms	(sqrt (sqrt (+ x 1.0)))
204.0ms	(/ (+ 1.0 0) (+ (* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0)))) (sqrt x)))
58.0ms	(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))

simplify104.0ms

Algorithm

egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 2 (88.0ms)

Iter	Nodes	Cost
0	676	1513
1	3301	1345
2	5002	1321

prune310.0ms

Filtered

179 candidates to 97 candidates (54.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	177	2	179
Fresh	2	6	8
Picked	1	0	1
Done	0	1	1
Total	180	9	189

Merged error: 0.0b

Counts

189 → 9

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))))
0.2b	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
0.2b	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
0.3b	(* (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))))

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

597×	`*-un-lft-identity`
420×	`sqrt-prod`
256×	`distribute-lft-out`
247×	`times-frac`
130×	`add-sqr-sqrt`
99×	`add-cube-cbrt`
71×	`swap-sqr`
33×	`associate-r` `associate-l`
20×	`pow1`
14×	`associate-/r/`
12×	`associate-/r*`
10×	`add-exp-log` `add-cbrt-cube`
9×	`sqrt-pow1` `flip3-+` `pow1/2` `flip-+` `unswap-sqr`
8×	`associate-/l*`
7×	`div-inv`
5×	`sqrt-div` `pow-prod-up`
4×	`associate-/l/` `add-log-exp`
3×	`pow-prod-down` `pow-sqr`
2×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `div-exp` `clear-num`
1×	`pow2` `frac-times` `pow-plus` `sqrt-unprod` `associate-r/` `associate-l/` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 316

Calls

4 calls:

12.0ms	(sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))))
12.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
13.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
49.0ms	(* (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))))

series1.2s

Counts

4 → 12

Calls

4 calls:

559.0ms	(sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))))
211.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
206.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
245.0ms	(* (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))))

simplify388.0ms

Algorithm

egg-herbie

Counts

328 → 328

Iterations

Useful iterations: 2 (127.0ms)

Iter	Nodes	Cost
0	827	3981
1	4531	3471
2	5001	3422

prune510.0ms

Filtered

328 candidates to 152 candidates (46.3%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	320	8	328
Fresh	4	3	7
Picked	1	0	1
Done	0	1	1
Total	325	12	337

Merged error: 0b

Counts

337 → 12

regimes43.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	6
1	16	6
2	16	6

end0.0ms

sample898.0ms

Algorithm

intervals

Results

214.0ms	8240×	body	80	nan
214.0ms	1719×	body	1280	valid
136.0ms	1296×	body	640	valid
106.0ms	4058×	body	80	valid
43.0ms	595×	body	320	valid
16.0ms	332×	body	160	valid

Details

sample35.0ms

simplify5.0ms

prune2.0ms

localize5.0ms

rewrite12.0ms

series238.0ms

simplify33.0ms

prune86.0ms

localize7.0ms

rewrite22.0ms

series263.0ms

simplify65.0ms

prune148.0ms

localize9.0ms

rewrite53.0ms

series440.0ms

simplify104.0ms

prune310.0ms

localize9.0ms

rewrite114.0ms

series1.2s

simplify388.0ms

prune510.0ms

regimes43.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample898.0ms

Profiling