Details

sample30.0ms

Algorithm

intervals

Results

7.0ms	280×	body	80	nan
5.0ms	42×	body	1280	valid
4.0ms	48×	body	640	valid
3.0ms	140×	body	80	valid
1.0ms	18×	body	320	valid
0.0ms	8×	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: 27.4b

Counts

2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

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

rewrite11.0ms

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))
7.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series104.0ms

Counts

2 → 6

Calls

2 calls:

30.0ms	(sqrt (+ x 1.0))
74.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify59.0ms

Algorithm

egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 3 (54.0ms)

Iter	Nodes	Cost
0	182	265
1	544	243
2	2020	233
3	5002	230

prune83.0ms

Filtered

41 candidates to 28 candidates (68.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	38	3	41
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	39	3	42

Merged error: 0.2b

Counts

42 → 3

localize10.0ms

Local error

Found 3 expressions with local error:

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

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 71

Calls

3 calls:

3.0ms	(sqrt (+ x 1.0))
7.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
9.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series242.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(sqrt (+ x 1.0))
62.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
145.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify48.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	341	624
1	1239	566
2	5002	533

prune169.0ms

Filtered

80 candidates to 53 candidates (66.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	72	8	80
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	74	9	83

Merged error: 0.0b

Counts

83 → 9

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 (+ (* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0)))) (sqrt x)))
0.3b	(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

106×	`sqrt-prod`
62×	`add-sqr-sqrt`
46×	`*-un-lft-identity`
40×	`sqrt-pow1`
32×	`sqrt-div`
31×	`pow1`
28×	`add-cube-cbrt`
20×	`pow1/2`
18×	`swap-sqr`
10×	`associate-r` `associate-l`
9×	`flip3-+` `times-frac` `pow-prod-up` `flip-+` `unswap-sqr`
8×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out`
5×	`pow-prod-down` `pow-sqr`
4×	`frac-times` `rem-sqrt-square` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`associate-r/` `associate-l/` `associate-/r/`
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 → 161

Calls

4 calls:

4.0ms	(sqrt (sqrt (+ x 1.0)))
4.0ms	(sqrt (sqrt (+ x 1.0)))
15.0ms	(/ 1.0 (+ (* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0)))) (sqrt x)))
18.0ms	(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))

series359.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(sqrt (sqrt (+ x 1.0)))
89.0ms	(sqrt (sqrt (+ x 1.0)))
149.0ms	(/ 1.0 (+ (* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0)))) (sqrt x)))
31.0ms	(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))

simplify74.0ms

Algorithm

egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	525	1350
1	2329	1176
2	5001	1152

prune313.0ms

Filtered

173 candidates to 92 candidates (53.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	172	1	173
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	172	10	182

Merged error: 0.0b

Counts

182 → 10

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

297×	`*-un-lft-identity`
274×	`sqrt-prod`
157×	`times-frac`
119×	`add-sqr-sqrt`
116×	`distribute-lft-out`
88×	`add-cube-cbrt`
41×	`swap-sqr`
27×	`associate-r` `associate-l`
20×	`pow1`
14×	`associate-/r/`
12×	`associate-/r*`
10×	`add-exp-log` `add-cbrt-cube`
9×	`sqrt-pow1` `pow1/2` `unswap-sqr`
7×	`flip3-+` `flip-+` `div-inv`
6×	`associate-/l*`
5×	`sqrt-div` `pow-prod-up`
4×	`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 → 250

Calls

4 calls:

13.0ms	(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
9.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
9.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
32.0ms	(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

series815.0ms

Counts

4 → 12

Calls

4 calls:

357.0ms	(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
138.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
145.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
175.0ms	(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

simplify113.0ms

Algorithm

egg-herbie

Counts

262 → 262

Iterations

Useful iterations: 2 (79.0ms)

Iter	Nodes	Cost
0	647	2845
1	3152	2529
2	5002	2489

prune470.0ms

Filtered

262 candidates to 137 candidates (52.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	259	3	262
Fresh	4	4	8
Picked	1	0	1
Done	0	1	1
Total	264	8	272

Merged error: 0b

Counts

272 → 8

regimes72.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	10
1	11	10

end0.0ms

sample847.0ms

Algorithm

intervals

Results

196.0ms	8027×	body	80	nan
195.0ms	1709×	body	1280	valid
120.0ms	1245×	body	640	valid
101.0ms	4127×	body	80	valid
41.0ms	609×	body	320	valid
14.0ms	310×	body	160	valid

Details

sample30.0ms

simplify5.0ms

prune2.0ms

localize5.0ms

rewrite11.0ms

series104.0ms

simplify59.0ms

prune83.0ms

localize10.0ms

rewrite22.0ms

series242.0ms

simplify48.0ms

prune169.0ms

localize9.0ms

rewrite47.0ms

series359.0ms

simplify74.0ms

prune313.0ms

localize9.0ms

rewrite78.0ms

series815.0ms

simplify113.0ms

prune470.0ms

regimes72.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample847.0ms

Profiling