Details

sample41.0ms

Algorithm

intervals

Results

9.0ms	263×	body	80	nan
7.0ms	52×	body	640	valid
6.0ms	34×	body	1280	valid
6.0ms	144×	body	80	valid
2.0ms	18×	body	320	valid
1.0ms	8×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	6
1	14	6
2	14	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: 18.3b

Counts

2 → 1

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.1b	(/ 1.0 (sqrt (+ x 1.0)))
0.3b	(/ 1.0 (sqrt x))
2.0b	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite145.0ms

Algorithm

rewrite-expression-head

Rules

1035×	`times-frac`
879×	`*-un-lft-identity`
747×	`add-sqr-sqrt`
714×	`add-cube-cbrt`
594×	`prod-diff`
566×	`sqrt-prod`
74×	`distribute-lft-out`
54×	`div-inv`
48×	`sqrt-div`
46×	`associate-/r/`
24×	`flip3-+` `flip-+`
22×	`fma-neg`
13×	`associate-/r*`
11×	`distribute-lft-out--`
9×	`difference-of-squares`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/l*` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num`
1×	`sub-neg` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `diff-log` `frac-sub` `flip--` `hypot-def`

Counts

4 → 758

Calls

4 calls:

3.0ms	(sqrt (+ x 1.0))
6.0ms	(/ 1.0 (sqrt (+ x 1.0)))
4.0ms	(/ 1.0 (sqrt x))
49.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series284.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(sqrt (+ x 1.0))
76.0ms	(/ 1.0 (sqrt (+ x 1.0)))
44.0ms	(/ 1.0 (sqrt x))
134.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify270.0ms

Algorithm

egg-herbie

Counts

770 → 770

Iterations

Useful iterations: 2 (95.0ms)

Iter	Nodes	Cost
0	1538	25021
1	4278	18390
2	5001	18355

prune1.1s

Filtered

770 candidates to 303 candidates (39.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	757	13	770
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	758	13	771

Merged error: 17.8b

Counts

771 → 13

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (sqrt (/ 1.0 (sqrt x))) (/ (sqrt 1.0) (sqrt (sqrt (+ x 1.0))))) (- (sqrt (/ 1.0 (sqrt x))) (/ (sqrt 1.0) (sqrt (sqrt (+ x 1.0))))))
0.3b	(/ 1.0 (sqrt x))
0.3b	(/ 1.0 (sqrt x))
9.1b	(- (sqrt (/ 1.0 (sqrt x))) (/ (sqrt 1.0) (sqrt (sqrt (+ x 1.0)))))

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

13524×	`sqrt-prod`
8194×	`times-frac`
6653×	`*-un-lft-identity`
5937×	`add-sqr-sqrt`
5747×	`add-cube-cbrt`
4950×	`prod-diff`
1652×	`distribute-rgt-in` `distribute-lft-in`
452×	`distribute-lft-out`
309×	`sqrt-div`
282×	`div-inv`
150×	`associate-/r/`
79×	`flip3-+` `flip-+`
56×	`difference-of-squares`
33×	`associate-r`
25×	`fma-neg`
12×	`associate-/r*`
10×	`add-exp-log` `add-cbrt-cube`
9×	`frac-times`
6×	`pow1` `associate-/l*` `add-log-exp`
5×	`flip3--` `associate-l` `frac-sub` `flip--`
4×	`expm1-log1p-u` `frac-add` `log1p-expm1-u` `distribute-lft-out--`
3×	`sub-neg` `associate-r/` `associate-l/`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num`
1×	`diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 5173

Calls

4 calls:

283.0ms	(* (+ (sqrt (/ 1.0 (sqrt x))) (/ (sqrt 1.0) (sqrt (sqrt (+ x 1.0))))) (- (sqrt (/ 1.0 (sqrt x))) (/ (sqrt 1.0) (sqrt (sqrt (+ x 1.0))))))
4.0ms	(/ 1.0 (sqrt x))
4.0ms	(/ 1.0 (sqrt x))
110.0ms	(- (sqrt (/ 1.0 (sqrt x))) (/ (sqrt 1.0) (sqrt (sqrt (+ x 1.0)))))

series1.2s

Counts

4 → 12

Calls

4 calls:

845.0ms	(* (+ (sqrt (/ 1.0 (sqrt x))) (/ (sqrt 1.0) (sqrt (sqrt (+ x 1.0))))) (- (sqrt (/ 1.0 (sqrt x))) (/ (sqrt 1.0) (sqrt (sqrt (+ x 1.0))))))
43.0ms	(/ 1.0 (sqrt x))
37.0ms	(/ 1.0 (sqrt x))
295.0ms	(- (sqrt (/ 1.0 (sqrt x))) (/ (sqrt 1.0) (sqrt (sqrt (+ x 1.0)))))

simplify2.5s

Algorithm

egg-herbie

Counts

5185 → 5185

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5003	342377

prune15.0s

Filtered

5185 candidates to 2438 candidates (47.0%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	5176	9	5185
Fresh	7	5	12
Picked	0	1	1
Done	0	0	0
Total	5183	15	5198

Merged error: 11.8b

Counts

5198 → 15

localize17.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (/ 1.0 (sqrt x)))
0.7b	(cbrt (/ 1.0 (sqrt x)))
0.7b	(cbrt (/ 1.0 (sqrt x)))
13.4b	(- (sqrt (* (* (cbrt (/ 1.0 (sqrt x))) (cbrt (/ 1.0 (sqrt x)))) (cbrt (/ 1.0 (sqrt x))))) (/ (sqrt 1.0) (sqrt (sqrt (+ x 1.0)))))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

487×	`sqrt-prod`
316×	`*-un-lft-identity`
300×	`times-frac`
286×	`add-sqr-sqrt`
266×	`add-cube-cbrt`
264×	`prod-diff`
66×	`cbrt-prod`
24×	`distribute-lft-out`
23×	`sqrt-div`
15×	`cbrt-div`
8×	`associate-/r/`
7×	`frac-sub` `div-inv` `difference-of-squares`
6×	`add-log-exp`
5×	`frac-times` `associate-*l/`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `flip3-+` `fma-neg` `add-cbrt-cube` `flip-+` `log1p-expm1-u`
3×	`pow1/3` `associate-*r/`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 396

Calls

4 calls:

3.0ms	(cbrt (/ 1.0 (sqrt x)))
3.0ms	(cbrt (/ 1.0 (sqrt x)))
3.0ms	(cbrt (/ 1.0 (sqrt x)))
47.0ms	(- (sqrt (* (* (cbrt (/ 1.0 (sqrt x))) (cbrt (/ 1.0 (sqrt x)))) (cbrt (/ 1.0 (sqrt x))))) (/ (sqrt 1.0) (sqrt (sqrt (+ x 1.0)))))

series832.0ms

Counts

4 → 12

Calls

4 calls:

178.0ms	(cbrt (/ 1.0 (sqrt x)))
184.0ms	(cbrt (/ 1.0 (sqrt x)))
176.0ms	(cbrt (/ 1.0 (sqrt x)))
293.0ms	(- (sqrt (* (* (cbrt (/ 1.0 (sqrt x))) (cbrt (/ 1.0 (sqrt x)))) (cbrt (/ 1.0 (sqrt x))))) (/ (sqrt 1.0) (sqrt (sqrt (+ x 1.0)))))

simplify217.0ms

Algorithm

egg-herbie

Counts

408 → 408

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1524	19868
1	4938	15268
2	5001	15268

prune1.1s

Filtered

408 candidates to 204 candidates (50.0%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	406	2	408
Fresh	2	11	13
Picked	0	1	1
Done	0	1	1
Total	408	15	423

Merged error: 11.8b

Counts

423 → 15

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1.0 (sqrt (+ x 1.0)))
0.3b	(/ 1.0 (sqrt x))
0.3b	(/ 1.0 (sqrt x))
26.4b	(fma (sqrt (/ 1.0 (sqrt x))) (sqrt (/ 1.0 (sqrt x))) (- (/ 1.0 (sqrt (+ x 1.0)))))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

58×	`*-un-lft-identity`
57×	`times-frac`
50×	`add-sqr-sqrt` `add-cube-cbrt`
40×	`sqrt-prod`
19×	`associate-/r*`
10×	`add-exp-log` `add-cbrt-cube`
9×	`associate-/l*`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `distribute-lft-out` `add-log-exp`
3×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`
2×	`sqrt-div` `associate-/r/`
1×	`flip3-+` `flip-+` `fma-udef`

Counts

4 → 139

Calls

4 calls:

6.0ms	(/ 1.0 (sqrt (+ x 1.0)))
4.0ms	(/ 1.0 (sqrt x))
4.0ms	(/ 1.0 (sqrt x))
1.0ms	(fma (sqrt (/ 1.0 (sqrt x))) (sqrt (/ 1.0 (sqrt x))) (- (/ 1.0 (sqrt (+ x 1.0)))))

series399.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(/ 1.0 (sqrt (+ x 1.0)))
40.0ms	(/ 1.0 (sqrt x))
35.0ms	(/ 1.0 (sqrt x))
252.0ms	(fma (sqrt (/ 1.0 (sqrt x))) (sqrt (/ 1.0 (sqrt x))) (- (/ 1.0 (sqrt (+ x 1.0)))))

simplify47.0ms

Algorithm

egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	423	1061
1	1523	968
2	5001	896

prune321.0ms

Filtered

151 candidates to 107 candidates (70.9%)

Pruning

17 alts after pruning (15 fresh and 2 done)

	Pruned	Kept	Total
New	146	5	151
Fresh	2	10	12
Picked	1	0	1
Done	0	2	2
Total	149	17	166

Merged error: 11.8b

Counts

166 → 17

regimes103.0ms

Accuracy

98.6% (0.2b remaining)

Error of 10.6b against oracle of 10.4b and baseline of 22.8b

bsearch53.0ms

Steps

Iters	Range		Point
8	8.601567399579238	18724.121991280714	6940.778788291299

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	38
1	59	38

end0.0ms

sample1.2s

Algorithm

intervals

Results

271.0ms	8059×	body	80	nan
249.0ms	1797×	body	640	valid
202.0ms	1152×	body	1280	valid
151.0ms	4100×	body	80	valid
61.0ms	608×	body	320	valid
23.0ms	343×	body	160	valid