Details

analyze5.0ms

Algorithm: search

sample19.0ms

Algorithm

intervals

Results

13.0ms

256×

body

valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	7
1	16	7
2	16	7

prune3.0ms

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: 0.3b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(- 1.0 (* x x))
0.0b	(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
0.0b	(/ (sqrt (- 1.0 (* x x))) x)
0.3b	(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

41×	`*-un-lft-identity`
33×	`times-frac`
30×	`add-sqr-sqrt`
25×	`add-cube-cbrt`
16×	`sqrt-prod`
8×	`log-prod` `distribute-lft-out` `add-log-exp`
7×	`add-exp-log` `associate-/l*`
6×	`add-cbrt-cube`
5×	`pow1` `div-inv` `difference-of-squares`
3×	`log-div` `associate-/r*`
2×	`distribute-rgt-out` `flip3--` `flip3-+` `sqrt-div` `frac-add` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `clear-num` `sum-log` `log-pow`

Counts

4 → 95

Calls

4 calls:

3.0ms	(- 1.0 (* x x))
23.0ms	(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
6.0ms	(/ (sqrt (- 1.0 (* x x))) x)
19.0ms	(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))

series32.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(- 1.0 (* x x))
7.0ms	(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
8.0ms	(/ (sqrt (- 1.0 (* x x))) x)
13.0ms	(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))

simplify52.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	492	956
1	1752	902
2	5001	897

prune187.0ms

Filtered

83 candidates to 107 candidates (-28.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	105	2	107
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	105	3	108

Merged error: 0b

Counts

108 → 3

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (log (/ 1 (sqrt x))) (log (+ (/ 1.0 (sqrt x)) (/ (sqrt (- 1.0 (* x x))) (sqrt x)))))
0.3b	(/ (sqrt (- 1.0 (* x x))) (sqrt x))
0.3b	(/ 1 (sqrt x))
0.3b	(/ 1.0 (sqrt x))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

112×	`times-frac`
104×	`*-un-lft-identity`
93×	`add-sqr-sqrt` `sqrt-prod`
82×	`add-cube-cbrt`
35×	`log-prod`
22×	`associate-+l+`
18×	`associate-/r*`
13×	`associate-+r+` `distribute-lft-out` `associate-/l*`
12×	`add-exp-log`
10×	`pow1` `add-cbrt-cube`
7×	`difference-of-squares`
6×	`div-inv`
4×	`log-div` `div-exp` `log-pow` `add-log-exp`
3×	`cbrt-undiv` `associate-+r-` `pow-flip` `frac-2neg` `clear-num`
2×	`flip3-+` `sqrt-div` `flip-+` `associate-/l/`
1×	`+-commutative` `associate-+l-` `rec-exp` `sqrt-undiv` `distribute-rgt-out` `flip3--` `sqrt-pow1` `pow1/2` `1-exp` `frac-add` `sum-log` `flip--` `inv-pow`

Counts

4 → 208

Calls

4 calls:

54.0ms	(+ (log (/ 1 (sqrt x))) (log (+ (/ 1.0 (sqrt x)) (/ (sqrt (- 1.0 (* x x))) (sqrt x)))))
7.0ms	(/ (sqrt (- 1.0 (* x x))) (sqrt x))
4.0ms	(/ 1 (sqrt x))
5.0ms	(/ 1.0 (sqrt x))

series36.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(+ (log (/ 1 (sqrt x))) (log (+ (/ 1.0 (sqrt x)) (/ (sqrt (- 1.0 (* x x))) (sqrt x)))))
5.0ms	(/ (sqrt (- 1.0 (* x x))) (sqrt x))
7.0ms	(/ 1 (sqrt x))
8.0ms	(/ 1.0 (sqrt x))

simplify86.0ms

Algorithm

egg-herbie

Counts

220 → 220

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	796	2055
1	3169	1885
2	5001	1841

prune345.0ms

Filtered

135 candidates to 220 candidates (-63.0%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	219	1	220
Fresh	1	0	1
Picked	1	0	1
Done	0	1	1
Total	221	2	223

Merged error: 0b

Counts

223 → 2

localize28.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `pow1/3` `add-cbrt-cube` `add-log-exp`

Counts

4 → 44

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)

series96.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(cbrt x)
26.0ms	(cbrt x)
22.0ms	(cbrt x)
24.0ms	(cbrt x)

simplify128.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 4 (26.0ms)

Iter	Nodes	Cost
0	59	204
1	101	188
2	205	148
3	559	144
4	2708	128
5	5002	128

prune90.0ms

Filtered

44 candidates to 56 candidates (-27.3%)

Pruning

2 alts after pruning (0 fresh and 2 done)

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

Merged error: 0b

Counts

58 → 2

regimes100.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	21
1	26	21
2	26	21

end0.0ms

analyze5.0ms

Algorithm: search

sample506.0ms

Algorithm

intervals

Results

410.0ms	8000×	body	80	valid
0.0ms	4×	body	80	nan

Details

analyze5.0ms

sample19.0ms

simplify5.0ms

prune3.0ms

localize10.0ms

rewrite54.0ms

series32.0ms

simplify52.0ms

prune187.0ms

localize15.0ms

rewrite79.0ms

series36.0ms

simplify86.0ms

prune345.0ms

localize28.0ms

rewrite6.0ms

series96.0ms

simplify128.0ms

prune90.0ms

regimes100.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

analyze5.0ms

sample506.0ms

Profiling