Details

analyze297.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	50%	0%	3
62.5%	37.5%	0%	4
68.7%	31.2%	0%	5
71.8%	28.1%	0%	6
73.4%	26.5%	0%	7
74.2%	25.8%	0%	8
74.6%	25.4%	0%	9
74.8%	25.2%	0%	10
74.9%	25.1%	0%	11
74.9%	25%	0%	12
74.9%	25%	0%	13
75%	25%	0%	14

sample75.0ms

Algorithm

intervals

Results

32.0ms	72×	body	1280	valid
15.0ms	50×	body	640	valid
13.0ms	29×	body	2560	valid
4.0ms	23×	body	320	valid
3.0ms	68×	body	80	valid
1.0ms	14×	body	160	valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	9	9
1	9	9

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: 54.7b

Counts

2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

1.0b	(+ x (sqrt (+ (* x x) 1.0)))
2.7b	(log (+ x (sqrt (+ (* x x) 1.0))))
17.2b	(sqrt (+ (* x x) 1.0))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity`
6×	`add-sqr-sqrt`
5×	`pow1` `add-cube-cbrt` `add-log-exp`
4×	`add-exp-log` `log-prod`
3×	`flip3-+` `sqrt-prod` `add-cbrt-cube` `flip-+`
2×	`log-div` `sqrt-div` `distribute-lft-out`
1×	`+-commutative` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `rem-log-exp` `sum-log` `log-pow`

Counts

3 → 42

Calls

3 calls:

5.0ms	(+ x (sqrt (+ (* x x) 1.0)))
5.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
4.0ms	(sqrt (+ (* x x) 1.0))

series16.0ms

Counts

3 → 9

Calls

3 calls:

4.0ms	(+ x (sqrt (+ (* x x) 1.0)))
8.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
3.0ms	(sqrt (+ (* x x) 1.0))

simplify36.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5003	592

prune105.0ms

Filtered

42 candidates to 51 candidates (-21.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	47	4	51
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	48	4	52

Merged error: 0.0b

Counts

52 → 4

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (/ x (sqrt 1.0)) (* 1/6 (pow (/ x (sqrt 1.0)) 3)))
0.1b	(* 1/6 (pow (/ x (sqrt 1.0)) 3))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

50×	`associate-r`
49×	`add-sqr-sqrt`
40×	`times-frac`
30×	`add-cube-cbrt` `*-un-lft-identity`
25×	`unpow-prod-down` `cube-prod`
20×	`sqrt-prod`
10×	`add-exp-log`
8×	`unswap-sqr`
4×	`prod-exp` `add-cbrt-cube` `add-log-exp`
3×	`associate-l`
2×	`pow1` `cube-div` `associate-*r/` `pow-exp` `div-inv` `sqr-pow`
1×	`cube-mult` `pow-to-exp` `sub-neg` `flip3--` `diff-log` `unpow3` `div-exp` `*-commutative` `frac-sub` `flip--` `cbrt-unprod`

Counts

2 → 87

Calls

2 calls:

8.0ms	(- (/ x (sqrt 1.0)) (* 1/6 (pow (/ x (sqrt 1.0)) 3)))
16.0ms	(* 1/6 (pow (/ x (sqrt 1.0)) 3))

series40.0ms

Counts

2 → 6

Calls

2 calls:

25.0ms	(- (/ x (sqrt 1.0)) (* 1/6 (pow (/ x (sqrt 1.0)) 3)))
15.0ms	(* 1/6 (pow (/ x (sqrt 1.0)) 3))

simplify41.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5245	932

prune130.0ms

Filtered

45 candidates to 93 candidates (-106.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	93	4	97

Merged error: 0.0b

Counts

97 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 0.125 (pow x 3))
0.1b	(/ 0.0625 (pow x 5))
13.1b	(log (- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
19.0b	(- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

72×	`add-sqr-sqrt`
71×	`times-frac`
68×	`*-un-lft-identity`
46×	`add-cube-cbrt`
26×	`unpow-prod-down`
19×	`associate-/r*`
15×	`add-exp-log`
14×	`cube-prod`
11×	`log-prod`
10×	`difference-of-squares` `sqr-pow`
9×	`add-log-exp`
8×	`add-cbrt-cube`
6×	`div-exp` `frac-sub` `associate-/l*` `distribute-lft-out--`
5×	`pow1` `log-div`
4×	`cube-mult` `unpow3` `distribute-lft-out`
2×	`cbrt-undiv` `pow-to-exp` `flip3--` `frac-2neg` `flip3-+` `diff-log` `frac-add` `pow-exp` `clear-num` `flip--` `flip-+` `div-inv`
1×	`sub-neg` `rem-log-exp` `sum-log` `log-pow` `associate--r+`

Counts

4 → 159

Calls

4 calls:

5.0ms	(/ 0.125 (pow x 3))
4.0ms	(/ 0.0625 (pow x 5))
29.0ms	(log (- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
33.0ms	(- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

series24.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(/ 0.125 (pow x 3))
4.0ms	(/ 0.0625 (pow x 5))
12.0ms	(log (- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
5.0ms	(- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

simplify39.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5269	2482

prune284.0ms

Filtered

110 candidates to 171 candidates (-55.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	171	0	171
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	171	4	175

Merged error: 0.0b

Counts

175 → 4

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 0.5 x) (/ 0.125 (pow x 3)))
0.0b	(+ x (+ x (- (/ 0.5 x) (/ 0.125 (pow x 3)))))
0.1b	(/ 0.125 (pow x 3))
11.2b	(log (+ x (+ x (- (/ 0.5 x) (/ 0.125 (pow x 3))))))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-sqr-sqrt`
54×	`*-un-lft-identity`
51×	`times-frac`
30×	`add-cube-cbrt`
15×	`add-log-exp`
14×	`unpow-prod-down` `cube-prod`
12×	`associate-/r*`
10×	`add-exp-log` `distribute-lft-out` `difference-of-squares`
6×	`log-prod` `add-cbrt-cube` `sqr-pow`
5×	`pow1` `sum-log`
4×	`cube-mult` `unpow3` `distribute-lft-out--`
3×	`div-exp` `associate-/l*`
2×	`associate-+r-` `log-div` `flip3-+` `diff-log` `flip-+`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `sub-neg` `associate-+r+` `flip3--` `frac-2neg` `rem-log-exp` `pow-exp` `clear-num` `log-pow` `frac-sub` `flip--` `div-inv`

Counts

4 → 124

Calls

4 calls:

25.0ms	(- (/ 0.5 x) (/ 0.125 (pow x 3)))
28.0ms	(+ x (+ x (- (/ 0.5 x) (/ 0.125 (pow x 3)))))
7.0ms	(/ 0.125 (pow x 3))
28.0ms	(log (+ x (+ x (- (/ 0.5 x) (/ 0.125 (pow x 3))))))

series23.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (/ 0.5 x) (/ 0.125 (pow x 3)))
4.0ms	(+ x (+ x (- (/ 0.5 x) (/ 0.125 (pow x 3)))))
3.0ms	(/ 0.125 (pow x 3))
9.0ms	(log (+ x (+ x (- (/ 0.5 x) (/ 0.125 (pow x 3))))))

simplify46.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5109	1750

prune164.0ms

Filtered

82 candidates to 136 candidates (-65.9%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	136	0	136
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	136	4	140

Merged error: 0.0b

Counts

140 → 4

regimes42.0ms

Accuracy

99.2% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 32.4b

bsearch47.0ms

Steps

Iters	Range		Point
11	5.764756221382738e-16	135160615.59329808	0.8911716591874946
7	-1.9044713414231773	-0.010053046314123988	-1.041530868832381

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	55
1	38	55

end0.0ms

analyze273.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	50%	0%	3
62.5%	37.5%	0%	4
68.7%	31.2%	0%	5
71.8%	28.1%	0%	6
73.4%	26.5%	0%	7
74.2%	25.8%	0%	8
74.6%	25.4%	0%	9
74.8%	25.2%	0%	10
74.9%	25.1%	0%	11
74.9%	25%	0%	12
74.9%	25%	0%	13
75%	25%	0%	14

sample2.2s

Algorithm

intervals

Results

1.1s	2317×	body	1280	valid
443.0ms	1542×	body	640	valid
285.0ms	821×	body	2560	valid
133.0ms	781×	body	320	valid
94.0ms	2142×	body	80	valid
44.0ms	397×	body	160	valid

Details

analyze297.0ms

sample75.0ms

simplify3.0ms

prune3.0ms

localize7.0ms

rewrite15.0ms

series16.0ms

simplify36.0ms

prune105.0ms

localize9.0ms

rewrite27.0ms

series40.0ms

simplify41.0ms

prune130.0ms

localize12.0ms

rewrite77.0ms

series24.0ms

simplify39.0ms

prune284.0ms

localize10.0ms

rewrite93.0ms

series23.0ms

simplify46.0ms

prune164.0ms

regimes42.0ms

bsearch47.0ms

simplify1.0ms

end0.0ms

analyze273.0ms

sample2.2s

Profiling