Details

analyze607.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
12.5%	87.4%	0.1%	5
18.7%	81.1%	0.1%	6
18.7%	76.5%	4.8%	7
28.1%	66.3%	5.6%	8
35.1%	55%	9.9%	9
36.3%	50.9%	12.8%	10
42.1%	42.4%	15.5%	11
47.5%	33.8%	18.7%	12
48.8%	30.7%	20.6%	13
51.8%	25.6%	22.5%	14

sample39.0ms

Algorithm

intervals

Results

8.0ms	171×	body	80	valid
8.0ms	31×	body	2560	valid
6.0ms	29×	body	1280	valid
2.0ms	11×	body	640	valid
1.0ms	23×	body	80	nan
1.0ms	3×	body	5120	valid
1.0ms	7×	body	320	valid
0.0ms	10×	body	80	invalid
0.0ms	4×	body	160	valid

simplify514.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	713	12
1	713	12

prune11.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 31.7b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* b_2 b_2) (* a c))
0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
0.9b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
21.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
18×	`times-frac`
16×	`add-cube-cbrt`
10×	`difference-of-squares`
8×	`sqrt-prod` `add-log-exp`
6×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
5×	`pow1` `distribute-lft-out--`
4×	`flip3--` `flip--`
3×	`associate-/r*`
2×	`sub-neg` `sqrt-div` `diff-log` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

4 → 82

Calls

4 calls:

4.0ms	(- (* b_2 b_2) (* a c))
10.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
7.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series75.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (* b_2 b_2) (* a c))
21.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
13.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
34.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify52.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5743	1403

prune135.0ms

Filtered

70 candidates to 94 candidates (-34.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	85	9	94
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	86	9	95

Merged error: 3.2b

Counts

95 → 9

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* b_2 b_2) (* a c))
0.1b	(/ (sqrt (- (* b_2 b_2) (* a c))) a)
6.5b	(- (/ (sqrt (- (* b_2 b_2) (* a c))) a) (/ b_2 a))
21.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

42×	`add-sqr-sqrt`
31×	`times-frac`
30×	`*-un-lft-identity`
22×	`add-cube-cbrt`
17×	`sqrt-prod`
8×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube` `associate-/l*` `difference-of-squares`
5×	`pow1`
4×	`flip3--` `sqrt-div` `flip--` `distribute-lft-out--`
3×	`associate-/r*` `div-inv`
2×	`sub-neg` `diff-log` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `distribute-rgt-out--` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `frac-sub` `sub-div`

Counts

4 → 91

Calls

4 calls:

4.0ms	(- (* b_2 b_2) (* a c))
6.0ms	(/ (sqrt (- (* b_2 b_2) (* a c))) a)
19.0ms	(- (/ (sqrt (- (* b_2 b_2) (* a c))) a) (/ b_2 a))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series67.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (* b_2 b_2) (* a c))
28.0ms	(/ (sqrt (- (* b_2 b_2) (* a c))) a)
19.0ms	(- (/ (sqrt (- (* b_2 b_2) (* a c))) a) (/ b_2 a))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify48.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4888	1599
1	4888	1599

prune115.0ms

Filtered

79 candidates to 103 candidates (-30.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	100	3	103
Fresh	4	4	8
Picked	0	1	1
Done	0	0	0
Total	104	8	112

Merged error: 3.2b

Counts

112 → 8

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* b_2 b_2) (* a c))
0.2b	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
0.9b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
21.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
18×	`*-un-lft-identity`
13×	`add-exp-log` `add-cube-cbrt` `associate-r`
11×	`times-frac`
9×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1`
6×	`associate-l`
5×	`flip3--` `sqrt-prod` `flip--`
4×	`prod-exp` `difference-of-squares`
3×	`unswap-sqr`
2×	`frac-times` `sub-neg` `sqrt-div` `diff-log` `div-exp` `associate-*l/` `cbrt-unprod` `distribute-lft-out--`
1×	`cbrt-undiv` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `associate-r/` `pow-prod-down` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 83

Calls

4 calls:

4.0ms	(- (* b_2 b_2) (* a c))
14.0ms	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
7.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series56.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (* b_2 b_2) (* a c))
21.0ms	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
13.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
15.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify37.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	4984	1258
1	4984	1258

prune107.0ms

Filtered

68 candidates to 95 candidates (-39.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	93	2	95
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	94	9	103

Merged error: 3.2b

Counts

103 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (fabs (cbrt (- (* b_2 b_2) (* a c)))) (/ (sqrt (cbrt (- (* b_2 b_2) (* a c)))) a))
12.9b	(- (* (fabs (cbrt (- (* b_2 b_2) (* a c)))) (/ (sqrt (cbrt (- (* b_2 b_2) (* a c)))) a)) (/ b_2 a))
21.9b	(cbrt (- (* b_2 b_2) (* a c)))
21.9b	(cbrt (- (* b_2 b_2) (* a c)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
31×	`associate-r`
30×	`times-frac`
26×	`add-cube-cbrt` `*-un-lft-identity`
20×	`sqrt-prod`
16×	`cbrt-prod`
9×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `add-log-exp`
4×	`cbrt-div` `unswap-sqr`
3×	`flip3--` `associate-r/` `associate-l*` `flip--`
2×	`pow1/3` `prod-exp` `cbrt-unprod`
1×	`cbrt-undiv` `sub-neg` `diff-log` `div-exp` `pow-prod-down` `*-commutative` `frac-sub` `div-inv` `sub-div`

Counts

4 → 91

Calls

4 calls:

14.0ms	(* (fabs (cbrt (- (* b_2 b_2) (* a c)))) (/ (sqrt (cbrt (- (* b_2 b_2) (* a c)))) a))
11.0ms	(- (* (fabs (cbrt (- (* b_2 b_2) (* a c)))) (/ (sqrt (cbrt (- (* b_2 b_2) (* a c)))) a)) (/ b_2 a))
4.0ms	(cbrt (- (* b_2 b_2) (* a c)))
4.0ms	(cbrt (- (* b_2 b_2) (* a c)))

series141.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (fabs (cbrt (- (* b_2 b_2) (* a c)))) (/ (sqrt (cbrt (- (* b_2 b_2) (* a c)))) a))
47.0ms	(- (* (fabs (cbrt (- (* b_2 b_2) (* a c)))) (/ (sqrt (cbrt (- (* b_2 b_2) (* a c)))) a)) (/ b_2 a))
23.0ms	(cbrt (- (* b_2 b_2) (* a c)))
24.0ms	(cbrt (- (* b_2 b_2) (* a c)))

simplify74.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	6132	2172

prune95.0ms

Filtered

74 candidates to 103 candidates (-39.2%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	103	0	103
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	103	9	112

Merged error: 3.2b

Counts

112 → 9

regimes285.0ms

Accuracy

84.9% (4.3b remaining)

Error of 9.9b against oracle of 5.6b and baseline of 33.8b

bsearch59.0ms

Steps

Iters	Range		Point
10	2.1444117740010884e-72	1.9790732744613812e-59	1.1872250410793767e-70
9	-5.654602357975462e+134	-8.834928222670775e+128	-1.563718320049384e+132

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	70	38
1	70	38

end0.0ms

sample1.1s

Algorithm

intervals

Results

254.0ms	1030×	body	2560	valid
224.0ms	5149×	body	80	valid
179.0ms	899×	body	1280	valid
71.0ms	448×	body	640	valid
41.0ms	132×	body	5120	valid
32.0ms	789×	body	80	nan
27.0ms	227×	body	320	valid
12.0ms	268×	body	80	invalid
11.0ms	115×	body	160	valid

Details

analyze607.0ms

sample39.0ms

simplify514.0ms

prune11.0ms

localize10.0ms

rewrite31.0ms

series75.0ms

simplify52.0ms

prune135.0ms

localize9.0ms

rewrite36.0ms

series67.0ms

simplify48.0ms

prune115.0ms

localize9.0ms

rewrite31.0ms

series56.0ms

simplify37.0ms

prune107.0ms

localize14.0ms

rewrite36.0ms

series141.0ms

simplify74.0ms

prune95.0ms

regimes285.0ms

bsearch59.0ms

simplify2.0ms

end0.0ms

sample1.1s

Profiling