Details

analyze585.0ms

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

sample94.0ms

Algorithm

intervals

Results

7.0ms	169×	body	80	valid
6.0ms	27×	body	2560	valid
6.0ms	29×	body	1280	valid
3.0ms	18×	body	640	valid
1.0ms	8×	body	320	valid
1.0ms	2×	body	5120	valid
0.0ms	3×	body	160	valid

simplify480.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	713	13
1	713	13

prune5.0ms

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: 34.3b

Counts

2 → 1

localize23.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* b_2 b_2) (* a c))
3.3b	(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
14.6b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
24.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
37×	`*-un-lft-identity`
21×	`times-frac`
17×	`add-cube-cbrt`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
8×	`sqrt-prod`
7×	`associate-/l*`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `distribute-rgt-neg-in`
4×	`flip3--` `flip--`
3×	`diff-log` `associate-/r*`
2×	`sub-neg` `sqrt-div` `associate-/l/`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `neg-log` `clear-num` `div-inv`

Counts

4 → 89

Calls

4 calls:

4.0ms	(- (* b_2 b_2) (* a c))
10.0ms	(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
8.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series63.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(- (* b_2 b_2) (* a c))
20.0ms	(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
14.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify68.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4936	1587
1	4936	1587

prune149.0ms

Filtered

72 candidates to 101 candidates (-40.3%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	90	11	101
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	90	12	102

Merged error: 7.7b

Counts

102 → 12

localize14.0ms

Local error

Found 4 expressions with local error:

3.3b	(/ (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
12.2b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
14.6b	(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
24.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

66×	`times-frac`
57×	`add-sqr-sqrt`
42×	`*-un-lft-identity`
28×	`add-cube-cbrt`
18×	`add-exp-log` `add-cbrt-cube`
14×	`difference-of-squares`
13×	`associate-/l*`
10×	`sqrt-prod` `associate-/r/`
9×	`associate-/r*`
7×	`cbrt-undiv` `flip3--` `div-exp` `flip--` `distribute-lft-out--`
6×	`div-inv` `add-log-exp`
5×	`pow1`
2×	`frac-2neg` `sqrt-div` `prod-exp` `clear-num` `cbrt-unprod`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-/l/`

Counts

4 → 126

Calls

4 calls:

12.0ms	(/ (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
7.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
10.0ms	(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series127.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(/ (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
13.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
59.0ms	(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify53.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5022	2592

prune151.0ms

Filtered

105 candidates to 138 candidates (-31.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	134	4	138
Fresh	6	4	10
Picked	0	1	1
Done	1	0	1
Total	141	9	150

Merged error: 7.6b

Counts

150 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* b_2 b_2) (* a c))
4.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)
12.2b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
24.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite28.0ms

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) c)
7.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series54.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (* b_2 b_2) (* a c))
20.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)
14.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify64.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4877	1395
1	4877	1395

prune112.0ms

Filtered

70 candidates to 94 candidates (-34.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	92	2	94
Fresh	2	5	7
Picked	0	1	1
Done	0	1	1
Total	94	9	103

Merged error: 7.6b

Counts

103 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* b_2 b_2) (* a c))
3.4b	(* (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
14.6b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
24.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
13×	`add-exp-log` `add-cube-cbrt` `associate-r`
11×	`times-frac`
10×	`add-log-exp`
9×	`add-cbrt-cube`
7×	`pow1` `associate-l`
5×	`flip3--` `sqrt-prod` `flip--`
4×	`prod-exp` `distribute-lft-out--` `difference-of-squares`
3×	`diff-log` `unswap-sqr`
2×	`frac-times` `sub-neg` `distribute-rgt-neg-in` `sqrt-div` `div-exp` `associate-*l/` `cbrt-unprod`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `associate-r/` `pow-prod-down` `neg-log` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 87

Calls

4 calls:

5.0ms	(- (* b_2 b_2) (* a c))
15.0ms	(* (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
8.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series55.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (* b_2 b_2) (* a c))
19.0ms	(* (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
16.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify43.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5147	1355

prune93.0ms

Filtered

71 candidates to 99 candidates (-39.4%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	98	1	99
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	98	10	108

Merged error: 7.6b

Counts

108 → 10

regimes293.0ms

Accuracy

95% (1.2b remaining)

Error of 6.8b against oracle of 5.6b and baseline of 29.7b

bsearch98.0ms

Steps

Iters	Range	Point
9	3.7777184466982954e+107	8.352834316001598e+114	3.086288419134239e+108
7	1.4874624683826671e-298	1.200825657964057e-296	5.771241894261535e-297
7	-1.4508746656358656e+154	-7.98298683749045e+151	-3.328450881346258e+153

Iters

Range

Point

3.7777184466982954e+107

8.352834316001598e+114

3.086288419134239e+108

1.4874624683826671e-298

1.200825657964057e-296

5.771241894261535e-297

-1.4508746656358656e+154

-7.98298683749045e+151

-3.328450881346258e+153

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	144	56
1	144	56

end0.0ms

sample1.8s

Algorithm

intervals

Results

266.0ms	1096×	body	2560	valid
201.0ms	5084×	body	80	valid
179.0ms	926×	body	1280	valid
71.0ms	466×	body	640	valid
31.0ms	106×	body	5120	valid
24.0ms	206×	body	320	valid
9.0ms	116×	body	160	valid

Details

analyze585.0ms

sample94.0ms

simplify480.0ms

prune5.0ms

localize23.0ms

rewrite33.0ms

series63.0ms

simplify68.0ms

prune149.0ms

localize14.0ms

rewrite38.0ms

series127.0ms

simplify53.0ms

prune151.0ms

localize11.0ms

rewrite28.0ms

series54.0ms

simplify64.0ms

prune112.0ms

localize12.0ms

rewrite35.0ms

series55.0ms

simplify43.0ms

prune93.0ms

regimes293.0ms

bsearch98.0ms

simplify3.0ms

end0.0ms

sample1.8s

Profiling