Details

analyze594.0ms

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

sample47.0ms

Algorithm

intervals

Results

10.0ms	28×	body	2560	valid
8.0ms	168×	body	80	valid
7.0ms	31×	body	1280	valid
2.0ms	14×	body	640	valid
2.0ms	9×	body	320	valid
1.0ms	34×	body	80	nan
1.0ms	4×	body	5120	valid
1.0ms	11×	body	80	invalid
0.0ms	2×	body	160	valid

simplify461.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (34.0ms)

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: 32.7b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.6b	(- (* b_2 b_2) (* a c))
0.9b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite41.0ms

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:

17.0ms	(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
4.0ms	(- (* b_2 b_2) (* a c))
9.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series60.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
7.0ms	(- (* b_2 b_2) (* a c))
14.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify52.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5405	1587

prune168.0ms

Filtered

72 candidates to 101 candidates (-40.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	91	10	101
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	92	10	102

Merged error: 5.1b

Counts

102 → 10

localize9.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* b_2 b_2) (* a c))
3.0b	(/ (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
9.5b	(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
22.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

66×	`times-frac`
53×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
28×	`add-cube-cbrt`
18×	`add-exp-log` `add-cbrt-cube`
13×	`associate-/l*`
12×	`difference-of-squares`
10×	`associate-/r/`
9×	`associate-/r*` `sqrt-prod`
7×	`cbrt-undiv` `flip3--` `div-exp` `flip--`
6×	`div-inv` `distribute-lft-out--` `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 → 123

Calls

4 calls:

4.0ms	(- (* b_2 b_2) (* a c))
15.0ms	(/ (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
10.0ms	(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series116.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (* b_2 b_2) (* a c))
43.0ms	(/ (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
53.0ms	(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify68.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4953	2501
1	4953	2501

prune178.0ms

Filtered

102 candidates to 135 candidates (-32.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	131	4	135
Fresh	3	6	9
Picked	1	0	1
Done	0	0	0
Total	135	10	145

Merged error: 5.1b

Counts

145 → 10

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
0.4b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.6b	(- (* b_2 b_2) (* a c))
22.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite30.0ms

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` `associate-/r*` `add-cbrt-cube`
5×	`pow1` `distribute-lft-out--`
4×	`flip3--` `flip--`
3×	`associate-/l*`
2×	`sub-neg` `sqrt-div` `diff-log` `associate-/r/`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv`

Counts

4 → 81

Calls

4 calls:

9.0ms	(/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
7.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
4.0ms	(- (* b_2 b_2) (* a c))
8.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series81.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
13.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
7.0ms	(- (* b_2 b_2) (* a c))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify56.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5408	1374

prune131.0ms

Filtered

69 candidates to 93 candidates (-34.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	92	1	93
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	93	10	103

Merged error: 5.1b

Counts

103 → 10

localize11.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* b_2 b_2) (* a c))
3.1b	(* (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ 1 a))
9.5b	(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
22.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-exp-log`
36×	`add-sqr-sqrt`
30×	`add-cbrt-cube`
23×	`*-un-lft-identity` `times-frac`
17×	`prod-exp`
16×	`add-cube-cbrt` `div-exp`
13×	`associate-r`
12×	`associate-l`
9×	`cbrt-undiv` `cbrt-unprod`
7×	`pow1`
6×	`associate-/r*` `sqrt-prod` `add-log-exp` `difference-of-squares`
4×	`flip3--` `associate-/r/` `flip--`
3×	`rec-exp` `1-exp` `div-inv` `distribute-lft-out--` `unswap-sqr`
2×	`sqrt-div`
1×	`frac-times` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `un-div-inv` `-commutative` `associate-/l`

Counts

4 → 114

Calls

4 calls:

6.0ms	(- (* b_2 b_2) (* a c))
17.0ms	(* (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ 1 a))
10.0ms	(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series114.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (* b_2 b_2) (* a c))
42.0ms	(* (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ 1 a))
53.0ms	(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify39.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5024	1809

prune121.0ms

Filtered

84 candidates to 126 candidates (-50.0%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	125	1	126
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	126	10	136

Merged error: 5.1b

Counts

136 → 10

regimes472.0ms

Accuracy

95.2% (1.1b remaining)

Error of 6.5b against oracle of 5.3b and baseline of 29.4b

bsearch89.0ms

Steps

Iters	Range	Point
6	1.0174475383635804e+117	8.787339607785109e+117	4.634965395107105e+117
11	-8.001116230681224e-287	6.944189910878404e-307	1.316439096055291e-307
8	-1.2674534969691883e+160	-5.2733010743997736e+156	-5.3488319803265095e+156

Iters

Range

Point

1.0174475383635804e+117

8.787339607785109e+117

4.634965395107105e+117

-8.001116230681224e-287

6.944189910878404e-307

1.316439096055291e-307

-1.2674534969691883e+160

-5.2733010743997736e+156

-5.3488319803265095e+156

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	179	63
1	179	63

end0.0ms

sample1.1s

Algorithm

intervals

Results

276.0ms	1074×	body	2560	valid
238.0ms	5091×	body	80	valid
193.0ms	897×	body	1280	valid
78.0ms	478×	body	640	valid
36.0ms	822×	body	80	nan
36.0ms	110×	body	5120	valid
27.0ms	216×	body	320	valid
12.0ms	134×	body	160	valid
11.0ms	226×	body	80	invalid

Details

analyze594.0ms

sample47.0ms

simplify461.0ms

prune5.0ms

localize12.0ms

rewrite41.0ms

series60.0ms

simplify52.0ms

prune168.0ms

localize9.0ms

rewrite37.0ms

series116.0ms

simplify68.0ms

prune178.0ms

localize9.0ms

rewrite30.0ms

series81.0ms

simplify56.0ms

prune131.0ms

localize11.0ms

rewrite40.0ms

series114.0ms

simplify39.0ms

prune121.0ms

regimes472.0ms

bsearch89.0ms

simplify3.0ms

end0.0ms

sample1.1s

Profiling