Details

sample241.0ms

Algorithm

intervals

Results

190.0ms	84×	body	80	nan
12.0ms	48×	body	2560	valid
9.0ms	175×	body	80	valid
4.0ms	21×	body	1280	valid
3.0ms	20×	body	640	valid
1.0ms	4×	body	5120	valid
1.0ms	10×	body	320	valid
0.0ms	3×	body	160	valid

simplify13.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	7
1	32	7
2	41	7
3	44	7
4	44	7

prune5.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 34.8b

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)
0.8b	(- (* b_2 b_2) (* a c))
1.4b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
21.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite31.0ms

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 → 91

Calls

4 calls:

10.0ms	(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
3.0ms	(- (* b_2 b_2) (* a c))
8.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series66.0ms

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))
21.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
21.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify41.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	360	964
1	1233	910
2	5002	901

prune130.0ms

Filtered

103 candidates to 72 candidates (30.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	96	7	103
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	97	7	104

Merged error: 5.0b

Counts

104 → 7

localize10.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b_2 b_2) (* a c))
5.7b	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
9.9b	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
21.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

162×	`times-frac`
146×	`add-sqr-sqrt`
113×	`*-un-lft-identity`
81×	`add-cube-cbrt`
32×	`difference-of-squares`
27×	`associate-/l*`
19×	`sqrt-prod`
16×	`distribute-lft-out--`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r/`
9×	`associate-/r*`
7×	`flip3--` `flip--`
6×	`div-inv` `add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `div-exp`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `clear-num`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip-+`

Counts

4 → 184

Calls

4 calls:

3.0ms	(- (* b_2 b_2) (* a c))
16.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
10.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
3.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series115.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (* b_2 b_2) (* a c))
39.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
56.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify104.0ms

Algorithm

egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	704	2894
1	3112	2747
2	5001	2727

prune219.0ms

Filtered

196 candidates to 144 candidates (26.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	192	4	196
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	195	8	203

Merged error: 4.9b

Counts

203 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.8b	(- (* b_2 b_2) (* a c))
14.7b	(/ a (* a c))
21.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 63

Calls

4 calls:

6.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
3.0ms	(- (* b_2 b_2) (* a c))
4.0ms	(/ a (* a c))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series33.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
7.0ms	(- (* b_2 b_2) (* a c))
2.0ms	(/ a (* a c))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify128.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 3 (122.0ms)

Iter	Nodes	Cost
0	272	414
1	936	374
2	4266	370
3	5002	369

prune87.0ms

Filtered

75 candidates to 53 candidates (29.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	74	1	75
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	75	8	83

Merged error: 4.9b

Counts

83 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (* (/ 1 c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
0.7b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.8b	(- (* b_2 b_2) (* a c))
21.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 85

Calls

4 calls:

12.0ms	(/ 1 (* (/ 1 c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
6.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
3.0ms	(- (* b_2 b_2) (* a c))
3.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series79.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(/ 1 (* (/ 1 c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
15.0ms	(- (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)))

simplify48.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	432	758
1	1848	634
2	5003	626

prune83.0ms

Filtered

97 candidates to 62 candidates (36.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	96	1	97
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	98	7	105

Merged error: 4.9b

Counts

105 → 7

regimes235.0ms

Accuracy

96.3% (0.9b remaining)

Error of 6.3b against oracle of 5.4b and baseline of 29.3b

bsearch94.0ms

Steps

Iters	Range	Point
9	3.740966656805541e+90	2.271321644956683e+99	1.8862236256436264e+99
10	-6.101116520471646e-307	2.9396268789097114e-297	1.6112937870416748e-307
8	-1.795609024723082e+157	-2.0984588557191883e+153	-3.1668736300451263e+153

Iters

Range

Point

3.740966656805541e+90

2.271321644956683e+99

1.8862236256436264e+99

-6.101116520471646e-307

2.9396268789097114e-297

1.6112937870416748e-307

-1.795609024723082e+157

-2.0984588557191883e+153

-3.1668736300451263e+153

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	21
1	36	21

end0.0ms

sample1.3s

Algorithm

intervals

Results

265.0ms	1070×	body	2560	valid
247.0ms	5891×	body	80	valid
184.0ms	904×	body	1280	valid
111.0ms	2786×	body	80	nan
66.0ms	426×	body	640	valid
35.0ms	121×	body	5120	valid
24.0ms	209×	body	320	valid
9.0ms	110×	body	160	valid

Details

sample241.0ms

simplify13.0ms

prune5.0ms

localize12.0ms

rewrite31.0ms

series66.0ms

simplify41.0ms

prune130.0ms

localize10.0ms

rewrite42.0ms

series115.0ms

simplify104.0ms

prune219.0ms

localize13.0ms

rewrite19.0ms

series33.0ms

simplify128.0ms

prune87.0ms

localize11.0ms

rewrite27.0ms

series79.0ms

simplify48.0ms

prune83.0ms

regimes235.0ms

bsearch94.0ms

simplify2.0ms

end0.0ms

sample1.3s

Profiling