Details

analyze595.0ms

Algorithm: search

sample40.0ms

Algorithm

intervals

Results

8.0ms	170×	body	80	valid
7.0ms	29×	body	2560	valid
6.0ms	30×	body	1280	valid
3.0ms	18×	body	640	valid
1.0ms	31×	body	80	nan
1.0ms	5×	body	320	valid
0.0ms	9×	body	80	invalid
0.0ms	1×	body	5120	valid
0.0ms	3×	body	160	valid

simplify398.0ms

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

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: 34.5b

Counts

2 → 1

localize13.0ms

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))
1.0b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.9b	(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))))
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series74.0ms

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))))
36.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify42.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (31.0ms)

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

prune136.0ms

Filtered

72 candidates to 103 candidates (-43.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	94	9	103
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	95	9	104

Merged error: 6.0b

Counts

104 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
0.6b	(- (* b_2 b_2) (* a c))
1.0b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite31.0ms

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 → 89

Calls

4 calls:

14.0ms	(* (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
3.0ms	(- (* b_2 b_2) (* a c))
8.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series53.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
7.0ms	(- (* b_2 b_2) (* a c))
13.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify51.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	420	880
1	1816	791
2	5002	772

prune114.0ms

Filtered

70 candidates to 101 candidates (-44.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	100	1	101
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	101	9	110

Merged error: 6.0b

Counts

110 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* b_2 b_2) (* a c))
11.3b	(- (neg b_2) (* (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (sqrt (- (* b_2 b_2) (* a c))))))
23.9b	(sqrt (- (* b_2 b_2) (* a c)))
23.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-log-exp`
9×	`add-sqr-sqrt`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
4×	`add-exp-log` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--`
3×	`diff-log`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`associate--l-` `neg-sub0` `neg-log` `difference-of-squares`

Counts

4 → 57

Calls

4 calls:

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

series49.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(- (* b_2 b_2) (* a c))
14.0ms	(- (neg b_2) (* (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (sqrt (- (* b_2 b_2) (* a c))))))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify95.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 3 (88.0ms)

Iter	Nodes	Cost
0	231	588
1	850	505
2	3394	487
3	5001	470

prune95.0ms

Filtered

54 candidates to 69 candidates (-27.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	68	1	69
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	69	9	78

Merged error: 6.0b

Counts

78 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

1.3b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
3.5b	(/ (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
11.5b	(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
23.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite40.0ms

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 → 127

Calls

4 calls:

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

series123.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
41.0ms	(/ (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
57.0ms	(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify68.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	566	1605
1	2658	1446
2	5001	1436

prune115.0ms

Filtered

105 candidates to 139 candidates (-32.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	136	3	139
Fresh	2	4	6
Picked	0	1	1
Done	1	1	2
Total	139	9	148

Merged error: 6.0b

Counts

148 → 9

regimes345.0ms

Accuracy

83.7% (4.7b remaining)

Error of 9.6b against oracle of 4.9b and baseline of 33.7b

bsearch491.0ms

Steps

Iters	Range		Point
9	9.676612481080008e+98	1.0820883755197331e+107	1.0629485869692184e+107
10	-1.927825129139351e-114	-1.1241075047455707e-128	-1.6074592617615095e-114

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	21
1	31	21

end0.0ms

analyze392.0ms

Algorithm: search

sample1.0s

Algorithm

intervals

Results

260.0ms	1062×	body	2560	valid
222.0ms	5143×	body	80	valid
177.0ms	888×	body	1280	valid
71.0ms	462×	body	640	valid
32.0ms	239×	body	320	valid
32.0ms	789×	body	80	nan
29.0ms	98×	body	5120	valid
12.0ms	239×	body	80	invalid
9.0ms	108×	body	160	valid

Details

analyze595.0ms

sample40.0ms

simplify398.0ms

prune5.0ms

localize13.0ms

rewrite31.0ms

series74.0ms

simplify42.0ms

prune136.0ms

localize12.0ms

rewrite31.0ms

series53.0ms

simplify51.0ms

prune114.0ms

localize12.0ms

rewrite16.0ms

series49.0ms

simplify95.0ms

prune95.0ms

localize10.0ms

rewrite40.0ms

series123.0ms

simplify68.0ms

prune115.0ms

regimes345.0ms

bsearch491.0ms

simplify2.0ms

end0.0ms

analyze392.0ms

sample1.0s

Profiling