Details

sample235.0ms

Algorithm

intervals

Results

184.0ms	16×	body	640	valid
10.0ms	191×	body	80	valid
6.0ms	25×	body	2560	valid
5.0ms	26×	body	1280	valid
4.0ms	106×	body	80	nan
1.0ms	10×	body	320	valid
1.0ms	3×	body	5120	valid
0.0ms	2×	body	160	valid

simplify366.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	7
1	22	7
2	25	7
3	27	7
4	29	7
5	29	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: 30.6b

Counts

2 → 1

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
1.0b	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.6b	(- (* b_2 b_2) (* a c))
20.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

35×	`*-un-lft-identity`
16×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `times-frac`
10×	`distribute-lft-out` `add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `distribute-rgt-neg-in` `associate-/l*`
3×	`associate-/r*` `sqrt-prod`
2×	`neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `div-exp` `neg-log` `clear-num` `div-inv`

Counts

4 → 80

Calls

4 calls:

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

series72.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(/ (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
14.0ms	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
7.0ms	(- (* b_2 b_2) (* a c))
24.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify142.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	338	783
1	1216	724
2	4971	703
3	5001	703

prune136.0ms

Filtered

69 candidates to 92 candidates (-33.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	84	8	92
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	85	8	93

Merged error: 4.3b

Counts

93 → 8

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
1.0b	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.6b	(- (* b_2 b_2) (* a c))
20.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 84

Calls

4 calls:

16.0ms	(* (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
7.0ms	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.0ms	(- (* b_2 b_2) (* a c))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series56.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(* (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
14.0ms	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
7.0ms	(- (* b_2 b_2) (* a c))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify50.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	428	816
1	1923	721
2	5001	680

prune111.0ms

Filtered

72 candidates to 96 candidates (-33.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	95	1	96
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	96	8	104

Merged error: 4.3b

Counts

104 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (* b_2 b_2) (* a c))
1.6b	(- (* b_2 b_2) (* a c))
20.7b	(sqrt (- (* b_2 b_2) (* a c)))
20.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `add-log-exp`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
4×	`add-exp-log` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 54

Calls

4 calls:

3.0ms	(- (* b_2 b_2) (* a c))
3.0ms	(- (* b_2 b_2) (* a c))
3.0ms	(sqrt (- (* b_2 b_2) (* a c)))
5.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series40.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify50.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 3 (45.0ms)

Iter	Nodes	Cost
0	138	388
1	451	366
2	1533	364
3	5001	362

prune89.0ms

Filtered

50 candidates to 66 candidates (-32.0%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	66	8	74

Merged error: 4.3b

Counts

74 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

1.6b	(/ (/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
1.6b	(- (* b_2 b_2) (* a c))
9.6b	(/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
20.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

186×	`times-frac`
154×	`add-sqr-sqrt`
153×	`*-un-lft-identity`
89×	`add-cube-cbrt`
32×	`distribute-lft-out--` `difference-of-squares`
30×	`associate-/l*`
19×	`sqrt-prod`
16×	`distribute-rgt-neg-in`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r*` `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 → 200

Calls

4 calls:

16.0ms	(/ (/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
3.0ms	(- (* b_2 b_2) (* a c))
11.0ms	(/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
3.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series118.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(/ (/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
7.0ms	(- (* b_2 b_2) (* a c))
51.0ms	(/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
16.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify104.0ms

Algorithm

egg-herbie

Counts

212 → 212

Iterations

Useful iterations: 2 (77.0ms)

Iter	Nodes	Cost
0	708	3365
1	3231	3197
2	5002	3171

prune200.0ms

Filtered

142 candidates to 212 candidates (-49.3%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	211	1	212
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	211	9	220

Merged error: 4.3b

Counts

220 → 9

regimes278.0ms

Accuracy

89.5% (3.0b remaining)

Error of 8.3b against oracle of 5.3b and baseline of 33.7b

bsearch92.0ms

Steps

Iters	Range		Point
6	4.369227440414888e+39	4.189107140407404e+40	3.0034033959378115e+40
10	1.1832138470333651e-290	1.0739610775224124e-280	2.183233669622837e-289
10	-3.692428373978256e+65	-2.9514001404867553e+50	-6.741241628846222e+60

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	25
1	43	25

end0.0ms

sample1.4s

Algorithm

intervals

Results

271.0ms	1065×	body	2560	valid
257.0ms	5895×	body	80	valid
180.0ms	885×	body	1280	valid
118.0ms	2830×	body	80	nan
74.0ms	447×	body	640	valid
31.0ms	100×	body	5120	valid
27.0ms	211×	body	320	valid
9.0ms	115×	body	160	valid

Details

sample235.0ms

simplify366.0ms

prune5.0ms

localize25.0ms

rewrite31.0ms

series72.0ms

simplify142.0ms

prune136.0ms

localize10.0ms

rewrite33.0ms

series56.0ms

simplify50.0ms

prune111.0ms

localize12.0ms

rewrite17.0ms

series40.0ms

simplify50.0ms

prune89.0ms

localize12.0ms

rewrite44.0ms

series118.0ms

simplify104.0ms

prune200.0ms

regimes278.0ms

bsearch92.0ms

simplify2.0ms

end0.0ms

sample1.4s

Profiling