Details

sample292.0ms

Algorithm

intervals

Results

11.0ms	203×	body	80	valid
7.0ms	31×	body	1280	valid
6.0ms	23×	body	2560	valid
3.0ms	79×	body	80	nan
3.0ms	17×	body	640	valid
2.0ms	4×	body	5120	valid
1.0ms	4×	body	320	valid
0.0ms	4×	body	160	valid

simplify11.0ms

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

prune4.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 32.9b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.6b	(- (* b_2 b_2) (* a c))
0.9b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 120

Calls

4 calls:

30.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
16.0ms	(- (* b_2 b_2) (* a c))
39.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
18.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series259.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
33.0ms	(- (* b_2 b_2) (* a c))
69.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
74.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify47.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	416	1177
1	1416	1122
2	5001	1109

prune282.0ms

Filtered

132 candidates to 81 candidates (61.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	123	9	132
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	124	9	133

Merged error: 6.2b

Counts

133 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.6b	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
9.4b	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
22.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

297×	`*-un-lft-identity`
258×	`times-frac`
243×	`add-sqr-sqrt`
105×	`add-cube-cbrt`
66×	`difference-of-squares`
64×	`distribute-lft-out`
46×	`associate-/l*`
45×	`sqrt-prod`
36×	`associate-l`
32×	`distribute-lft-out--`
20×	`associate-/l/`
15×	`associate-/r*`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r/`
7×	`flip3--` `flip--` `unswap-sqr`
6×	`div-inv` `add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `div-exp`
3×	`frac-2neg` `clear-num`
2×	`flip3-+` `sqrt-div` `swap-sqr` `*-commutative` `flip-+`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 278

Calls

4 calls:

23.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
43.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
31.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
19.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series477.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
155.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
188.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
62.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify121.0ms

Algorithm

egg-herbie

Counts

290 → 290

Iterations

Useful iterations: 2 (87.0ms)

Iter	Nodes	Cost
0	796	4143
1	3496	3915
2	5001	3895

prune538.0ms

Filtered

290 candidates to 161 candidates (55.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	284	6	290
Fresh	5	3	8
Picked	1	0	1
Done	0	0	0
Total	290	9	299

Merged error: 6.1b

Counts

299 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

1.6b	(/ (* (/ 1 (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) (/ a (/ (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) c))) a)
3.1b	(* (/ 1 (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) (/ a (/ (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) c)))
22.1b	(sqrt (- (* b_2 b_2) (* a c)))
22.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite626.0ms

Algorithm

rewrite-expression-head

Rules

2815×	`add-sqr-sqrt`
2590×	`times-frac`
1982×	`*-un-lft-identity`
1758×	`sqrt-prod`
1694×	`associate-/r*`
1450×	`add-cube-cbrt`
1110×	`frac-times`
619×	`associate-/l/`
570×	`associate-r`
543×	`associate-/l*`
494×	`difference-of-squares`
245×	`distribute-lft-out--`
173×	`associate-l`
116×	`clear-num`
114×	`frac-2neg` `unswap-sqr`
96×	`add-exp-log`
95×	`associate-/r/`
74×	`associate-*r/`
58×	`div-inv`
54×	`add-cbrt-cube`
49×	`div-exp`
30×	`associate-*l/`
25×	`cbrt-undiv`
24×	`sqrt-div` `prod-exp`
12×	`flip3--` `flip--` `cbrt-unprod`
9×	`*-commutative`
8×	`pow1`
6×	`rec-exp` `1-exp`
4×	`swap-sqr` `un-div-inv` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`pow-prod-down`

Counts

4 → 2191

Calls

4 calls:

211.0ms	(/ (* (/ 1 (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) (/ a (/ (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) c))) a)
143.0ms	(* (/ 1 (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) (/ a (/ (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) c)))
19.0ms	(sqrt (- (* b_2 b_2) (* a c)))
17.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series350.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(/ (* (/ 1 (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) (/ a (/ (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) c))) a)
133.0ms	(* (/ 1 (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) (/ a (/ (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) c)))
57.0ms	(sqrt (- (* b_2 b_2) (* a c)))
63.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify417.0ms

Algorithm

egg-herbie

Counts

2203 → 2203

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5001	49743

prune5.1s

Filtered

2203 candidates to 1202 candidates (54.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	2201	2	2203
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	2203	9	2212

Merged error: 6.1b

Counts

2212 → 9

localize20.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.6b	(/ (/ (* (cbrt 1) (* (cbrt 1) a)) (/ (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c) (cbrt 1))) a)
1.8b	(/ (* (cbrt 1) (* (cbrt 1) a)) (/ (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c) (cbrt 1)))
22.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite6.5s

Algorithm

rewrite-expression-head

Rules

92237×	`times-frac`
67349×	`add-sqr-sqrt`
44331×	`*-un-lft-identity`
31553×	`add-cube-cbrt`
28351×	`cbrt-prod`
16375×	`unswap-sqr`
13640×	`associate-r`
8188×	`associate-l`
7324×	`difference-of-squares`
5709×	`associate-/l*`
3674×	`sqrt-prod`
3661×	`distribute-lft-out--`
1425×	`div-inv`
1366×	`*-commutative`
320×	`associate-/r*`
287×	`add-cbrt-cube`
259×	`associate-/l/`
225×	`associate-/r/`
190×	`cbrt-undiv`
100×	`cbrt-unprod`
87×	`add-exp-log`
46×	`div-exp`
18×	`prod-exp`
13×	`frac-2neg` `clear-num`
7×	`flip3--` `flip--`
6×	`add-log-exp`
5×	`pow1`
2×	`sqrt-div` `swap-sqr`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 27953

Calls

4 calls:

22.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.3s	(/ (/ (* (cbrt 1) (* (cbrt 1) a)) (/ (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c) (cbrt 1))) a)
183.0ms	(/ (* (cbrt 1) (* (cbrt 1) a)) (/ (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c) (cbrt 1)))
16.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series430.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
129.0ms	(/ (/ (* (cbrt 1) (* (cbrt 1) a)) (/ (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c) (cbrt 1))) a)
165.0ms	(/ (* (cbrt 1) (* (cbrt 1) a)) (/ (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c) (cbrt 1)))
66.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify7.4s

Algorithm

egg-herbie

Counts

27965 → 27965

Iterations

Useful iterations: 0 (251.0ms)

Iter	Nodes	Cost
0	22551	842657

prune1.6m

Filtered

27965 candidates to 18068 candidates (64.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	27962	3	27965
Fresh	2	5	7
Picked	1	0	1
Done	0	1	1
Total	27965	9	27974

Merged error: 6.1b

Counts

27974 → 9

regimes213.0ms

Accuracy

87.4% (3.3b remaining)

Error of 8.7b against oracle of 5.4b and baseline of 31.6b

bsearch137.0ms

Steps

Iters	Range		Point
9	4.546949039871578e+116	7.0067478635952275e+121	7.369869774752497e+119
4	2.7062129888597453e-95	4.861630376334293e-95	2.7444235711350233e-95
9	-6.621891359339352e+42	-4.1115514380901975e+36	-4.8085485579241775e+39

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	27
1	45	27

end0.0ms

sample1.0s

Algorithm

intervals

Results

218.0ms	1063×	body	2560	valid
207.0ms	5848×	body	80	valid
135.0ms	850×	body	1280	valid
89.0ms	2860×	body	80	nan
58.0ms	465×	body	640	valid
26.0ms	105×	body	5120	valid
23.0ms	234×	body	320	valid
8.0ms	120×	body	160	valid