Details

sample60.0ms

Algorithm

intervals

Results

13.0ms	204×	body	80	valid
11.0ms	29×	body	2560	valid
8.0ms	25×	body	1280	valid
6.0ms	98×	body	80	nan
4.0ms	15×	body	640	valid
1.0ms	2×	body	5120	valid
1.0ms	4×	body	320	valid
0.0ms	3×	body	160	valid

simplify8.0ms

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

prune2.0ms

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: 31.3b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.8b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.4b	(- (* b_2 b_2) (* a c))
21.5b	(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:

13.0ms	(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
8.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(- (* b_2 b_2) (* a c))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series254.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
69.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
37.0ms	(- (* b_2 b_2) (* a c))
60.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify47.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	368	965
1	1241	910
2	5001	901

prune234.0ms

Filtered

103 candidates to 72 candidates (69.9%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	93	10	103
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	93	11	104

Merged error: 5.2b

Counts

104 → 11

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
0.8b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.4b	(- (* b_2 b_2) (* a c))
21.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite35.0ms

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:

15.0ms	(* (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
11.0ms	(- (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)))

series250.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(* (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
70.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
36.0ms	(- (* b_2 b_2) (* a c))
59.0ms	(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	428	881
1	1823	791
2	5002	771

prune206.0ms

Filtered

101 candidates to 70 candidates (69.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	100	1	101
Fresh	0	9	9
Picked	1	0	1
Done	0	1	1
Total	101	11	112

Merged error: 5.2b

Counts

112 → 11

localize13.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (* b_2 b_2) (* a c))
2.2b	(/ (/ (+ 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))
21.5b	(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:

4.0ms	(- (* b_2 b_2) (* a c))
15.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
11.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series443.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(- (* b_2 b_2) (* a c))
154.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
190.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
65.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify107.0ms

Algorithm

egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 2 (79.0ms)

Iter	Nodes	Cost
0	725	2899
1	3167	2743
2	5002	2723

prune448.0ms

Filtered

196 candidates to 144 candidates (73.5%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	193	3	196
Fresh	1	8	9
Picked	1	0	1
Done	0	1	1
Total	195	12	207

Merged error: 5.2b

Counts

207 → 12

localize12.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (* b_2 b_2) (* a c))
1.5b	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
2.2b	(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
21.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

831×	`times-frac`
545×	`add-sqr-sqrt`
448×	`*-un-lft-identity`
352×	`add-cube-cbrt`
96×	`difference-of-squares`
74×	`associate-/l*`
51×	`sqrt-prod`
48×	`distribute-lft-out--`
25×	`associate-/r*`
22×	`div-inv`
18×	`add-exp-log` `add-cbrt-cube`
9×	`cbrt-undiv` `div-exp`
6×	`add-log-exp`
5×	`pow1` `associate-/r/`
2×	`flip3--` `frac-2neg` `sqrt-div` `clear-num` `flip--`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-/l/`

Counts

4 → 437

Calls

4 calls:

4.0ms	(- (* b_2 b_2) (* a c))
11.0ms	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
23.0ms	(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series398.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(- (* b_2 b_2) (* a c))
168.0ms	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
136.0ms	(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
61.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify98.0ms

Algorithm

egg-herbie

Counts

449 → 449

Iterations

Useful iterations: 1 (34.0ms)

Iter	Nodes	Cost
0	1541	7328
1	5001	6762

prune922.0ms

Filtered

449 candidates to 297 candidates (66.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	447	2	449
Fresh	2	8	10
Picked	1	0	1
Done	0	1	1
Total	450	11	461

Merged error: 5.2b

Counts

461 → 11

regimes287.0ms

Accuracy

94.6% (1.3b remaining)

Error of 7.0b against oracle of 5.7b and baseline of 29.5b

bsearch166.0ms

Steps

Iters	Range		Point
10	1.4182100026226751e+88	1.1634796338171106e+98	1.0676041056623592e+96
6	1.973933084062596e-270	1.1184640472519091e-269	2.513932384429884e-270
10	-7.412295145025422e+71	-1.299336563286216e+62	-9.592767440209079e+66

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	21
1	38	21

end0.0ms

sample1.5s

Algorithm

intervals

Results

345.0ms	1109×	body	2560	valid
306.0ms	5830×	body	80	valid
228.0ms	901×	body	1280	valid
151.0ms	2891×	body	80	nan
89.0ms	440×	body	640	valid
39.0ms	105×	body	5120	valid
35.0ms	215×	body	320	valid
11.0ms	113×	body	160	valid

Details

sample60.0ms

simplify8.0ms

prune2.0ms

localize10.0ms

rewrite31.0ms

series254.0ms

simplify47.0ms

prune234.0ms

localize12.0ms

rewrite35.0ms

series250.0ms

simplify51.0ms

prune206.0ms

localize13.0ms

rewrite42.0ms

series443.0ms

simplify107.0ms

prune448.0ms

localize12.0ms

rewrite76.0ms

series398.0ms

simplify98.0ms

prune922.0ms

regimes287.0ms

bsearch166.0ms

simplify1.0ms

end0.0ms

sample1.5s

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