Details

sample42.0ms

Algorithm

intervals

Results

9.0ms	38×	body	2560	valid
8.0ms	188×	body	80	valid
6.0ms	28×	body	1280	valid
4.0ms	91×	body	80	nan
1.0ms	9×	body	640	valid
1.0ms	9×	body	320	valid
1.0ms	3×	body	5120	valid
0.0ms	1×	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: 35.1b

Counts

2 → 1

localize8.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.5b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.2b	(- (* b_2 b_2) (* a c))
24.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite30.0ms

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	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
8.0ms	(- (- 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)))

series270.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
83.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
35.0ms	(- (* b_2 b_2) (* a c))
57.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify46.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (33.0ms)

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

prune218.0ms

Filtered

103 candidates to 72 candidates (69.9%)

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: 6.7b

Counts

104 → 7

localize10.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b_2 b_2) (* a c))
2.5b	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
10.2b	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
24.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite43.0ms

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))
17.0ms	(/ (/ (+ 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)))

series429.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(- (* b_2 b_2) (* a c))
149.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
183.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
63.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify106.0ms

Algorithm

egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 2 (80.0ms)

Iter	Nodes	Cost
0	725	2897
1	3210	2743
2	5003	2723

prune428.0ms

Filtered

196 candidates to 144 candidates (73.5%)

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: 6.6b

Counts

203 → 8

localize10.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b_2 b_2) (* a c))
2.5b	(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
3.3b	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
24.9b	(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))
22.0ms	(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
10.0ms	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series407.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(- (* b_2 b_2) (* a c))
130.0ms	(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
170.0ms	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
69.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify96.0ms

Algorithm

egg-herbie

Counts

449 → 449

Iterations

Useful iterations: 1 (35.0ms)

Iter	Nodes	Cost
0	1541	7328
1	5001	6762

prune908.0ms

Filtered

449 candidates to 297 candidates (66.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	448	1	449
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	449	8	457

Merged error: 6.6b

Counts

457 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

2.2b	(/ (/ a (/ (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) c)) (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
2.5b	(/ (/ (/ a (/ (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) c)) (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) a)
24.9b	(sqrt (- (* b_2 b_2) (* a c)))
24.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite895.0ms

Algorithm

rewrite-expression-head

Rules

15078×	`times-frac`
9183×	`add-sqr-sqrt`
7371×	`*-un-lft-identity`
6341×	`sqrt-prod`
5561×	`add-cube-cbrt`
1810×	`difference-of-squares`
986×	`associate-/l*`
905×	`distribute-lft-out--`
190×	`div-inv`
56×	`associate-/r/`
27×	`add-exp-log` `add-cbrt-cube`
16×	`cbrt-undiv` `div-exp`
14×	`sqrt-div`
12×	`associate-/r*`
7×	`flip3--` `flip--`
6×	`pow1`
4×	`add-log-exp`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `associate-/l/`

Counts

4 → 4612

Calls

4 calls:

42.0ms	(/ (/ a (/ (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) c)) (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
183.0ms	(/ (/ (/ a (/ (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) c)) (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) a)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series432.0ms

Counts

4 → 12

Calls

4 calls:

166.0ms	(/ (/ a (/ (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) c)) (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
133.0ms	(/ (/ (/ a (/ (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) c)) (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) a)
63.0ms	(sqrt (- (* b_2 b_2) (* a c)))
69.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.3s

Algorithm

egg-herbie

Counts

4624 → 4624

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5001	157496

prune10.0s

Filtered

4624 candidates to 2184 candidates (47.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	4624	0	4624
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	4624	8	4632

Merged error: 6.6b

Counts

4632 → 8

regimes186.0ms

Accuracy

87.6% (3.2b remaining)

Error of 8.6b against oracle of 5.4b and baseline of 31.4b

bsearch166.0ms

Steps

Iters	Range		Point
7	0.008549975533169097	1.4731263457460937	1.4443031837246074
11	2.4846096868578852e-275	5.196307842503446e-248	1.357539342643855e-271
9	-9.112560713544067e+45	-3.791798387983387e+40	-2.0716165250948376e+45

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	23
1	40	23

end0.0ms

sample1.3s

Algorithm

intervals

Results

281.0ms	1111×	body	2560	valid
266.0ms	5875×	body	80	valid
177.0ms	861×	body	1280	valid
126.0ms	2877×	body	80	nan
71.0ms	439×	body	640	valid
38.0ms	114×	body	5120	valid
26.0ms	210×	body	320	valid
10.0ms	115×	body	160	valid