Details

sample239.0ms

Algorithm

intervals

Results

194.0ms	32×	body	2560	valid
10.0ms	186×	body	80	valid
6.0ms	29×	body	1280	valid
4.0ms	88×	body	80	nan
3.0ms	19×	body	640	valid
1.0ms	3×	body	5120	valid
1.0ms	5×	body	320	valid
0.0ms	4×	body	160	valid

simplify12.0ms

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: 34.9b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.4b	(- (* b_2 b_2) (* a c))
0.7b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
24.6b	(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))))
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series70.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
8.0ms	(- (* b_2 b_2) (* a c))
23.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify43.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (32.0ms)

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

prune146.0ms

Filtered

72 candidates to 103 candidates (-43.1%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	92	11	103
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	92	12	104

Merged error: 5.7b

Counts

104 → 12

localize14.0ms

Local error

Found 4 expressions with local error:

1.7b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
3.3b	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
10.7b	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
24.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

162×	`times-frac`
150×	`add-sqr-sqrt`
115×	`*-un-lft-identity`
81×	`add-cube-cbrt`
34×	`difference-of-squares`
27×	`associate-/l*`
20×	`sqrt-prod`
17×	`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 → 187

Calls

4 calls:

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

series130.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
42.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
60.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify103.0ms

Algorithm

egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 2 (77.0ms)

Iter	Nodes	Cost
0	704	2957
1	3098	2807
2	5001	2787

prune235.0ms

Filtered

148 candidates to 199 candidates (-34.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	194	5	199
Fresh	5	5	10
Picked	1	0	1
Done	0	1	1
Total	200	11	211

Merged error: 5.6b

Counts

211 → 11

localize10.0ms

Local error

Found 4 expressions with local error:

1.6b	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
1.7b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
3.3b	(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
24.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

831×	`times-frac`
549×	`add-sqr-sqrt`
450×	`*-un-lft-identity`
352×	`add-cube-cbrt`
98×	`difference-of-squares`
74×	`associate-/l*`
52×	`sqrt-prod`
49×	`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 → 440

Calls

4 calls:

11.0ms	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
7.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
25.0ms	(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series127.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
14.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
45.0ms	(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify99.0ms

Algorithm

egg-herbie

Counts

452 → 452

Iterations

Useful iterations: 1 (33.0ms)

Iter	Nodes	Cost
0	1557	7387
1	5001	6822

prune308.0ms

Filtered

301 candidates to 452 candidates (-50.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	451	1	452
Fresh	1	8	9
Picked	1	0	1
Done	0	1	1
Total	453	10	463

Merged error: 5.6b

Counts

463 → 10

localize10.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
0.4b	(- (* b_2 b_2) (* a c))
1.7b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
24.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
121×	`add-sqr-sqrt`
94×	`*-un-lft-identity`
68×	`add-cube-cbrt`
26×	`difference-of-squares`
22×	`associate-/r*`
16×	`sqrt-prod`
15×	`add-exp-log`
13×	`distribute-lft-out--`
9×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`div-exp`
6×	`pow1`
5×	`div-inv`
3×	`cbrt-undiv` `flip3--` `flip--` `associate-/l*`
2×	`sub-neg` `rec-exp` `sqrt-div` `diff-log` `1-exp`
1×	`rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `associate-/r/` `inv-pow`

Counts

4 → 154

Calls

4 calls:

10.0ms	(/ 1 (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
4.0ms	(- (* b_2 b_2) (* a c))
7.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series60.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(/ 1 (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
7.0ms	(- (* b_2 b_2) (* a c))
13.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
15.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify69.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	586	1942
1	2438	1777
2	5001	1652

prune92.0ms

Filtered

80 candidates to 166 candidates (-107.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	165	1	166
Fresh	2	6	8
Picked	1	0	1
Done	0	1	1
Total	168	8	176

Merged error: 5.6b

Counts

176 → 8

regimes396.0ms

Accuracy

95.6% (1.1b remaining)

Error of 6.6b against oracle of 5.6b and baseline of 29.5b

bsearch100.0ms

Steps

Iters	Range		Point
9	7.012417207579252e+108	6.866534780894548e+114	1.454923480981544e+112
9	1.2200408170786086e-290	8.84342883157487e-286	2.8478470013750334e-287
9	-8.123118303304505e+80	-8.66777673642249e+74	-8.031427702574679e+80

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	18
1	37	18
2	37	18

end0.0ms

sample1.4s

Algorithm

intervals

Results

267.0ms	1104×	body	2560	valid
251.0ms	5862×	body	80	valid
184.0ms	924×	body	1280	valid
118.0ms	2905×	body	80	nan
67.0ms	432×	body	640	valid
34.0ms	109×	body	5120	valid
27.0ms	216×	body	320	valid
9.0ms	120×	body	160	valid

Details

sample239.0ms

simplify12.0ms

prune5.0ms

localize11.0ms

rewrite31.0ms

series70.0ms

simplify43.0ms

prune146.0ms

localize14.0ms

rewrite45.0ms

series130.0ms

simplify103.0ms

prune235.0ms

localize10.0ms

rewrite80.0ms

series127.0ms

simplify99.0ms

prune308.0ms

localize10.0ms

rewrite32.0ms

series60.0ms

simplify69.0ms

prune92.0ms

regimes396.0ms

bsearch100.0ms

simplify2.0ms

end0.0ms

sample1.4s

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