Details

sample296.0ms

Algorithm

intervals

Results

10.0ms	183×	body	80	valid
10.0ms	40×	body	2560	valid
6.0ms	27×	body	1280	valid
4.0ms	25×	body	640	valid
4.0ms	93×	body	80	nan
1.0ms	5×	body	320	valid
0.0ms	5×	body	160	valid
0.0ms	1×	body	5120	valid

simplify15.0ms

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

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: 35.0b

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)
1.6b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.6b	(- (* b_2 b_2) (* a c))
23.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite44.0ms

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:

23.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
8.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(- (* b_2 b_2) (* a c))
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series284.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
84.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
38.0ms	(- (* b_2 b_2) (* a c))
70.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify42.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	358	790
1	1261	727
2	5001	705

prune224.0ms

Filtered

92 candidates to 69 candidates (75.0%)

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: 3.4b

Counts

93 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (* b_2 b_2) (* a c))
4.7b	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
9.1b	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
23.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite50.0ms

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:

4.0ms	(- (* b_2 b_2) (* a c))
16.0ms	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
16.0ms	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series413.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(- (* b_2 b_2) (* a c))
141.0ms	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
171.0ms	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
64.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify114.0ms

Algorithm

egg-herbie

Counts

212 → 212

Iterations

Useful iterations: 2 (85.0ms)

Iter	Nodes	Cost
0	729	3368
1	3320	3193
2	5001	3167

prune462.0ms

Filtered

212 candidates to 142 candidates (67.0%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	209	3	212
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	211	9	220

Merged error: 3.4b

Counts

220 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (* b_2 b_2) (* a c))
2.9b	(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
4.7b	(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
23.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

951×	`times-frac`
585×	`add-sqr-sqrt`
584×	`*-un-lft-identity`
392×	`add-cube-cbrt`
96×	`distribute-lft-out--` `difference-of-squares`
83×	`associate-/l*`
51×	`sqrt-prod`
48×	`distribute-rgt-neg-in`
28×	`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 → 485

Calls

4 calls:

4.0ms	(- (* b_2 b_2) (* a c))
14.0ms	(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
27.0ms	(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series440.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(- (* b_2 b_2) (* a c))
184.0ms	(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
156.0ms	(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
66.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify126.0ms

Algorithm

egg-herbie

Counts

497 → 497

Iterations

Useful iterations: 1 (38.0ms)

Iter	Nodes	Cost
0	1536	8628
1	5001	7982

prune944.0ms

Filtered

497 candidates to 298 candidates (60.0%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	496	1	497
Fresh	1	6	7
Picked	0	1	1
Done	1	0	1
Total	498	8	506

Merged error: 3.4b

Counts

506 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (* b_2 b_2) (* a c))
1.8b	(/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)
4.7b	(/ (/ 1 (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)) a)
23.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite228.0ms

Algorithm

rewrite-expression-head

Rules

3489×	`times-frac`
1827×	`add-sqr-sqrt`
1826×	`*-un-lft-identity`
1346×	`add-cube-cbrt`
267×	`associate-/l*`
240×	`distribute-lft-out--` `difference-of-squares`
123×	`sqrt-prod`
120×	`distribute-rgt-neg-in`
58×	`div-inv`
41×	`add-exp-log`
28×	`div-exp`
23×	`add-cbrt-cube`
13×	`cbrt-undiv`
6×	`associate-/r*` `add-log-exp`
5×	`pow1`
4×	`associate-/r/`
3×	`rec-exp` `1-exp`
2×	`flip3--` `frac-2neg` `sqrt-div` `div-sub` `clear-num` `flip--` `associate-/l/`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 1142

Calls

4 calls:

4.0ms	(- (* b_2 b_2) (* a c))
19.0ms	(/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)
62.0ms	(/ (/ 1 (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)) a)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series296.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- (* b_2 b_2) (* a c))
91.0ms	(/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)
107.0ms	(/ (/ 1 (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)) a)
65.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify283.0ms

Algorithm

egg-herbie

Counts

1154 → 1154

Iterations

Useful iterations: 1 (72.0ms)

Iter	Nodes	Cost
0	4248	24731
1	5001	24063

prune2.2s

Filtered

1154 candidates to 573 candidates (49.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	1154	0	1154
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	1154	8	1162

Merged error: 3.4b

Counts

1162 → 8

regimes218.0ms

Accuracy

89.7% (2.8b remaining)

Error of 8.3b against oracle of 5.5b and baseline of 32.5b

bsearch193.0ms

Steps

Iters	Range		Point
10	5.784266650655042e-35	2.405238705649324e-23	8.53686088976077e-24
10	2.4778899333688215e-172	3.4510099890326105e-162	2.4991402273322868e-172
11	-3.334524116472281e+99	-2.3662890435539516e+79	-1.599359189869806e+99

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	25
1	43	25

end0.0ms

sample1.3s

Algorithm

intervals

Results

287.0ms	1089×	body	2560	valid
270.0ms	5799×	body	80	valid
189.0ms	879×	body	1280	valid
128.0ms	2960×	body	80	nan
74.0ms	446×	body	640	valid
37.0ms	118×	body	5120	valid
31.0ms	239×	body	320	valid
11.0ms	133×	body	160	valid