Details

sample281.0ms

Algorithm

intervals

Results

8.0ms	40×	body	2560	valid
6.0ms	181×	body	80	valid
6.0ms	36×	body	1280	valid
4.0ms	21×	body	640	valid
3.0ms	100×	body	80	nan
0.0ms	5×	body	320	valid
0.0ms	1×	body	5120	valid
0.0ms	2×	body	160	valid

simplify13.0ms

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

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.8b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.4b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
0.6b	(- (* b_2 b_2) (* a c))
23.6b	(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)))

series271.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
69.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
39.0ms	(- (* b_2 b_2) (* a c))
70.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify45.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (33.0ms)

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

prune232.0ms

Filtered

92 candidates to 69 candidates (75.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.4b	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
10.5b	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
23.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

186×	`times-frac`
158×	`add-sqr-sqrt`
157×	`*-un-lft-identity`
89×	`add-cube-cbrt`
34×	`distribute-lft-out--` `difference-of-squares`
30×	`associate-/l*`
20×	`sqrt-prod`
17×	`distribute-rgt-neg-in`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r*` `associate-/r/`
8×	`add-log-exp`
7×	`flip3--` `flip--`
6×	`div-inv`
5×	`pow1`
4×	`cbrt-undiv` `div-exp`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `diff-log` `clear-num`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 206

Calls

4 calls:

8.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
17.0ms	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
14.0ms	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series450.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
145.0ms	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
172.0ms	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
60.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify113.0ms

Algorithm

egg-herbie

Counts

218 → 218

Iterations

Useful iterations: 2 (86.0ms)

Iter	Nodes	Cost
0	741	3477
1	3329	3295
2	5001	3269

prune512.0ms

Filtered

218 candidates to 147 candidates (67.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
2.7b	(/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)
4.4b	(/ (/ 1 (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)) a)
23.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite243.0ms

Algorithm

rewrite-expression-head

Rules

3489×	`times-frac`
1831×	`add-sqr-sqrt`
1830×	`*-un-lft-identity`
1346×	`add-cube-cbrt`
267×	`associate-/l*`
242×	`distribute-lft-out--` `difference-of-squares`
124×	`sqrt-prod`
121×	`distribute-rgt-neg-in`
58×	`div-inv`
41×	`add-exp-log`
28×	`div-exp`
23×	`add-cbrt-cube`
13×	`cbrt-undiv`
8×	`add-log-exp`
6×	`associate-/r*`
5×	`pow1`
4×	`associate-/r/`
3×	`rec-exp` `1-exp`
2×	`flip3--` `frac-2neg` `sqrt-div` `diff-log` `div-sub` `clear-num` `flip--` `associate-/l/`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `neg-log`

Counts

4 → 1148

Calls

4 calls:

9.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
21.0ms	(/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)
66.0ms	(/ (/ 1 (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)) a)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series345.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
94.0ms	(/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)
111.0ms	(/ (/ 1 (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)) a)
67.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify260.0ms

Algorithm

egg-herbie

Counts

1160 → 1160

Iterations

Useful iterations: 1 (66.0ms)

Iter	Nodes	Cost
0	4287	24836
1	5001	24170

prune2.4s

Filtered

1160 candidates to 577 candidates (49.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.4b	(/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (cbrt a)) c)
1.5b	(/ (/ (cbrt 1) (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (cbrt a)) c)) (cbrt a))
23.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite1.3s

Algorithm

rewrite-expression-head

Rules

22500×	`times-frac`
11592×	`add-sqr-sqrt`
11591×	`*-un-lft-identity`
8467×	`add-cube-cbrt`
8286×	`cbrt-prod`
1562×	`distribute-lft-out--` `difference-of-squares`
903×	`associate-/l*`
784×	`sqrt-prod`
781×	`distribute-rgt-neg-in`
181×	`div-inv`
23×	`add-exp-log`
14×	`add-cbrt-cube`
13×	`cbrt-undiv` `div-exp`
9×	`associate-/r*`
8×	`add-log-exp`
7×	`associate-/r/`
5×	`pow1`
2×	`flip3--` `frac-2neg` `sqrt-div` `diff-log` `div-sub` `clear-num` `flip--` `associate-/l/`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `neg-log`

Counts

4 → 6260

Calls

4 calls:

9.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
19.0ms	(/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (cbrt a)) c)
247.0ms	(/ (/ (cbrt 1) (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (cbrt a)) c)) (cbrt a))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series497.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
234.0ms	(/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (cbrt a)) c)
113.0ms	(/ (/ (cbrt 1) (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (cbrt a)) c)) (cbrt a))
65.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.7s

Algorithm

egg-herbie

Counts

6272 → 6272

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5544	191452

prune24.2s

Filtered

6272 candidates to 3769 candidates (60.1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 6.0b

regimes239.0ms

Accuracy

88.8% (2.7b remaining)

Error of 8.4b against oracle of 5.7b and baseline of 30.2b

bsearch171.0ms

Steps

Iters	Range		Point
7	4.0940537712502537e+21	1.2145431101494081e+23	9.700127799776669e+22
10	-1.5615949759157218e-303	2.965657841234824e-295	6.86161349307731e-300
10	-2693.2368339428763	-1.4570494276460042e-08	-2655.8773955326765

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	55	44
1	55	44

end0.0ms

sample1.0s

Algorithm

intervals

Results

230.0ms	1142×	body	2560	valid
198.0ms	5759×	body	80	valid
151.0ms	938×	body	1280	valid
94.0ms	2985×	body	80	nan
59.0ms	468×	body	640	valid
22.0ms	90×	body	5120	valid
22.0ms	230×	body	320	valid
7.0ms	113×	body	160	valid