Details

sample283.0ms

Algorithm

intervals

Results

7.0ms	172×	body	80	valid
6.0ms	34×	body	2560	valid
5.0ms	32×	body	1280	valid
2.0ms	79×	body	80	nan
2.0ms	9×	body	5120	valid
2.0ms	16×	body	640	valid
1.0ms	9×	body	320	valid
0.0ms	3×	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

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: 35.6b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.6b	(- (* b_2 b_2) (* a c))
1.2b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite43.0ms

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:

22.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
3.0ms	(- (* b_2 b_2) (* a c))
7.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series273.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
33.0ms	(- (* b_2 b_2) (* a c))
77.0ms	(+ (- b_2) (sqrt (- (* 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

prune239.0ms

Filtered

92 candidates to 69 candidates (75.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	82	10	92
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	83	10	93

Merged error: 6.1b

Counts

93 → 10

localize11.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.6b	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
8.6b	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
23.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite55.0ms

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))))
16.0ms	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
12.0ms	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series444.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
143.0ms	(/ (/ (+ 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)))))
59.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify112.0ms

Algorithm

egg-herbie

Counts

218 → 218

Iterations

Useful iterations: 2 (84.0ms)

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

prune503.0ms

Filtered

218 candidates to 147 candidates (67.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	213	5	218
Fresh	4	5	9
Picked	1	0	1
Done	0	0	0
Total	218	10	228

Merged error: 6.0b

Counts

228 → 10

localize11.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
2.1b	(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
3.6b	(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
23.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

951×	`times-frac`
589×	`add-sqr-sqrt`
588×	`*-un-lft-identity`
392×	`add-cube-cbrt`
98×	`distribute-lft-out--` `difference-of-squares`
83×	`associate-/l*`
52×	`sqrt-prod`
49×	`distribute-rgt-neg-in`
28×	`associate-/r*`
22×	`div-inv`
18×	`add-exp-log` `add-cbrt-cube`
9×	`cbrt-undiv` `div-exp`
8×	`add-log-exp`
5×	`pow1` `associate-/r/`
2×	`flip3--` `frac-2neg` `sqrt-div` `diff-log` `clear-num` `flip--`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `neg-log` `associate-/l/`

Counts

4 → 491

Calls

4 calls:

8.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
14.0ms	(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
29.0ms	(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series474.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
186.0ms	(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
157.0ms	(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
59.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify103.0ms

Algorithm

egg-herbie

Counts

503 → 503

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1582	8734
1	5001	8086

prune1.1s

Filtered

503 candidates to 304 candidates (60.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	500	3	503
Fresh	4	5	9
Picked	0	1	1
Done	0	0	0
Total	504	9	513

Merged error: 6.0b

Counts

513 → 9

localize19.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* b_2 b_2) (* a c))
0.8b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0b	(/ (/ (cbrt a) (/ 1 c)) (cbrt a))
23.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

1422×	`times-frac`
661×	`add-sqr-sqrt`
660×	`*-un-lft-identity`
656×	`add-cube-cbrt`
525×	`cbrt-prod`
83×	`associate-/l*`
50×	`div-inv`
19×	`add-exp-log`
11×	`div-exp`
10×	`add-log-exp`
8×	`add-cbrt-cube`
7×	`associate-/r/`
6×	`cbrt-undiv` `associate-/r*`
5×	`pow1`
4×	`sqrt-prod`
3×	`flip3--` `diff-log` `flip--`
2×	`sub-neg` `sqrt-div` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `rec-exp` `distribute-rgt-neg-in` `frac-2neg` `sqrt-pow1` `pow1/2` `1-exp` `neg-log` `clear-num` `associate-/l/`

Counts

4 → 651

Calls

4 calls:

4.0ms	(- (* b_2 b_2) (* a c))
8.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
25.0ms	(/ (/ (cbrt a) (/ 1 c)) (cbrt a))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series178.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(- (* b_2 b_2) (* a c))
71.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
7.0ms	(/ (/ (cbrt a) (/ 1 c)) (cbrt a))
67.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify115.0ms

Algorithm

egg-herbie

Counts

663 → 663

Iterations

Useful iterations: 1 (42.0ms)

Iter	Nodes	Cost
0	2234	9191
1	5001	7963

prune1.8s

Filtered

663 candidates to 416 candidates (62.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	661	2	663
Fresh	2	5	7
Picked	1	0	1
Done	0	1	1
Total	664	8	672

Merged error: 6.0b

Counts

672 → 8

regimes159.0ms

Accuracy

81.8% (4.3b remaining)

Error of 9.7b against oracle of 5.4b and baseline of 29.1b

bsearch107.0ms

Steps

Iters	Range		Point
9	4.546949039871578e+116	7.0067478635952275e+121	8.403598091093321e+118
10	-1.0320842654441656e-69	-6.354733239957269e-82	-2.7633434444009994e-73

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	15
1	34	15

end0.0ms

sample966.0ms

Algorithm

intervals

Results

202.0ms	1054×	body	2560	valid
188.0ms	5814×	body	80	valid
135.0ms	890×	body	1280	valid
85.0ms	2860×	body	80	nan
57.0ms	470×	body	640	valid
25.0ms	111×	body	5120	valid
21.0ms	235×	body	320	valid
7.0ms	126×	body	160	valid