Details

sample291.0ms

Algorithm

intervals

Results

7.0ms	37×	body	2560	valid
6.0ms	180×	body	80	valid
4.0ms	75×	body	80	nan
4.0ms	23×	body	1280	valid
2.0ms	17×	body	640	valid
1.0ms	9×	body	320	valid
1.0ms	3×	body	5120	valid
0.0ms	3×	body	160	valid

simplify16.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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)
0.6b	(- (* b_2 b_2) (* a c))
1.3b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.1b	(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:

24.0ms	(/ (+ (- 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)))

series269.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
33.0ms	(- (* b_2 b_2) (* a c))
76.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
69.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify46.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (33.0ms)

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

prune213.0ms

Filtered

92 candidates to 69 candidates (75.0%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	84	8	92
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	84	9	93

Merged error: 5.9b

Counts

93 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
2.4b	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
8.7b	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
23.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite52.0ms

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))))
19.0ms	(/ (/ (+ 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)))

series440.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
142.0ms	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
165.0ms	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
62.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify113.0ms

Algorithm

egg-herbie

Counts

218 → 218

Iterations

Useful iterations: 2 (85.0ms)

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

prune451.0ms

Filtered

218 candidates to 147 candidates (67.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	215	3	218
Fresh	3	4	7
Picked	0	1	1
Done	1	0	1
Total	219	8	227

Merged error: 5.8b

Counts

227 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.9b	(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
1.0b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
2.4b	(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
23.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite94.0ms

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:

13.0ms	(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
8.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
29.0ms	(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series461.0ms

Counts

4 → 12

Calls

4 calls:

178.0ms	(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
70.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
156.0ms	(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
57.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify107.0ms

Algorithm

egg-herbie

Counts

503 → 503

Iterations

Useful iterations: 1 (39.0ms)

Iter	Nodes	Cost
0	1582	8735
1	5001	8087

prune934.0ms

Filtered

503 candidates to 304 candidates (60.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	502	1	503
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	503	8	511

Merged error: 5.8b

Counts

511 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
0.6b	(- (* b_2 b_2) (* a c))
1.3b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
23.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
123×	`add-sqr-sqrt`
96×	`*-un-lft-identity`
70×	`add-cube-cbrt`
26×	`difference-of-squares`
24×	`associate-/r*`
16×	`sqrt-prod`
15×	`add-exp-log`
13×	`distribute-lft-out--`
9×	`associate-/r/` `add-cbrt-cube`
8×	`add-log-exp`
7×	`flip3--` `div-exp` `flip--`
6×	`pow1`
5×	`div-inv`
3×	`cbrt-undiv` `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` `inv-pow`

Counts

4 → 162

Calls

4 calls:

13.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
3.0ms	(- (* 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)))

series288.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
37.0ms	(- (* b_2 b_2) (* a c))
67.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
62.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify72.0ms

Algorithm

egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	569	2100
1	2561	1900
2	5002	1763

prune218.0ms

Filtered

174 candidates to 86 candidates (49.4%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	174	0	174
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	174	8	182

Merged error: 5.8b

Counts

182 → 8

regimes263.0ms

Accuracy

87.6% (3.3b remaining)

Error of 8.6b against oracle of 5.4b and baseline of 31.5b

bsearch153.0ms

Steps

Iters	Range	Point
10	8.485467515044765e-21	0.011261476250181132	0.000518782715372617
10	-4.4782599006234366e-147	-2.1964053429920463e-160	-2.2271387790640654e-160
10	-1.5021501144069279e+69	-2.501148282372368e+59	-1.2963688795759268e+64

Iters

Range

Point

8.485467515044765e-21

0.011261476250181132

0.000518782715372617

-4.4782599006234366e-147

-2.1964053429920463e-160

-2.2271387790640654e-160

-1.5021501144069279e+69

-2.501148282372368e+59

-1.2963688795759268e+64

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	23
1	40	23

end0.0ms

sample994.0ms

Algorithm

intervals

Results

211.0ms	1050×	body	2560	valid
195.0ms	5824×	body	80	valid
141.0ms	884×	body	1280	valid
90.0ms	2907×	body	80	nan
60.0ms	490×	body	640	valid
22.0ms	243×	body	320	valid
22.0ms	92×	body	5120	valid
8.0ms	130×	body	160	valid