Details

sample303.0ms

Algorithm

intervals

Results

9.0ms	166×	body	80	valid
8.0ms	33×	body	2560	valid
8.0ms	39×	body	1280	valid
4.0ms	22×	body	640	valid
3.0ms	77×	body	80	nan
1.0ms	12×	body	320	valid
1.0ms	2×	body	5120	valid
0.0ms	2×	body	160	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: 35.7b

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)
0.5b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
0.6b	(- (* b_2 b_2) (* a c))
20.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite46.0ms

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)
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)))

series279.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
75.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
39.0ms	(- (* b_2 b_2) (* a c))
71.0ms	(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

prune225.0ms

Filtered

92 candidates to 69 candidates (75.0%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	85	7	92
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	86	7	93

Merged error: 4.4b

Counts

93 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.8b	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
8.0b	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
20.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite57.0ms

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))))
20.0ms	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
13.0ms	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series451.0ms

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)
169.0ms	(/ (+ 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

218 → 218

Iterations

Useful iterations: 2 (85.0ms)

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

prune488.0ms

Filtered

218 candidates to 147 candidates (67.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	215	3	218
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	216	9	225

Merged error: 4.4b

Counts

225 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.8b	(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
4.8b	(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
20.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite104.0ms

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:

9.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
14.0ms	(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
31.0ms	(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series476.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
183.0ms	(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
161.0ms	(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
59.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify109.0ms

Algorithm

egg-herbie

Counts

503 → 503

Iterations

Useful iterations: 1 (35.0ms)

Iter	Nodes	Cost
0	1582	8734
1	5001	8085

prune1.0s

Filtered

503 candidates to 303 candidates (60.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	500	3	503
Fresh	2	5	7
Picked	1	0	1
Done	0	1	1
Total	503	9	512

Merged error: 4.4b

Counts

512 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
0.6b	(- (* b_2 b_2) (* a c))
0.6b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
20.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

159×	`times-frac`
128×	`add-sqr-sqrt`
127×	`*-un-lft-identity`
75×	`add-cube-cbrt`
26×	`distribute-lft-out--` `difference-of-squares`
25×	`associate-/r*`
16×	`sqrt-prod`
15×	`add-exp-log`
13×	`distribute-rgt-neg-in`
10×	`add-log-exp`
9×	`add-cbrt-cube`
7×	`div-exp`
6×	`pow1`
5×	`div-inv`
3×	`cbrt-undiv` `flip3--` `diff-log` `flip--` `associate-/l*`
2×	`sub-neg` `rec-exp` `sqrt-div` `1-exp`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `clear-num` `associate-/r/` `inv-pow`

Counts

4 → 169

Calls

4 calls:

14.0ms	(/ 1 (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
3.0ms	(- (* b_2 b_2) (* a c))
8.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series274.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(/ 1 (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
33.0ms	(- (* b_2 b_2) (* a c))
71.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
62.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify78.0ms

Algorithm

egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	621	2277
1	2654	2085
2	5001	1944

prune226.0ms

Filtered

181 candidates to 82 candidates (45.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	179	2	181
Fresh	2	5	7
Picked	0	1	1
Done	0	1	1
Total	181	9	190

Merged error: 4.4b

Counts

190 → 9

regimes170.0ms

Accuracy

92.8% (1.7b remaining)

Error of 7.2b against oracle of 5.4b and baseline of 29.8b

bsearch101.0ms

Steps

Iters	Range	Point
7	3.0106008231332273e+28	3.853441604264477e+30	3.7841174599135035e+30
7	-2.7658122324780073e-177	-4.963613050543331e-179	-1.3880501838027266e-178
2	-4.193597519284562e+95	-3.5355996581575456e+95	-4.111347786643685e+95

Iters

Range

Point

3.0106008231332273e+28

3.853441604264477e+30

3.7841174599135035e+30

-2.7658122324780073e-177

-4.963613050543331e-179

-1.3880501838027266e-178

-4.193597519284562e+95

-3.5355996581575456e+95

-4.111347786643685e+95

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	23
1	41	23

end0.0ms

sample1.2s

Algorithm

intervals

Results

280.0ms	1137×	body	2560	valid
253.0ms	5779×	body	80	valid
180.0ms	893×	body	1280	valid
119.0ms	2863×	body	80	nan
74.0ms	464×	body	640	valid
34.0ms	107×	body	5120	valid
33.0ms	249×	body	320	valid
9.0ms	110×	body	160	valid