Details

analyze1.1s

Algorithm

sampling

Space saved by range analysis: 0.146413%

Space saved by search: 25.539477%

Guaranteed chance to sample good point: 74.712503%

sample45.0ms

Algorithm

intervals

Results

11.0ms	158×	body	80	valid
9.0ms	39×	body	1280	valid
8.0ms	32×	body	2560	valid
2.0ms	14×	body	640	valid
1.0ms	9×	body	320	valid
1.0ms	2×	body	5120	valid
0.0ms	9×	body	80	nan
0.0ms	6×	body	80	invalid
0.0ms	2×	body	160	valid

simplify395.0ms

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

prune5.0ms

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: 34.5b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.6b	(- (* b_2 b_2) (* a c))
1.0b	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite30.0ms

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:

10.0ms	(/ (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
3.0ms	(- (* b_2 b_2) (* a c))
7.0ms	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series71.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(/ (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
7.0ms	(- (* b_2 b_2) (* a c))
13.0ms	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify141.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	338	783
1	1216	724
2	4971	703
3	5001	703

prune139.0ms

Filtered

69 candidates to 92 candidates (-33.3%)

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: 6.7b

Counts

93 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
2.5b	(/ (/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
8.7b	(/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
22.1b	(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	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
16.0ms	(/ (/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
14.0ms	(/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series119.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
40.0ms	(/ (/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
53.0ms	(/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify108.0ms

Algorithm

egg-herbie

Counts

218 → 218

Iterations

Useful iterations: 2 (78.0ms)

Iter	Nodes	Cost
0	716	3474
1	3237	3299
2	5002	3273

prune231.0ms

Filtered

147 candidates to 218 candidates (-48.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	217	1	218
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	220	6	226

Merged error: 6.6b

Counts

226 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
2.2b	(/ (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)
2.5b	(/ (/ 1 (/ (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)) a)
22.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite225.0ms

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:

8.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
14.0ms	(/ (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)
62.0ms	(/ (/ 1 (/ (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)) a)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series82.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
19.0ms	(/ (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)
29.0ms	(/ (/ 1 (/ (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)) a)
20.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify274.0ms

Algorithm

egg-herbie

Counts

1160 → 1160

Iterations

Useful iterations: 1 (77.0ms)

Iter	Nodes	Cost
0	4286	24834
1	5001	24168

prune995.0ms

Filtered

577 candidates to 1160 candidates (-101.0%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	1160	0	1160
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	1160	6	1166

Merged error: 6.6b

Counts

1166 → 6

localize9.0ms

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))
1.0b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
22.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite36.0ms

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:

12.0ms	(/ 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)
3.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series62.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
7.0ms	(- (* b_2 b_2) (* a c))
13.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify71.0ms

Algorithm

egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	564	2096
1	2553	1897
2	5001	1761

prune105.0ms

Filtered

86 candidates to 174 candidates (-102.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	174	0	174
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	174	6	180

Merged error: 6.6b

Counts

180 → 6

Details

analyze1.1s

sample45.0ms

simplify395.0ms

prune5.0ms

localize12.0ms

rewrite30.0ms

series71.0ms

simplify141.0ms

prune139.0ms

localize11.0ms

rewrite52.0ms

series119.0ms

simplify108.0ms

prune231.0ms

localize13.0ms

rewrite225.0ms

series82.0ms

simplify274.0ms

prune995.0ms

localize9.0ms

rewrite36.0ms

series62.0ms

simplify71.0ms

prune105.0ms

regimes218.0ms

bsearch2.0ms

Profiling