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%

sample41.0ms

Algorithm

intervals

Results

8.0ms	163×	body	80	valid
8.0ms	30×	body	2560	valid
6.0ms	30×	body	1280	valid
2.0ms	14×	body	640	valid
2.0ms	5×	body	5120	valid
1.0ms	8×	body	320	valid
1.0ms	8×	body	80	nan
1.0ms	6×	body	160	valid
0.0ms	5×	body	80	invalid

simplify374.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	7
1	32	7
2	41	7
3	44	7
4	44	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: 35.9b

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)
1.2b	(- (* b_2 b_2) (* a c))
1.7b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
24.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 91

Calls

4 calls:

10.0ms	(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
3.0ms	(- (* b_2 b_2) (* a c))
8.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series60.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
7.0ms	(- (* b_2 b_2) (* a c))
14.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify43.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	360	964
1	1233	910
2	5002	901

prune138.0ms

Filtered

72 candidates to 103 candidates (-43.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	95	8	103
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	95	9	104

Merged error: 5.8b

Counts

104 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
4.7b	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
9.0b	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
24.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

162×	`times-frac`
150×	`add-sqr-sqrt`
115×	`*-un-lft-identity`
81×	`add-cube-cbrt`
34×	`difference-of-squares`
27×	`associate-/l*`
20×	`sqrt-prod`
17×	`distribute-lft-out--`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r/`
9×	`associate-/r*`
7×	`flip3--` `flip--`
6×	`div-inv` `add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `div-exp`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `clear-num`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip-+`

Counts

4 → 187

Calls

4 calls:

7.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
14.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
11.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
3.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series125.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
41.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
58.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify102.0ms

Algorithm

egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	704	2957
1	3098	2807
2	5001	2787

prune216.0ms

Filtered

148 candidates to 199 candidates (-34.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	196	3	199
Fresh	4	3	7
Picked	0	1	1
Done	0	1	1
Total	200	8	208

Merged error: 5.7b

Counts

208 → 8

localize10.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.4b	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
4.7b	(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
24.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

831×	`times-frac`
549×	`add-sqr-sqrt`
450×	`*-un-lft-identity`
352×	`add-cube-cbrt`
98×	`difference-of-squares`
74×	`associate-/l*`
52×	`sqrt-prod`
49×	`distribute-lft-out--`
25×	`associate-/r*`
22×	`div-inv`
18×	`add-exp-log` `add-cbrt-cube`
9×	`cbrt-undiv` `div-exp`
6×	`add-log-exp`
5×	`pow1` `associate-/r/`
2×	`flip3--` `frac-2neg` `sqrt-div` `clear-num` `flip--`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-/l/`

Counts

4 → 440

Calls

4 calls:

7.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
10.0ms	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
25.0ms	(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series123.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
53.0ms	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
44.0ms	(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify96.0ms

Algorithm

egg-herbie

Counts

452 → 452

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1557	7387
1	5001	6822

prune289.0ms

Filtered

301 candidates to 452 candidates (-50.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	450	2	452
Fresh	2	3	5
Picked	0	1	1
Done	1	1	2
Total	453	7	460

Merged error: 5.7b

Counts

460 → 7

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ 1 c))
1.2b	(- (* b_2 b_2) (* a c))
1.2b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
24.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

789×	`times-frac`
493×	`add-sqr-sqrt`
406×	`*-un-lft-identity`
320×	`add-cube-cbrt`
86×	`difference-of-squares`
46×	`sqrt-prod`
44×	`add-exp-log`
43×	`distribute-lft-out--`
40×	`div-inv`
32×	`div-exp`
29×	`associate-/r/`
24×	`associate-/l*`
17×	`flip3--` `flip--`
16×	`add-cbrt-cube`
13×	`associate-/r*`
8×	`cbrt-undiv` `rec-exp` `1-exp` `add-log-exp`
5×	`pow1`
2×	`sub-neg` `sqrt-div` `diff-log`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `associate-/l/`

Counts

4 → 423

Calls

4 calls:

20.0ms	(/ (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ 1 c))
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)))

series57.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(/ (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ 1 c))
7.0ms	(- (* b_2 b_2) (* a c))
14.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify101.0ms

Algorithm

egg-herbie

Counts

435 → 435

Iterations

Useful iterations: 1 (36.0ms)

Iter	Nodes	Cost
0	1746	7647
1	5002	6938

prune270.0ms

Filtered

171 candidates to 435 candidates (-154.4%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	434	1	435
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	434	8	442

Merged error: 5.7b

Counts

442 → 8

Details

analyze1.1s

sample41.0ms

simplify374.0ms

prune5.0ms

localize12.0ms

rewrite51.0ms

series60.0ms

simplify43.0ms

prune138.0ms

localize10.0ms

rewrite45.0ms

series125.0ms

simplify102.0ms

prune216.0ms

localize10.0ms

rewrite79.0ms

series123.0ms

simplify96.0ms

prune289.0ms

localize11.0ms

rewrite69.0ms

series57.0ms

simplify101.0ms

prune270.0ms

regimes358.0ms

bsearch2.0ms

Profiling