Details

analyze600.0ms

Algorithm: search

sample43.0ms

Algorithm

intervals

Results

9.0ms	33×	body	2560	valid
8.0ms	164×	body	80	valid
5.0ms	25×	body	1280	valid
4.0ms	22×	body	640	valid
2.0ms	5×	body	5120	valid
1.0ms	21×	body	80	nan
0.0ms	10×	body	80	invalid
0.0ms	3×	body	320	valid
0.0ms	4×	body	160	valid

simplify404.0ms

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: 35.5b

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)
0.8b	(- (* b_2 b_2) (* a c))
1.4b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite32.0ms

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)))

series75.0ms

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))))
37.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify42.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (31.0ms)

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

prune145.0ms

Filtered

72 candidates to 103 candidates (-43.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	95	8	103
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	96	8	104

Merged error: 6.0b

Counts

104 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
4.0b	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
10.1b	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
23.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite44.0ms

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))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series127.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
43.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
57.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify107.0ms

Algorithm

egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 2 (80.0ms)

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

prune245.0ms

Filtered

148 candidates to 199 candidates (-34.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	196	3	199
Fresh	3	4	7
Picked	0	1	1
Done	0	0	0
Total	199	8	207

Merged error: 6.0b

Counts

207 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.8b	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
4.0b	(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
23.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite77.0ms

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)
11.0ms	(/ 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)))

series125.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
54.0ms	(/ 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)
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify100.0ms

Algorithm

egg-herbie

Counts

452 → 452

Iterations

Useful iterations: 1 (33.0ms)

Iter	Nodes	Cost
0	1557	7387
1	5001	6822

prune312.0ms

Filtered

301 candidates to 452 candidates (-50.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	451	1	452
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	452	8	460

Merged error: 6.0b

Counts

460 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

0.9b	(/ (cbrt a) (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
1.0b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.3b	(/ (/ (cbrt a) (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) (cbrt a))
23.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite188.0ms

Algorithm

rewrite-expression-head

Rules

2760×	`times-frac`
1725×	`add-sqr-sqrt`
1428×	`*-un-lft-identity`
1132×	`add-cube-cbrt`
945×	`cbrt-prod`
296×	`difference-of-squares`
151×	`sqrt-prod`
148×	`distribute-lft-out--`
143×	`associate-/l*`
58×	`div-inv`
28×	`associate-/r*`
18×	`add-exp-log`
11×	`add-cbrt-cube`
9×	`cbrt-undiv` `div-exp`
8×	`associate-/r/`
6×	`add-log-exp`
5×	`pow1`
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 → 1187

Calls

4 calls:

13.0ms	(/ (cbrt a) (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
7.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
46.0ms	(/ (/ (cbrt a) (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) (cbrt a))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series179.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(/ (cbrt a) (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
13.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
45.0ms	(/ (/ (cbrt a) (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) (cbrt a))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify279.0ms

Algorithm

egg-herbie

Counts

1199 → 1199

Iterations

Useful iterations: 1 (58.0ms)

Iter	Nodes	Cost
0	3025	26777
1	5002	26551

prune1.0s

Filtered

837 candidates to 1199 candidates (-43.2%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	1198	1	1199
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	1198	9	1207

Merged error: 6.0b

Counts

1207 → 9

regimes273.0ms

Accuracy

92.8% (1.8b remaining)

Error of 7.3b against oracle of 5.5b and baseline of 30.2b

bsearch554.0ms

Steps

Iters	Range	Point
7	3.8886842228499026e+98	3.359393108224228e+100	2.604391320577748e+100
5	7.838277524248008e-290	2.1747419004339243e-289	1.8433204270074619e-289
8	-2.902940677005763e+70	-9.589703364714103e+67	-1.2027723040293916e+70

Iters

Range

Point

3.8886842228499026e+98

3.359393108224228e+100

2.604391320577748e+100

7.838277524248008e-290

2.1747419004339243e-289

1.8433204270074619e-289

-2.902940677005763e+70

-9.589703364714103e+67

-1.2027723040293916e+70

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	23
1	41	23
2	41	23

end0.0ms

analyze398.0ms

Algorithm: search

sample1.1s

Algorithm

intervals

Results

265.0ms	1003×	body	2560	valid
226.0ms	5149×	body	80	valid
188.0ms	906×	body	1280	valid
76.0ms	468×	body	640	valid
32.0ms	106×	body	5120	valid
29.0ms	712×	body	80	nan
29.0ms	241×	body	320	valid
11.0ms	249×	body	80	invalid
11.0ms	127×	body	160	valid

Details

analyze600.0ms

sample43.0ms

simplify404.0ms

prune5.0ms

localize12.0ms

rewrite32.0ms

series75.0ms

simplify42.0ms

prune145.0ms

localize11.0ms

rewrite44.0ms

series127.0ms

simplify107.0ms

prune245.0ms

localize11.0ms

rewrite77.0ms

series125.0ms

simplify100.0ms

prune312.0ms

localize14.0ms

rewrite188.0ms

series179.0ms

simplify279.0ms

prune1.0s

regimes273.0ms

bsearch554.0ms

simplify2.0ms

end0.0ms

analyze398.0ms

sample1.1s

Profiling