Details

sample1.2s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 25.430298%

Guaranteed chance to sample good point: 74.712503%

Results

13.0ms	47×	body	2560	valid
8.0ms	165×	body	80	valid
4.0ms	18×	body	1280	valid
2.0ms	11×	body	640	valid
2.0ms	5×	body	5120	valid
1.0ms	22×	body	80	nan
1.0ms	7×	body	320	valid
0.0ms	6×	body	80	invalid
0.0ms	3×	body	160	valid

simplify363.0ms

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

prune6.0ms

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: 34.3b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.2b	(- (* b_2 b_2) (* a c))
1.1b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
25.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite48.0ms

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))))
5.0ms	(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)))

simplify41.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (31.0ms)

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

prune144.0ms

Filtered

72 candidates to 103 candidates (-43.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	94	9	103
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	95	9	104

Merged error: 5.2b

Counts

104 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

0.5b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
4.6b	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
8.5b	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
25.1b	(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)))

series126.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
42.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
55.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
15.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify106.0ms

Algorithm

egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 2 (80.0ms)

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

prune236.0ms

Filtered

148 candidates to 199 candidates (-34.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	197	2	199
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	199	9	208

Merged error: 5.2b

Counts

208 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

4.6b	(/ (* (/ 1 (* (cbrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (cbrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))) (/ a (/ (cbrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) c))) a)
25.1b	(sqrt (- (* b_2 b_2) (* a c)))
25.1b	(sqrt (- (* b_2 b_2) (* a c)))
25.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

105×	`add-exp-log`
55×	`div-exp`
42×	`add-cbrt-cube`
30×	`prod-exp`
25×	`cbrt-undiv`
12×	`add-sqr-sqrt` `cbrt-unprod`
9×	`add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
7×	`pow1`
6×	`rec-exp` `sqrt-div` `1-exp`
4×	`add-log-exp`
3×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `times-frac` `pow1/2` `associate-/r*` `flip--` `associate-/l/`
1×	`frac-times` `frac-2neg` `associate-r/` `associate-l/` `clear-num` `div-inv` `associate-/l*`

Counts

4 → 97

Calls

4 calls:

36.0ms	(/ (* (/ 1 (* (cbrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (cbrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))) (/ a (/ (cbrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) c))) a)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series64.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(/ (* (/ 1 (* (cbrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (cbrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))) (/ a (/ (cbrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) c))) a)
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify72.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	634	1935
1	2887	1470
2	5001	1364

prune120.0ms

Filtered

67 candidates to 109 candidates (-62.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	108	1	109
Fresh	0	7	7
Picked	1	0	1
Done	0	1	1
Total	109	9	118

Merged error: 5.2b

Counts

118 → 9

localize26.0ms

Local error

Found 4 expressions with local error:

25.1b	(sqrt (- (* b_2 b_2) (* a c)))
25.1b	(sqrt (- (* b_2 b_2) (* a c)))
25.1b	(sqrt (- (* b_2 b_2) (* a c)))
25.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
8×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-div`
4×	`add-exp-log` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `add-cbrt-cube` `flip--` `add-log-exp`

Counts

4 → 60

Calls

4 calls:

4.0ms	(sqrt (- (* b_2 b_2) (* a c)))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series50.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify47.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (40.0ms)

Iter	Nodes	Cost
0	120	452
1	399	440
2	1280	436
3	5001	432

prune102.0ms

Filtered

60 candidates to 72 candidates (-20.0%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	71	1	72
Fresh	0	7	7
Picked	1	0	1
Done	0	1	1
Total	72	9	81

Merged error: 5.2b

Counts

81 → 9

regimes368.0ms

Accuracy

83.2% (4.5b remaining)

Error of 10.0b against oracle of 5.4b and baseline of 32.5b

bsearch75.0ms

Steps

Iters	Range		Point
7	1.1579948223382339e+139	1.9869642291463526e+141	2.1178372893628633e+139
7	-5.105947952450567e-24	-7.037819008108055e-26	-7.1626607957578e-26

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	12
1	28	12

end0.0ms

sample2.2s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 25.430298%

Guaranteed chance to sample good point: 74.712503%

Results

303.0ms	1132×	body	2560	valid
242.0ms	5100×	body	80	valid
198.0ms	899×	body	1280	valid
76.0ms	436×	body	640	valid
38.0ms	118×	body	5120	valid
28.0ms	220×	body	320	valid
23.0ms	513×	body	80	nan
10.0ms	181×	body	80	invalid
8.0ms	95×	body	160	valid

Details

sample1.2s

simplify363.0ms

prune6.0ms

localize11.0ms

rewrite48.0ms

series60.0ms

simplify41.0ms

prune144.0ms

localize11.0ms

rewrite44.0ms

series126.0ms

simplify106.0ms

prune236.0ms

localize17.0ms

rewrite54.0ms

series64.0ms

simplify72.0ms

prune120.0ms

localize26.0ms

rewrite19.0ms

series50.0ms

simplify47.0ms

prune102.0ms

regimes368.0ms

bsearch75.0ms

simplify2.0ms

end0.0ms

sample2.2s

Profiling