Details

sample4.3s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 25.430298%

Guaranteed chance to sample good point: 74.712503%

Results

9.0ms	34×	body	2560	valid
8.0ms	153×	body	80	valid
6.0ms	26×	body	1280	valid
3.0ms	19×	body	640	valid
3.0ms	9×	body	5120	valid
1.0ms	8×	body	320	valid
1.0ms	17×	body	80	nan
1.0ms	7×	body	160	valid
0.0ms	3×	body	80	invalid

simplify389.0ms

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: 34.5b

Counts

2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
1.0b	(- (* b_2 b_2) (* a c))
2.0b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.9b	(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)))

series79.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(/ (- (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))))
41.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify44.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (32.0ms)

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

prune135.0ms

Filtered

72 candidates to 103 candidates (-43.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	97	6	103
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	97	7	104

Merged error: 4.4b

Counts

104 → 7

localize11.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b_2 b_2) (* a c))
3.0b	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
10.7b	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
23.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

162×	`times-frac`
146×	`add-sqr-sqrt`
113×	`*-un-lft-identity`
81×	`add-cube-cbrt`
32×	`difference-of-squares`
27×	`associate-/l*`
19×	`sqrt-prod`
16×	`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 → 184

Calls

4 calls:

3.0ms	(- (* b_2 b_2) (* a c))
14.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
10.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
3.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series116.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(- (* b_2 b_2) (* a c))
39.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
56.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify101.0ms

Algorithm

egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	704	2894
1	3112	2747
2	5001	2727

prune215.0ms

Filtered

144 candidates to 196 candidates (-36.1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	194	2	196
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	194	9	203

Merged error: 4.3b

Counts

203 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b_2 b_2) (* a c))
2.0b	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
3.0b	(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
23.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

831×	`times-frac`
545×	`add-sqr-sqrt`
448×	`*-un-lft-identity`
352×	`add-cube-cbrt`
96×	`difference-of-squares`
74×	`associate-/l*`
51×	`sqrt-prod`
48×	`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 → 437

Calls

4 calls:

3.0ms	(- (* b_2 b_2) (* a c))
10.0ms	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
22.0ms	(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series112.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (* b_2 b_2) (* a c))
50.0ms	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
42.0ms	(/ (/ 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

449 → 449

Iterations

Useful iterations: 1 (33.0ms)

Iter	Nodes	Cost
0	1530	7327
1	5001	6764

prune290.0ms

Filtered

297 candidates to 449 candidates (-51.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	448	1	449
Fresh	1	5	6
Picked	1	0	1
Done	1	1	2
Total	451	7	458

Merged error: 4.3b

Counts

458 → 7

localize9.0ms

Local error

Found 4 expressions with local error:

0.5b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.5b	(/ 1 (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
1.0b	(- (* b_2 b_2) (* a c))
23.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
121×	`add-sqr-sqrt`
94×	`*-un-lft-identity`
68×	`add-cube-cbrt`
26×	`difference-of-squares`
22×	`associate-/r*`
16×	`sqrt-prod`
15×	`add-exp-log`
13×	`distribute-lft-out--`
9×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`div-exp`
6×	`pow1`
5×	`div-inv`
3×	`cbrt-undiv` `flip3--` `flip--` `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` `associate-/r/` `inv-pow`

Counts

4 → 154

Calls

4 calls:

7.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
14.0ms	(/ 1 (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
3.0ms	(- (* b_2 b_2) (* a c))
3.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series54.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
22.0ms	(/ 1 (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
7.0ms	(- (* b_2 b_2) (* a c))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify68.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	586	1945
1	2424	1777
2	5001	1652

prune91.0ms

Filtered

80 candidates to 166 candidates (-107.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	166	0	166
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	166	7	173

Merged error: 4.3b

Counts

173 → 7

regimes342.0ms

Accuracy

94.5% (1.3b remaining)

Error of 6.7b against oracle of 5.4b and baseline of 29.3b

bsearch127.0ms

Steps

Iters	Range	Point
3	1.433683835719374e+51	1.9520437317060034e+51	1.6250885047030717e+51
10	-5.480791718689084e-283	-3.7202024166099145e-295	-3.7587850315147714e-295
7	-1.426441565162669e+132	-1.6299128782325728e+130	-5.234826811305653e+130

Iters

Range

Point

1.433683835719374e+51

1.9520437317060034e+51

1.6250885047030717e+51

-5.480791718689084e-283

-3.7202024166099145e-295

-3.7587850315147714e-295

-1.426441565162669e+132

-1.6299128782325728e+130

-5.234826811305653e+130

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	21
1	38	21

end0.0ms

sample5.4s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 25.430298%

Guaranteed chance to sample good point: 74.712503%

Results

269.0ms	1022×	body	2560	valid
232.0ms	5175×	body	80	valid
196.0ms	938×	body	1280	valid
69.0ms	424×	body	640	valid
35.0ms	105×	body	5120	valid
28.0ms	228×	body	320	valid
22.0ms	509×	body	80	nan
9.0ms	108×	body	160	valid
7.0ms	155×	body	80	invalid

Details

sample4.3s

simplify389.0ms

prune5.0ms

localize13.0ms

rewrite32.0ms

series79.0ms

simplify44.0ms

prune135.0ms

localize11.0ms

rewrite40.0ms

series116.0ms

simplify101.0ms

prune215.0ms

localize10.0ms

rewrite71.0ms

series112.0ms

simplify96.0ms

prune290.0ms

localize9.0ms

rewrite34.0ms

series54.0ms

simplify68.0ms

prune91.0ms

regimes342.0ms

bsearch127.0ms

simplify2.0ms

end0.0ms

sample5.4s

Profiling