Details

sample4.2s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 25.430298%

Guaranteed chance to sample good point: 74.712503%

Results

8.0ms	169×	body	80	valid
8.0ms	31×	body	2560	valid
6.0ms	26×	body	1280	valid
6.0ms	15×	body	640	valid
1.0ms	22×	body	80	nan
1.0ms	6×	body	320	valid
1.0ms	8×	body	160	valid
0.0ms	1×	body	5120	valid
0.0ms	2×	body	80	invalid

simplify399.0ms

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: 34.8b

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))
1.9b	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
24.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite32.0ms

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:

11.0ms	(/ (+ (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)))

series76.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(/ (+ (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)))

simplify143.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (31.0ms)

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

prune148.0ms

Filtered

69 candidates to 92 candidates (-33.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	83	9	92
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	83	10	93

Merged error: 7.6b

Counts

93 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.0b	(/ (/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
11.5b	(/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
24.3b	(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))))
17.0ms	(/ (/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
13.0ms	(/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series123.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
41.0ms	(/ (/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
54.0ms	(/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify110.0ms

Algorithm

egg-herbie

Counts

218 → 218

Iterations

Useful iterations: 2 (81.0ms)

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

prune235.0ms

Filtered

147 candidates to 218 candidates (-48.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	213	5	218
Fresh	4	4	8
Picked	1	0	1
Done	1	0	1
Total	219	9	228

Merged error: 7.5b

Counts

228 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.6b	(/ a (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
3.0b	(/ (/ a (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
24.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

951×	`times-frac`
589×	`add-sqr-sqrt`
588×	`*-un-lft-identity`
392×	`add-cube-cbrt`
98×	`distribute-lft-out--` `difference-of-squares`
83×	`associate-/l*`
52×	`sqrt-prod`
49×	`distribute-rgt-neg-in`
28×	`associate-/r*`
22×	`div-inv`
18×	`add-exp-log` `add-cbrt-cube`
9×	`cbrt-undiv` `div-exp`
8×	`add-log-exp`
5×	`pow1` `associate-/r/`
2×	`flip3--` `frac-2neg` `sqrt-div` `diff-log` `clear-num` `flip--`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `neg-log` `associate-/l/`

Counts

4 → 491

Calls

4 calls:

8.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
14.0ms	(/ a (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
30.0ms	(/ (/ a (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series120.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
53.0ms	(/ a (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
42.0ms	(/ (/ a (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify105.0ms

Algorithm

egg-herbie

Counts

503 → 503

Iterations

Useful iterations: 1 (33.0ms)

Iter	Nodes	Cost
0	1569	8733
1	5001	8087

prune311.0ms

Filtered

303 candidates to 503 candidates (-66.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	499	4	503
Fresh	4	4	8
Picked	1	0	1
Done	0	0	0
Total	504	8	512

Merged error: 7.5b

Counts

512 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ 1 (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
0.6b	(- (* b_2 b_2) (* a c))
0.8b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
24.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

159×	`times-frac`
128×	`add-sqr-sqrt`
127×	`*-un-lft-identity`
75×	`add-cube-cbrt`
26×	`distribute-lft-out--` `difference-of-squares`
25×	`associate-/r*`
16×	`sqrt-prod`
15×	`add-exp-log`
13×	`distribute-rgt-neg-in`
10×	`add-log-exp`
9×	`add-cbrt-cube`
7×	`div-exp`
6×	`pow1`
5×	`div-inv`
3×	`cbrt-undiv` `flip3--` `diff-log` `flip--` `associate-/l*`
2×	`sub-neg` `rec-exp` `sqrt-div` `1-exp`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `clear-num` `associate-/r/` `inv-pow`

Counts

4 → 169

Calls

4 calls:

14.0ms	(/ 1 (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
3.0ms	(- (* b_2 b_2) (* a c))
8.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series65.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(/ 1 (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
7.0ms	(- (* b_2 b_2) (* a c))
13.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify73.0ms

Algorithm

egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	618	2273
1	2704	2086
2	5001	1951

prune95.0ms

Filtered

80 candidates to 181 candidates (-126.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	180	1	181
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	182	7	189

Merged error: 7.5b

Counts

189 → 7

regimes258.0ms

Accuracy

95.8% (1.0b remaining)

Error of 6.9b against oracle of 5.9b and baseline of 30.0b

bsearch153.0ms

Steps

Iters	Range	Point
8	4.6990622557082946e+114	3.0474584296678195e+118	7.682169507017298e+116
7	1.2005288392595164e-274	5.018607504575318e-273	1.6085559335864354e-274
9	-3.8655664909399325e+103	-5.1680927356807795e+98	-5.4890512934303715e+101

Iters

Range

Point

4.6990622557082946e+114

3.0474584296678195e+118

7.682169507017298e+116

1.2005288392595164e-274

5.018607504575318e-273

1.6085559335864354e-274

-3.8655664909399325e+103

-5.1680927356807795e+98

-5.4890512934303715e+101

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	23
1	44	23
2	44	23

end0.0ms

sample5.2s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 25.430298%

Guaranteed chance to sample good point: 74.712503%

Results

268.0ms	1084×	body	2560	valid
230.0ms	5118×	body	80	valid
179.0ms	890×	body	1280	valid
73.0ms	445×	body	640	valid
31.0ms	240×	body	320	valid
31.0ms	105×	body	5120	valid
24.0ms	588×	body	80	nan
10.0ms	118×	body	160	valid
7.0ms	168×	body	80	invalid

Details

sample4.2s

simplify399.0ms

prune5.0ms

localize12.0ms

rewrite32.0ms

series76.0ms

simplify143.0ms

prune148.0ms

localize15.0ms

rewrite52.0ms

series123.0ms

simplify110.0ms

prune235.0ms

localize12.0ms

rewrite98.0ms

series120.0ms

simplify105.0ms

prune311.0ms

localize13.0ms

rewrite38.0ms

series65.0ms

simplify73.0ms

prune95.0ms

regimes258.0ms

bsearch153.0ms

simplify2.0ms

end0.0ms

sample5.2s

Profiling