Details

analyze596.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
12.5%	87.4%	0.1%	5
18.7%	81.1%	0.1%	6
18.7%	76.5%	4.8%	7
28.1%	66.3%	5.6%	8
35.1%	55%	9.9%	9
36.3%	50.9%	12.8%	10
42.1%	42.4%	15.5%	11
47.5%	33.8%	18.7%	12
48.8%	30.7%	20.6%	13
51.8%	25.6%	22.5%	14

sample40.0ms

Algorithm

intervals

Results

11.0ms	38×	body	2560	valid
8.0ms	172×	body	80	valid
5.0ms	22×	body	1280	valid
2.0ms	12×	body	640	valid
1.0ms	9×	body	320	valid
1.0ms	21×	body	80	nan
1.0ms	2×	body	5120	valid
0.0ms	8×	body	80	invalid
0.0ms	1×	body	160	valid

simplify398.0ms

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: 31.5b

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)
0.6b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
0.6b	(- (* b_2 b_2) (* a c))
20.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite30.0ms

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

series73.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
13.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
7.0ms	(- (* b_2 b_2) (* a c))
36.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify42.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (32.0ms)

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

prune141.0ms

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

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
0.6b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
0.6b	(- (* b_2 b_2) (* a c))
20.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
13×	`add-exp-log` `add-cube-cbrt` `associate-r`
11×	`times-frac`
10×	`add-log-exp`
9×	`add-cbrt-cube`
7×	`pow1` `associate-l`
5×	`flip3--` `sqrt-prod` `flip--`
4×	`prod-exp` `distribute-lft-out--` `difference-of-squares`
3×	`diff-log` `unswap-sqr`
2×	`frac-times` `sub-neg` `distribute-rgt-neg-in` `sqrt-div` `div-exp` `associate-*l/` `cbrt-unprod`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `associate-r/` `pow-prod-down` `neg-log` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 89

Calls

4 calls:

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

series51.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(* (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
15.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
7.0ms	(- (* b_2 b_2) (* a c))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify50.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	420	880
1	1816	791
2	5002	772

prune115.0ms

Filtered

71 candidates to 101 candidates (-42.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	101	0	101
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	101	9	110

Merged error: 5.2b

Counts

110 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))))
0.6b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
0.6b	(- (* b_2 b_2) (* a c))
20.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

165×	`times-frac`
130×	`add-sqr-sqrt`
129×	`*-un-lft-identity`
77×	`add-cube-cbrt`
27×	`associate-/r*`
26×	`distribute-lft-out--` `difference-of-squares`
16×	`sqrt-prod`
15×	`add-exp-log`
13×	`distribute-rgt-neg-in`
10×	`add-log-exp`
9×	`associate-/r/` `add-cbrt-cube`
7×	`flip3--` `div-exp` `flip--`
6×	`pow1`
5×	`div-inv`
3×	`cbrt-undiv` `diff-log` `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` `inv-pow`

Counts

4 → 177

Calls

4 calls:

13.0ms	(/ 1 (/ a (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))))
8.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.0ms	(- (* b_2 b_2) (* a c))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series65.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(/ 1 (/ a (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))))
13.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
7.0ms	(- (* b_2 b_2) (* a c))
16.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify74.0ms

Algorithm

egg-herbie

Counts

189 → 189

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	587	2454
1	2706	2223
2	5001	2068

prune121.0ms

Filtered

87 candidates to 189 candidates (-117.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	188	1	189
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	189	9	198

Merged error: 5.1b

Counts

198 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt a)
0.6b	(cbrt a)
0.6b	(cbrt a)
20.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
5×	`pow1`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`pow1/3` `sqrt-prod`
2×	`sqrt-div`
1×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `flip--`

Counts

4 → 48

Calls

4 calls:

1.0ms	(cbrt a)
1.0ms	(cbrt a)
1.0ms	(cbrt a)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series80.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(cbrt a)
21.0ms	(cbrt a)
23.0ms	(cbrt a)
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify48.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 3 (44.0ms)

Iter	Nodes	Cost
0	175	266
1	498	251
2	1529	220
3	5002	216

prune56.0ms

Filtered

48 candidates to 60 candidates (-25.0%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	59	1	60
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	59	10	69

Merged error: 5.1b

Counts

69 → 10

regimes404.0ms

Accuracy

87.8% (3.5b remaining)

Error of 9.1b against oracle of 5.6b and baseline of 34.1b

bsearch633.0ms

Steps

Iters	Range	Point
10	5.062418134828583e+119	2.5207468392485318e+137	1.332818306264271e+120
9	-6.234410346416956e-134	-1.820693896833703e-143	-2.9778949532193474e-139
5	-2.4670159271123566e+95	-7.925003913201869e+94	-9.137429639253266e+94

Iters

Range

Point

5.062418134828583e+119

2.5207468392485318e+137

1.332818306264271e+120

-6.234410346416956e-134

-1.820693896833703e-143

-2.9778949532193474e-139

-2.4670159271123566e+95

-7.925003913201869e+94

-9.137429639253266e+94

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	24
1	42	24
2	42	24

end0.0ms

analyze396.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
12.5%	87.4%	0.1%	5
18.7%	81.1%	0.1%	6
18.7%	76.5%	4.8%	7
28.1%	66.3%	5.6%	8
35.1%	55%	9.9%	9
36.3%	50.9%	12.8%	10
42.1%	42.4%	15.5%	11
47.5%	33.8%	18.7%	12
48.8%	30.7%	20.6%	13
51.8%	25.6%	22.5%	14

sample1.1s

Algorithm

intervals

Results

269.0ms	1072×	body	2560	valid
226.0ms	5129×	body	80	valid
183.0ms	896×	body	1280	valid
72.0ms	454×	body	640	valid
38.0ms	121×	body	5120	valid
33.0ms	756×	body	80	nan
28.0ms	221×	body	320	valid
10.0ms	232×	body	80	invalid
9.0ms	107×	body	160	valid

Details

analyze596.0ms

sample40.0ms

simplify398.0ms

prune5.0ms

localize12.0ms

rewrite30.0ms

series73.0ms

simplify42.0ms

prune141.0ms

localize10.0ms

rewrite31.0ms

series51.0ms

simplify50.0ms

prune115.0ms

localize11.0ms

rewrite37.0ms

series65.0ms

simplify74.0ms

prune121.0ms

localize15.0ms

rewrite8.0ms

series80.0ms

simplify48.0ms

prune56.0ms

regimes404.0ms

bsearch633.0ms

simplify2.0ms

end0.0ms

analyze396.0ms

sample1.1s

Profiling