Details

sample264.0ms

Algorithm

intervals

Results

205.0ms	187×	body	80	valid
10.0ms	39×	body	2560	valid
6.0ms	27×	body	1280	valid
4.0ms	90×	body	80	nan
2.0ms	10×	body	640	valid
1.0ms	9×	body	320	valid
0.0ms	3×	body	160	valid

simplify387.0ms

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: 32.1b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.8b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.2b	(- (* b_2 b_2) (* a c))
22.8b	(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)
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)))

series67.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
22.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
7.0ms	(- (* b_2 b_2) (* a c))
21.0ms	(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

prune148.0ms

Filtered

72 candidates to 103 candidates (-43.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	93	10	103
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	94	10	104

Merged error: 4.3b

Counts

104 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- (* b_2 b_2) (* a c))) a)
1.2b	(- (* b_2 b_2) (* a c))
7.5b	(- (/ (neg b_2) a) (/ (sqrt (- (* b_2 b_2) (* a c))) a))
22.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
38×	`*-un-lft-identity`
37×	`times-frac`
24×	`add-cube-cbrt`
17×	`sqrt-prod`
8×	`add-log-exp`
7×	`distribute-lft-out--`
6×	`add-exp-log` `add-cbrt-cube` `associate-/l*` `difference-of-squares`
5×	`pow1`
4×	`flip3--` `sqrt-div` `flip--`
3×	`distribute-rgt-neg-in` `associate-/r*` `div-inv`
2×	`sub-neg` `diff-log` `associate-/l/`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `rem-sqrt-square` `distribute-rgt-out--` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `clear-num` `frac-sub` `sub-div`

Counts

4 → 97

Calls

4 calls:

6.0ms	(/ (sqrt (- (* b_2 b_2) (* a c))) a)
3.0ms	(- (* b_2 b_2) (* a c))
35.0ms	(- (/ (neg b_2) a) (/ (sqrt (- (* b_2 b_2) (* a c))) a))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series68.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(/ (sqrt (- (* b_2 b_2) (* a c))) a)
7.0ms	(- (* b_2 b_2) (* a c))
17.0ms	(- (/ (neg b_2) a) (/ (sqrt (- (* b_2 b_2) (* a c))) a))
15.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify147.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	388	1005
1	1221	965
2	4837	951
3	5001	951

prune118.0ms

Filtered

79 candidates to 109 candidates (-38.0%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	109	0	109
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	109	10	119

Merged error: 4.3b

Counts

119 → 10

localize10.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
0.8b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.2b	(- (* b_2 b_2) (* a c))
22.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite34.0ms

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:

15.0ms	(* (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
10.0ms	(- (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))
14.0ms	(- (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)))

simplify53.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (42.0ms)

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

prune108.0ms

Filtered

71 candidates to 101 candidates (-42.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	100	1	101
Fresh	3	5	8
Picked	0	1	1
Done	0	1	1
Total	103	8	111

Merged error: 4.3b

Counts

111 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b_2 b_2) (* a c))
22.8b	(sqrt (- (* b_2 b_2) (* a c)))
22.8b	(sqrt (- (* b_2 b_2) (* a c)))
22.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-div` `add-log-exp`
4×	`add-exp-log` `flip3--` `add-cbrt-cube` `flip--`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`sub-neg` `diff-log`

Counts

4 → 57

Calls

4 calls:

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

series44.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (* 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)))

simplify52.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 3 (46.0ms)

Iter	Nodes	Cost
0	138	420
1	451	403
2	1533	400
3	5001	397

prune77.0ms

Filtered

55 candidates to 69 candidates (-25.5%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	69	0	69
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	69	8	77

Merged error: 4.3b

Counts

77 → 8

regimes299.0ms

Accuracy

84.5% (4.4b remaining)

Error of 9.9b against oracle of 5.5b and baseline of 34.1b

bsearch60.0ms

Steps

Iters	Range		Point
9	1.8477877744450244e+138	2.968449638874272e+144	1.8778214273286598e+138
8	-3.448821841393933e-48	-1.783175304196574e-52	-2.755594647721125e-52

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	15
1	31	15

end0.0ms

sample1.3s

Algorithm

intervals

Results

269.0ms	1058×	body	2560	valid
258.0ms	5854×	body	80	valid
181.0ms	882×	body	1280	valid
116.0ms	2753×	body	80	nan
72.0ms	446×	body	640	valid
35.0ms	111×	body	5120	valid
28.0ms	230×	body	320	valid
10.0ms	128×	body	160	valid

Details

sample264.0ms

simplify387.0ms

prune5.0ms

localize11.0ms

rewrite32.0ms

series67.0ms

simplify42.0ms

prune148.0ms

localize13.0ms

rewrite51.0ms

series68.0ms

simplify147.0ms

prune118.0ms

localize10.0ms

rewrite34.0ms

series51.0ms

simplify53.0ms

prune108.0ms

localize17.0ms

rewrite16.0ms

series44.0ms

simplify52.0ms

prune77.0ms

regimes299.0ms

bsearch60.0ms

simplify2.0ms

end0.0ms

sample1.3s

Profiling