Details

analyze446.0ms

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
21.8%	71.8%	6.4%	7
31.2%	62.4%	6.4%	8
35.9%	55.4%	8.7%	9
37.8%	48.8%	13.4%	10
42.7%	42.3%	15%	11
47.7%	34.2%	18.1%	12
49.1%	30.4%	20.5%	13
51.9%	25.8%	22.3%	14

sample41.0ms

Algorithm

intervals

Results

9.0ms	173×	body	80	valid
8.0ms	28×	body	2560	valid
7.0ms	28×	body	1280	valid
4.0ms	21×	body	640	valid
1.0ms	23×	body	80	nan
1.0ms	14×	body	80	invalid
1.0ms	2×	body	5120	valid
0.0ms	2×	body	320	valid
0.0ms	2×	body	160	valid

simplify206.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (204.0ms)

Iter	Nodes	Cost
0	1931	16
1	1931	16

prune10.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 33.6b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* a 2.0))
0.3b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
1.4b	(- (* b b) (* 4.0 (* a c)))
25.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
13×	`*-un-lft-identity`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
7×	`add-cube-cbrt`
6×	`times-frac` `sqrt-prod` `associate-/l*` `difference-of-squares`
5×	`pow1`
4×	`flip3--` `flip--`
3×	`distribute-lft-out--`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `diff-log` `div-exp` `associate-/l/`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 70

Calls

4 calls:

10.0ms	(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* a 2.0))
7.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
4.0ms	(- (* b b) (* 4.0 (* a c)))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series62.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* a 2.0))
16.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
8.0ms	(- (* b b) (* 4.0 (* a c)))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify38.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5340	1316

prune158.0ms

Filtered

62 candidates to 82 candidates (-32.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	73	9	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	74	9	83

Merged error: 5.5b

Counts

83 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (* (/ a (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) 2.0))
0.3b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
1.4b	(- (* b b) (* 4.0 (* a c)))
25.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-exp-log`
13×	`add-cbrt-cube`
12×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `div-exp`
8×	`pow1` `add-log-exp`
7×	`add-cube-cbrt`
6×	`prod-exp`
4×	`cbrt-undiv` `sqrt-prod`
3×	`rec-exp` `flip3--` `times-frac` `1-exp` `flip--` `associate-/l*`
2×	`sub-neg` `pow-flip` `sqrt-div` `diff-log` `cbrt-unprod` `difference-of-squares`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `associate-l/` `clear-num` `associate-/r` `associate-/r/` `div-inv` `distribute-lft-out--` `inv-pow`

Counts

4 → 73

Calls

4 calls:

12.0ms	(/ 1 (* (/ a (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) 2.0))
7.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
4.0ms	(- (* b b) (* 4.0 (* a c)))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series71.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(/ 1 (* (/ a (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) 2.0))
14.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
10.0ms	(- (* b b) (* 4.0 (* a c)))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify37.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	4995	1244
1	4995	1244

prune121.0ms

Filtered

57 candidates to 85 candidates (-49.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	83	2	85
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	84	10	94

Merged error: 5.4b

Counts

94 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (* b b) (* 4.0 (* a c)))
1.4b	(- (* b b) (* 4.0 (* a c)))
25.1b	(sqrt (- (* b b) (* 4.0 (* a c))))
25.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 52

Calls

4 calls:

4.0ms	(- (* b b) (* 4.0 (* a c)))
4.0ms	(- (* b b) (* 4.0 (* a c)))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series44.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(- (* b b) (* 4.0 (* a c)))
8.0ms	(- (* b b) (* 4.0 (* a c)))
13.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify35.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5246	824

prune170.0ms

Filtered

50 candidates to 64 candidates (-28.0%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	62	2	64
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	63	11	74

Merged error: 5.4b

Counts

74 → 11

localize23.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (* b b) (* 4.0 (* a c)))
25.1b	(sqrt (- (* b b) (* 4.0 (* a c))))
25.1b	(sqrt (- (* b b) (* 4.0 (* a c))))
25.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite17.0ms

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 → 56

Calls

4 calls:

4.0ms	(- (* b b) (* 4.0 (* a c)))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series49.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(- (* b b) (* 4.0 (* a c)))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
13.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify35.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5246	878

prune181.0ms

Filtered

55 candidates to 68 candidates (-23.6%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	68	0	68
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	68	11	79

Merged error: 5.4b

Counts

79 → 11

regimes328.0ms

Accuracy

82.3% (5.0b remaining)

Error of 11.0b against oracle of 5.9b and baseline of 34.4b

bsearch68.0ms

Steps

Iters	Range		Point
11	2.5768488364311154e-56	1.4507623154081424e-34	6.933902366594144e-45
10	-5.918052934994761e+78	-3.0446503434624485e+67	-2.655941584775036e+72

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	92	40
1	92	40

end0.0ms

sample1.2s

Algorithm

intervals

Results

322.0ms	1100×	body	2560	valid
273.0ms	5122×	body	80	valid
220.0ms	900×	body	1280	valid
91.0ms	475×	body	640	valid
37.0ms	97×	body	5120	valid
34.0ms	683×	body	80	nan
30.0ms	208×	body	320	valid
21.0ms	402×	body	80	invalid
11.0ms	98×	body	160	valid

Details

analyze446.0ms

sample41.0ms

simplify206.0ms

prune10.0ms

localize11.0ms

rewrite27.0ms

series62.0ms

simplify38.0ms

prune158.0ms

localize12.0ms

rewrite29.0ms

series71.0ms

simplify37.0ms

prune121.0ms

localize15.0ms

rewrite17.0ms

series44.0ms

simplify35.0ms

prune170.0ms

localize23.0ms

rewrite17.0ms

series49.0ms

simplify35.0ms

prune181.0ms

regimes328.0ms

bsearch68.0ms

simplify2.0ms

end0.0ms

sample1.2s

Profiling