Details

analyze529.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
6.2%	93.6%	0.2%	8
25%	74.9%	0.2%	9
28.1%	71.7%	0.2%	10
29.6%	70.2%	0.2%	11
53%	46.8%	0.2%	12
71.3%	28.5%	0.2%	13
71.7%	28.1%	0.2%	14

sample22.0ms

Algorithm

intervals

Results

11.0ms	256×	body	80	valid
1.0ms	16×	body	80	invalid

simplify159.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (157.0ms)

Iter	Nodes	Cost
0	4841	15
1	4841	15

prune4.0ms

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: 24.8b

Counts

2 → 1

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.2b	(- (* b c) (* a d))
24.2b	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
7×	`add-log-exp`
5×	`add-exp-log` `add-cbrt-cube`
3×	`pow1` `associate-/r` `associate-/l`
2×	`flip3--` `flip3-+` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

3 → 54

Calls

3 calls:

4.0ms	(+ (* c c) (* d d))
4.0ms	(- (* b c) (* a d))
8.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

series43.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(+ (* c c) (* d d))
10.0ms	(- (* b c) (* a d))
27.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

simplify47.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5785	976

prune95.0ms

Filtered

49 candidates to 63 candidates (-28.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	57	6	63
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	58	6	64

Merged error: 19.4b

Counts

64 → 6

localize12.0ms

Local error

Found 4 expressions with local error:

6.5b	(/ b (+ (* c c) (* d d)))
7.1b	(/ a (+ (* c c) (* d d)))
8.5b	(* d (/ a (+ (* c c) (* d d))))
9.7b	(* c (/ b (+ (* c c) (* d d))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-sqr-sqrt`
38×	`times-frac`
36×	`add-cube-cbrt` `*-un-lft-identity`
30×	`associate-r`
18×	`add-exp-log` `add-cbrt-cube`
8×	`pow1` `associate-/r/`
6×	`associate-l` `associate-/r` `associate-/l`
4×	`cbrt-undiv` `flip3-+` `div-exp` `prod-exp` `cbrt-unprod` `flip-+` `div-inv` `add-log-exp` `unswap-sqr`
2×	`frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `-commutative`

Counts

4 → 126

Calls

4 calls:

5.0ms	(/ b (+ (* c c) (* d d)))
5.0ms	(/ a (+ (* c c) (* d d)))
9.0ms	(* d (/ a (+ (* c c) (* d d))))
9.0ms	(* c (/ b (+ (* c c) (* d d))))

series57.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(/ b (+ (* c c) (* d d)))
15.0ms	(/ a (+ (* c c) (* d d)))
13.0ms	(* d (/ a (+ (* c c) (* d d))))
15.0ms	(* c (/ b (+ (* c c) (* d d))))

simplify58.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5147	1682

prune158.0ms

Filtered

104 candidates to 138 candidates (-32.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	134	4	138
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	136	8	144

Merged error: 19.3b

Counts

144 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

7.1b	(/ a (+ (* c c) (* d d)))
8.5b	(* d (/ a (+ (* c c) (* d d))))
28.0b	(sqrt (+ (* c c) (* d d)))
28.0b	(sqrt (+ (* c c) (* d d)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
19×	`times-frac`
15×	`associate-r`
11×	`add-exp-log` `add-cbrt-cube`
8×	`pow1`
6×	`sqrt-prod`
4×	`flip3-+` `sqrt-div` `associate-/r/` `flip-+` `add-log-exp`
3×	`associate-l` `associate-/r` `associate-/l`
2×	`cbrt-undiv` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `-commutative`

Counts

4 → 93

Calls

4 calls:

5.0ms	(/ a (+ (* c c) (* d d)))
9.0ms	(* d (/ a (+ (* c c) (* d d))))
4.0ms	(sqrt (+ (* c c) (* d d)))
6.0ms	(sqrt (+ (* c c) (* d d)))

series39.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(/ a (+ (* c c) (* d d)))
13.0ms	(* d (/ a (+ (* c c) (* d d))))
6.0ms	(sqrt (+ (* c c) (* d d)))
6.0ms	(sqrt (+ (* c c) (* d d)))

simplify68.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4954	1169
1	4954	1169

prune119.0ms

Filtered

82 candidates to 105 candidates (-28.0%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	104	1	105
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	105	8	113

Merged error: 19.3b

Counts

113 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

6.5b	(/ b (+ (* c c) (* d d)))
9.7b	(* c (/ b (+ (* c c) (* d d))))
28.0b	(sqrt (+ (* c c) (* d d)))
28.0b	(sqrt (+ (* c c) (* d d)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
19×	`times-frac`
15×	`associate-r`
11×	`add-exp-log` `add-cbrt-cube`
8×	`pow1`
6×	`sqrt-prod`
4×	`flip3-+` `sqrt-div` `associate-/r/` `flip-+` `add-log-exp`
3×	`associate-l` `associate-/r` `associate-/l`
2×	`cbrt-undiv` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `-commutative`

Counts

4 → 93

Calls

4 calls:

5.0ms	(/ b (+ (* c c) (* d d)))
9.0ms	(* c (/ b (+ (* c c) (* d d))))
4.0ms	(sqrt (+ (* c c) (* d d)))
4.0ms	(sqrt (+ (* c c) (* d d)))

series38.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(/ b (+ (* c c) (* d d)))
12.0ms	(* c (/ b (+ (* c c) (* d d))))
6.0ms	(sqrt (+ (* c c) (* d d)))
6.0ms	(sqrt (+ (* c c) (* d d)))

simplify56.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5209	1169

prune95.0ms

Filtered

82 candidates to 105 candidates (-28.0%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	105	0	105
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	105	8	113

Merged error: 19.3b

Counts

113 → 8

regimes324.0ms

Accuracy

20.1% (2.6b remaining)

Error of 24.4b against oracle of 21.8b and baseline of 25.1b

bsearch39.0ms

Steps

Iters	Range		Point
11	2.872627748793113e-19	15435.245138455997	2.206658626264936e-10
7	-4.346316898740244e-112	-1.6826481347851376e-113	-3.4420726088017006e-112

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	93	75
1	93	75

end0.0ms

sample576.0ms

Algorithm

intervals

Results

352.0ms	8000×	body	80	valid
23.0ms	480×	body	80	invalid

Details

analyze529.0ms

sample22.0ms

simplify159.0ms

prune4.0ms

localize13.0ms

rewrite17.0ms

series43.0ms

simplify47.0ms

prune95.0ms

localize12.0ms

rewrite33.0ms

series57.0ms

simplify58.0ms

prune158.0ms

localize13.0ms

rewrite26.0ms

series39.0ms

simplify68.0ms

prune119.0ms

localize16.0ms

rewrite25.0ms

series38.0ms

simplify56.0ms

prune95.0ms

regimes324.0ms

bsearch39.0ms

simplify2.0ms

end0.0ms

sample576.0ms

Profiling