Details

analyze2.4s

Algorithm

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	99.7%	0.3%	7
0%	99.7%	0.3%	8
0%	99.7%	0.3%	9
0%	99.7%	0.3%	10
0%	99.7%	0.3%	11
0%	99.7%	0.3%	12
5.1%	94.6%	0.3%	13
7%	92.7%	0.3%	14

sample50.0ms

Algorithm

intervals

Results

19.0ms	256×	body	80	valid
8.0ms	104×	body	80	nan
4.0ms	45×	body	80	invalid

simplify42.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4904	18
1	4904	18

prune20.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 14.6b

Counts

2 → 2

localize14.0ms

Local error

Found 4 expressions with local error:

1.5b	(* w0 (sqrt (- 1.0 (* (pow (* M (/ D (* 2.0 d))) 2.0) (/ h l)))))
4.8b	(* M (/ D (* 2.0 d)))
5.9b	(sqrt (- 1.0 (* (pow (* M (/ D (* 2.0 d))) 2.0) (/ h l))))
10.4b	(* (pow (* M (/ D (* 2.0 d))) 2.0) (/ h l))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-exp-log`
34×	`add-sqr-sqrt`
26×	`associate-r`
25×	`prod-exp`
20×	`add-cbrt-cube`
19×	`add-cube-cbrt` `*-un-lft-identity`
14×	`times-frac`
12×	`div-exp`
11×	`associate-l`
9×	`pow1`
8×	`pow-exp`
7×	`sqrt-prod` `cbrt-unprod` `unswap-sqr`
4×	`sqrt-div` `associate-*r/` `add-log-exp`
3×	`cbrt-undiv` `*-commutative` `sqr-pow`
2×	`pow-to-exp` `flip3--` `pow-prod-down` `flip--` `div-inv`
1×	`unpow-prod-down` `rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 111

Calls

4 calls:

7.0ms	(* w0 (sqrt (- 1.0 (* (pow (* M (/ D (* 2.0 d))) 2.0) (/ h l)))))
7.0ms	(* M (/ D (* 2.0 d)))
4.0ms	(sqrt (- 1.0 (* (pow (* M (/ D (* 2.0 d))) 2.0) (/ h l))))
9.0ms	(* (pow (* M (/ D (* 2.0 d))) 2.0) (/ h l))

series545.0ms

Counts

4 → 12

Calls

4 calls:

181.0ms	(* w0 (sqrt (- 1.0 (* (pow (* M (/ D (* 2.0 d))) 2.0) (/ h l)))))
6.0ms	(* M (/ D (* 2.0 d)))
148.0ms	(sqrt (- 1.0 (* (pow (* M (/ D (* 2.0 d))) 2.0) (/ h l))))
210.0ms	(* (pow (* M (/ D (* 2.0 d))) 2.0) (/ h l))

simplify37.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5600	1864

prune264.0ms

Filtered

82 candidates to 123 candidates (-50.0%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	114	9	123
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	116	9	125

Merged error: 8.2b

Counts

125 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

4.1b	(* h (pow (* M (/ D (* 2.0 d))) 2.0))
4.8b	(* M (/ D (* 2.0 d)))
5.7b	(/ (* h (pow (* M (/ D (* 2.0 d))) 2.0)) l)
5.9b	(sqrt (- 1.0 (/ (* h (pow (* M (/ D (* 2.0 d))) 2.0)) l)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-exp-log`
24×	`prod-exp`
20×	`add-sqr-sqrt` `add-cbrt-cube`
14×	`*-un-lft-identity`
13×	`div-exp`
12×	`add-cube-cbrt` `associate-r`
8×	`pow-exp`
7×	`pow1`
6×	`times-frac` `associate-l` `cbrt-unprod`
5×	`sqrt-prod`
4×	`cbrt-undiv` `add-log-exp`
3×	`associate-/r*` `unswap-sqr`
2×	`pow-to-exp` `sqrt-div` `*-commutative` `div-inv` `sqr-pow`
1×	`unpow-prod-down` `rem-sqrt-square` `flip3--` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `clear-num` `flip--` `associate-/l` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 95

Calls

4 calls:

5.0ms	(* h (pow (* M (/ D (* 2.0 d))) 2.0))
7.0ms	(* M (/ D (* 2.0 d)))
6.0ms	(/ (* h (pow (* M (/ D (* 2.0 d))) 2.0)) l)
6.0ms	(sqrt (- 1.0 (/ (* h (pow (* M (/ D (* 2.0 d))) 2.0)) l)))

series401.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(* h (pow (* M (/ D (* 2.0 d))) 2.0))
6.0ms	(* M (/ D (* 2.0 d)))
181.0ms	(/ (* h (pow (* M (/ D (* 2.0 d))) 2.0)) l)
121.0ms	(sqrt (- 1.0 (/ (* h (pow (* M (/ D (* 2.0 d))) 2.0)) l)))

simplify29.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5084	1475

prune203.0ms

Filtered

73 candidates to 107 candidates (-46.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	105	2	107
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	108	8	116

Merged error: 8.0b

Counts

116 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

4.8b	(* M (/ D (* 2.0 d)))
5.7b	(/ (* (* h (pow (* M (/ D (* 2.0 d))) (/ 2.0 2))) (pow (* M (/ D (* 2.0 d))) (/ 2.0 2))) l)
5.9b	(sqrt (- 1.0 (/ (* (* h (pow (* M (/ D (* 2.0 d))) (/ 2.0 2))) (pow (* M (/ D (* 2.0 d))) (/ 2.0 2))) l)))
6.0b	(* h (pow (* M (/ D (* 2.0 d))) (/ 2.0 2)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

259×	`add-exp-log`
144×	`prod-exp`
73×	`div-exp`
56×	`pow-exp`
24×	`add-cbrt-cube`
20×	`add-sqr-sqrt`
14×	`pow-to-exp` `*-un-lft-identity`
12×	`add-cube-cbrt` `associate-r`
8×	`cbrt-unprod`
7×	`pow1`
6×	`times-frac` `associate-l`
5×	`cbrt-undiv` `sqrt-prod`
4×	`add-log-exp`
3×	`associate-/r*` `unswap-sqr`
2×	`sqrt-div` `*-commutative` `div-inv` `sqr-pow`
1×	`unpow-prod-down` `rem-sqrt-square` `flip3--` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `clear-num` `flip--` `associate-/l` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 132

Calls

4 calls:

7.0ms	(* M (/ D (* 2.0 d)))
11.0ms	(/ (* (* h (pow (* M (/ D (* 2.0 d))) (/ 2.0 2))) (pow (* M (/ D (* 2.0 d))) (/ 2.0 2))) l)
8.0ms	(sqrt (- 1.0 (/ (* (* h (pow (* M (/ D (* 2.0 d))) (/ 2.0 2))) (pow (* M (/ D (* 2.0 d))) (/ 2.0 2))) l)))
6.0ms	(* h (pow (* M (/ D (* 2.0 d))) (/ 2.0 2)))

series389.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(* M (/ D (* 2.0 d)))
166.0ms	(/ (* (* h (pow (* M (/ D (* 2.0 d))) (/ 2.0 2))) (pow (* M (/ D (* 2.0 d))) (/ 2.0 2))) l)
122.0ms	(sqrt (- 1.0 (/ (* (* h (pow (* M (/ D (* 2.0 d))) (/ 2.0 2))) (pow (* M (/ D (* 2.0 d))) (/ 2.0 2))) l)))
94.0ms	(* h (pow (* M (/ D (* 2.0 d))) (/ 2.0 2)))

simplify40.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5282	2404

prune234.0ms

Filtered

74 candidates to 144 candidates (-94.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	142	2	144
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	146	6	152

Merged error: 7.7b

Counts

152 → 6

localize18.0ms

Local error

Found 4 expressions with local error:

4.8b	(* M (/ D (* 2.0 d)))
5.9b	(sqrt (- 1.0 (/ (* h (pow (* M (/ D (* 2.0 d))) (/ 2.0 2))) (/ l (pow (* M (/ D (* 2.0 d))) (/ 2.0 2))))))
6.0b	(* h (pow (* M (/ D (* 2.0 d))) (/ 2.0 2)))
6.2b	(/ l (pow (* M (/ D (* 2.0 d))) (/ 2.0 2)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-exp-log`
28×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
20×	`add-cube-cbrt`
18×	`times-frac` `prod-exp`
17×	`add-cbrt-cube`
12×	`div-exp` `associate-r`
8×	`pow-exp`
7×	`pow1`
6×	`associate-l` `sqr-pow`
5×	`unpow-prod-down` `associate-/r*` `sqrt-prod` `cbrt-unprod`
4×	`add-log-exp`
3×	`cbrt-undiv` `associate-/l*` `unswap-sqr`
2×	`pow-to-exp` `sqrt-div` `*-commutative` `div-inv`
1×	`rem-sqrt-square` `flip3--` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-*r/` `pow-prod-down` `clear-num` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 109

Calls

4 calls:

7.0ms	(* M (/ D (* 2.0 d)))
13.0ms	(sqrt (- 1.0 (/ (* h (pow (* M (/ D (* 2.0 d))) (/ 2.0 2))) (/ l (pow (* M (/ D (* 2.0 d))) (/ 2.0 2))))))
6.0ms	(* h (pow (* M (/ D (* 2.0 d))) (/ 2.0 2)))
5.0ms	(/ l (pow (* M (/ D (* 2.0 d))) (/ 2.0 2)))

series326.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(* M (/ D (* 2.0 d)))
123.0ms	(sqrt (- 1.0 (/ (* h (pow (* M (/ D (* 2.0 d))) (/ 2.0 2))) (/ l (pow (* M (/ D (* 2.0 d))) (/ 2.0 2))))))
94.0ms	(* h (pow (* M (/ D (* 2.0 d))) (/ 2.0 2)))
102.0ms	(/ l (pow (* M (/ D (* 2.0 d))) (/ 2.0 2)))

simplify55.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4974	1979
1	4974	1979

prune244.0ms

Filtered

88 candidates to 121 candidates (-37.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	121	0	121
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	121	6	127

Merged error: 7.7b

Counts

127 → 6

regimes866.0ms

Accuracy

0% (1.1b remaining)

Error of 8.4b against oracle of 7.3b and baseline of 8.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	57	32
1	57	32

end0.0ms

sample1.5s

Algorithm

intervals

Results

641.0ms	8000×	body	80	valid
277.0ms	3199×	body	80	nan
118.0ms	1402×	body	80	invalid

Details

analyze2.4s

sample50.0ms

simplify42.0ms

prune20.0ms

localize14.0ms

rewrite29.0ms

series545.0ms

simplify37.0ms

prune264.0ms

localize14.0ms

rewrite27.0ms

series401.0ms

simplify29.0ms

prune203.0ms

localize16.0ms

rewrite39.0ms

series389.0ms

simplify40.0ms

prune234.0ms

localize18.0ms

rewrite35.0ms

series326.0ms

simplify55.0ms

prune244.0ms

regimes866.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.5s

Profiling