Details

analyze2.2s

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

sample55.0ms

Algorithm

intervals

Results

19.0ms	256×	body	80	valid
9.0ms	113×	body	80	nan
3.0ms	44×	body	80	invalid

simplify59.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5261	18

prune16.0ms

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: 13.1b

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)))))
2.6b	(/ (* M D) (* 2.0 d))
3.7b	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
11.1b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

67×	`add-exp-log`
35×	`add-sqr-sqrt`
27×	`prod-exp`
23×	`add-cbrt-cube`
19×	`div-exp` `associate-r`
17×	`add-cube-cbrt` `*-un-lft-identity`
14×	`times-frac`
12×	`associate-l`
10×	`pow-exp`
8×	`unswap-sqr`
7×	`pow1` `unpow-prod-down` `sqrt-prod` `cbrt-unprod`
5×	`cbrt-undiv`
4×	`sqrt-div` `add-log-exp`
3×	`associate-*r/` `div-inv` `sqr-pow`
2×	`pow-to-exp` `flip3--` `*-commutative` `flip--`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `clear-num` `associate-/r` `associate-/l`

Counts

4 → 113

Calls

4 calls:

6.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
9.0ms	(/ (* M D) (* 2.0 d))
2.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
11.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series556.0ms

Counts

4 → 12

Calls

4 calls:

183.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
6.0ms	(/ (* M D) (* 2.0 d))
151.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
216.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify32.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5176	1989

prune248.0ms

Filtered

85 candidates to 125 candidates (-47.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	117	8	125
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	118	9	127

Merged error: 6.3b

Counts

127 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

3.7b	(* (/ D d) (/ M 2.0))
3.7b	(sqrt (- 1.0 (/ (* h (pow (* (/ D d) (/ M 2.0)) 2.0)) l)))
4.2b	(* h (pow (* (/ D d) (/ M 2.0)) 2.0))
6.6b	(/ (* h (pow (* (/ D d) (/ M 2.0)) 2.0)) l)

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 120

Calls

4 calls:

11.0ms	(* (/ D d) (/ M 2.0))
4.0ms	(sqrt (- 1.0 (/ (* h (pow (* (/ D d) (/ M 2.0)) 2.0)) l)))
6.0ms	(* h (pow (* (/ D d) (/ M 2.0)) 2.0))
7.0ms	(/ (* h (pow (* (/ D d) (/ M 2.0)) 2.0)) l)

series388.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(* (/ D d) (/ M 2.0))
110.0ms	(sqrt (- 1.0 (/ (* h (pow (* (/ D d) (/ M 2.0)) 2.0)) l)))
97.0ms	(* h (pow (* (/ D d) (/ M 2.0)) 2.0))
174.0ms	(/ (* h (pow (* (/ D d) (/ M 2.0)) 2.0)) l)

simplify64.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4978	1742
1	4978	1742

prune235.0ms

Filtered

96 candidates to 132 candidates (-37.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	130	2	132
Fresh	3	4	7
Picked	1	0	1
Done	0	1	1
Total	134	7	141

Merged error: 5.8b

Counts

141 → 7

localize22.0ms

Local error

Found 4 expressions with local error:

3.7b	(* (/ D d) (/ M 2.0))
3.7b	(sqrt (- 1.0 (/ (* (* h (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2))) (pow (* (/ D d) (/ M 2.0)) (/ 2.0 2))) l)))
4.9b	(* h (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2)))
6.6b	(/ (* (* h (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2))) (pow (* (/ D d) (/ M 2.0)) (/ 2.0 2))) l)

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

361×	`add-exp-log`
180×	`prod-exp`
125×	`div-exp`
80×	`pow-exp`
41×	`add-sqr-sqrt`
27×	`add-cbrt-cube`
25×	`*-un-lft-identity` `times-frac`
23×	`add-cube-cbrt`
18×	`associate-r`
16×	`pow-to-exp` `associate-l`
8×	`cbrt-unprod`
7×	`pow1` `cbrt-undiv`
6×	`unswap-sqr`
5×	`sqrt-prod`
4×	`add-log-exp`
3×	`associate-/r*` `div-inv`
2×	`sqrt-div` `*-commutative` `sqr-pow`
1×	`frac-times` `unpow-prod-down` `rem-sqrt-square` `flip3--` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `flip--` `associate-/l*` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 170

Calls

4 calls:

11.0ms	(* (/ D d) (/ M 2.0))
5.0ms	(sqrt (- 1.0 (/ (* (* h (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2))) (pow (* (/ D d) (/ M 2.0)) (/ 2.0 2))) l)))
6.0ms	(* h (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2)))
13.0ms	(/ (* (* h (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2))) (pow (* (/ D d) (/ M 2.0)) (/ 2.0 2))) l)

series405.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(* (/ D d) (/ M 2.0))
125.0ms	(sqrt (- 1.0 (/ (* (* h (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2))) (pow (* (/ D d) (/ M 2.0)) (/ 2.0 2))) l)))
97.0ms	(* h (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2)))
178.0ms	(/ (* (* h (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2))) (pow (* (/ D d) (/ M 2.0)) (/ 2.0 2))) l)

simplify45.0ms

Algorithm

egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5226	2957

prune309.0ms

Filtered

96 candidates to 182 candidates (-89.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	179	3	182
Fresh	0	5	5
Picked	1	0	1
Done	1	0	1
Total	181	8	189

Merged error: 5.6b

Counts

189 → 8

localize23.0ms

Local error

Found 4 expressions with local error:

3.7b	(* (/ M 2.0) (/ D d))
3.7b	(* (/ M 2.0) (/ D d))
3.7b	(sqrt (- 1.0 (* (* (/ (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2)) (cbrt l)) (/ h (cbrt l))) (/ (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2)) (cbrt l)))))
6.3b	(* (/ (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2)) (cbrt l)) (/ h (cbrt l)))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

134×	`add-sqr-sqrt`
114×	`times-frac`
96×	`add-exp-log`
63×	`add-cube-cbrt` `*-un-lft-identity`
60×	`associate-l`
48×	`associate-r`
38×	`div-exp`
36×	`add-cbrt-cube`
35×	`cbrt-prod`
32×	`prod-exp`
23×	`unswap-sqr`
12×	`cbrt-undiv` `cbrt-unprod` `sqr-pow`
11×	`pow1`
10×	`pow-exp`
6×	`unpow-prod-down` `div-inv`
4×	`add-log-exp`
3×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/` `sqrt-prod` `*-commutative`
2×	`pow-to-exp` `sqrt-div`
1×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `flip--`

Counts

4 → 218

Calls

4 calls:

11.0ms	(* (/ M 2.0) (/ D d))
11.0ms	(* (/ M 2.0) (/ D d))
2.0ms	(sqrt (- 1.0 (* (* (/ (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2)) (cbrt l)) (/ h (cbrt l))) (/ (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2)) (cbrt l)))))
25.0ms	(* (/ (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2)) (cbrt l)) (/ h (cbrt l)))

series436.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(* (/ M 2.0) (/ D d))
6.0ms	(* (/ M 2.0) (/ D d))
159.0ms	(sqrt (- 1.0 (* (* (/ (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2)) (cbrt l)) (/ h (cbrt l))) (/ (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2)) (cbrt l)))))
266.0ms	(* (/ (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2)) (cbrt l)) (/ h (cbrt l)))

simplify53.0ms

Algorithm

egg-herbie

Counts

230 → 230

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5257	4096

prune560.0ms

Filtered

172 candidates to 230 candidates (-33.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	229	1	230
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	230	8	238

Merged error: 5.6b

Counts

238 → 8

regimes820.0ms

Accuracy

23.4% (1.7b remaining)

Error of 8.7b against oracle of 7.0b and baseline of 9.2b

bsearch3.0s

Steps

Iters	Range		Point
2	1.384640335353379e-163	1.6774437931652256e-163	1.4172298698894145e-163
6	-1.0043249162272177e-220	-1.7051474662594792e-221	-9.863874069977466e-221

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	66	115
1	66	115

end0.0ms

analyze2.2s

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

sample1.4s

Algorithm

intervals

Results

622.0ms	8000×	body	80	valid
240.0ms	3074×	body	80	nan
110.0ms	1337×	body	80	invalid

Details

analyze2.2s

sample55.0ms

simplify59.0ms

prune16.0ms

localize14.0ms

rewrite33.0ms

series556.0ms

simplify32.0ms

prune248.0ms

localize14.0ms

rewrite32.0ms

series388.0ms

simplify64.0ms

prune235.0ms

localize22.0ms

rewrite46.0ms

series405.0ms

simplify45.0ms

prune309.0ms

localize23.0ms

rewrite60.0ms

series436.0ms

simplify53.0ms

prune560.0ms

regimes820.0ms

bsearch3.0s

simplify2.0ms

end0.0ms

analyze2.2s

sample1.4s

Profiling