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

sample52.0ms

Algorithm

intervals

Results

19.0ms	256×	body	80	valid
8.0ms	99×	body	80	nan
4.0ms	54×	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

prune15.0ms

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: 16.1b

Counts

2 → 2

localize18.0ms

Local error

Found 4 expressions with local error:

2.4b	(* w0 (sqrt (- 1.0 (* (pow (* M (/ D (* 2.0 d))) 2.0) (/ h l)))))
5.4b	(* M (/ D (* 2.0 d)))
5.7b	(sqrt (- 1.0 (* (pow (* M (/ D (* 2.0 d))) 2.0) (/ h l))))
10.8b	(* (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)))
3.0ms	(sqrt (- 1.0 (* (pow (* M (/ D (* 2.0 d))) 2.0) (/ h l))))
8.0ms	(* (pow (* M (/ D (* 2.0 d))) 2.0) (/ h l))

series547.0ms

Counts

4 → 12

Calls

4 calls:

179.0ms	(* w0 (sqrt (- 1.0 (* (pow (* M (/ D (* 2.0 d))) 2.0) (/ h l)))))
7.0ms	(* M (/ D (* 2.0 d)))
147.0ms	(sqrt (- 1.0 (* (pow (* M (/ D (* 2.0 d))) 2.0) (/ h l))))
213.0ms	(* (pow (* M (/ D (* 2.0 d))) 2.0) (/ h l))

simplify34.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5600	1864

prune240.0ms

Filtered

82 candidates to 123 candidates (-50.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	115	8	123
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	117	8	125

Merged error: 9.4b

Counts

125 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

3.6b	(/ (* h (pow (* M (/ D (* 2.0 d))) 2.0)) l)
5.4b	(* M (/ D (* 2.0 d)))
5.7b	(sqrt (- 1.0 (/ (* h (pow (* M (/ D (* 2.0 d))) 2.0)) l)))
7.8b	(* h (pow (* M (/ D (* 2.0 d))) 2.0))

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:

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

series408.0ms

Counts

4 → 12

Calls

4 calls:

175.0ms	(/ (* h (pow (* M (/ D (* 2.0 d))) 2.0)) l)
6.0ms	(* M (/ D (* 2.0 d)))
129.0ms	(sqrt (- 1.0 (/ (* h (pow (* M (/ D (* 2.0 d))) 2.0)) l)))
97.0ms	(* h (pow (* M (/ D (* 2.0 d))) 2.0))

simplify31.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5084	1475

prune201.0ms

Filtered

73 candidates to 107 candidates (-46.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	105	2	107
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	108	7	115

Merged error: 8.9b

Counts

115 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

5.1b	(* h (pow (* M (/ D (* 2.0 d))) (/ 2.0 2)))
5.4b	(* M (/ D (* 2.0 d)))
5.4b	(* M (/ D (* 2.0 d)))
5.7b	(sqrt (- 1.0 (/ (* (* h (pow (* M (/ D (* 2.0 d))) (/ 2.0 2))) (pow (* M (/ D (* 2.0 d))) (/ 2.0 2))) l)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-exp-log`
24×	`add-cbrt-cube`
23×	`add-sqr-sqrt`
19×	`associate-r`
18×	`prod-exp`
15×	`*-un-lft-identity`
13×	`add-cube-cbrt`
9×	`pow1` `associate-l` `cbrt-unprod`
6×	`times-frac` `div-exp`
5×	`sqrt-prod`
4×	`cbrt-undiv` `pow-exp` `add-log-exp` `unswap-sqr`
3×	`*-commutative`
2×	`sqrt-div` `associate-*r/` `pow-prod-down` `div-inv` `sqr-pow`
1×	`pow-to-exp` `unpow-prod-down` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 96

Calls

4 calls:

8.0ms	(* h (pow (* M (/ D (* 2.0 d))) (/ 2.0 2)))
7.0ms	(* M (/ D (* 2.0 d)))
7.0ms	(* M (/ D (* 2.0 d)))
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)))

series232.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(* h (pow (* M (/ D (* 2.0 d))) (/ 2.0 2)))
6.0ms	(* M (/ D (* 2.0 d)))
6.0ms	(* M (/ D (* 2.0 d)))
126.0ms	(sqrt (- 1.0 (/ (* (* h (pow (* M (/ D (* 2.0 d))) (/ 2.0 2))) (pow (* M (/ D (* 2.0 d))) (/ 2.0 2))) l)))

simplify29.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5122	1382

prune230.0ms

Filtered

73 candidates to 108 candidates (-47.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	107	1	108
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	109	6	115

Merged error: 8.9b

Counts

115 → 6

localize20.0ms

Local error

Found 4 expressions with local error:

5.0b	(/ (* M D) (* 2.0 d))
5.1b	(* h (pow (* M (/ D (* 2.0 d))) (/ 2.0 2)))
5.4b	(* M (/ D (* 2.0 d)))
5.7b	(sqrt (- 1.0 (/ (* (* h (pow (* M (/ D (* 2.0 d))) (/ 2.0 2))) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) l)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 90

Calls

4 calls:

6.0ms	(/ (* M D) (* 2.0 d))
6.0ms	(* h (pow (* M (/ D (* 2.0 d))) (/ 2.0 2)))
7.0ms	(* M (/ D (* 2.0 d)))
12.0ms	(sqrt (- 1.0 (/ (* (* h (pow (* M (/ D (* 2.0 d))) (/ 2.0 2))) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) l)))

series238.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(/ (* M D) (* 2.0 d))
98.0ms	(* h (pow (* M (/ D (* 2.0 d))) (/ 2.0 2)))
6.0ms	(* M (/ D (* 2.0 d)))
128.0ms	(sqrt (- 1.0 (/ (* (* h (pow (* M (/ D (* 2.0 d))) (/ 2.0 2))) (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) l)))

simplify77.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	5140	1324

prune179.0ms

Filtered

68 candidates to 102 candidates (-50.0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	101	1	102
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	101	7	108

Merged error: 8.5b

Counts

108 → 7

regimes1.0s

Accuracy

35% (1.3b remaining)

Error of 8.4b against oracle of 7.1b and baseline of 9.1b

bsearch1.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	160	108
1	160	108

end0.0ms

sample1.5s

Algorithm

intervals

Results

635.0ms	8000×	body	80	valid
246.0ms	3057×	body	80	nan
110.0ms	1331×	body	80	invalid

Details

analyze2.4s

sample52.0ms

simplify42.0ms

prune15.0ms

localize18.0ms

rewrite29.0ms

series547.0ms

simplify34.0ms

prune240.0ms

localize14.0ms

rewrite27.0ms

series408.0ms

simplify31.0ms

prune201.0ms

localize16.0ms

rewrite32.0ms

series232.0ms

simplify29.0ms

prune230.0ms

localize20.0ms

rewrite33.0ms

series238.0ms

simplify77.0ms

prune179.0ms

regimes1.0s

bsearch1.0ms

simplify3.0ms

end0.0ms

sample1.5s

Profiling