Details

analyze2.5s

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	100×	body	80	nan
3.0ms	39×	body	80	invalid

simplify44.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (42.0ms)

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: 13.3b

Counts

2 → 2

localize14.0ms

Local error

Found 4 expressions with local error:

2.6b	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
4.0b	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
6.4b	(/ (* M D) (* 2.0 d))
10.5b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite30.0ms

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:

7.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
4.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
6.0ms	(/ (* M D) (* 2.0 d))
10.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series562.0ms

Counts

4 → 12

Calls

4 calls:

186.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
152.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
6.0ms	(/ (* M D) (* 2.0 d))
218.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify33.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5373	1965

prune246.0ms

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: 8.4b

Counts

127 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

4.0b	(sqrt (- 1.0 (/ (* h (pow (* (/ D d) (/ M 2.0)) 2.0)) l)))
4.2b	(/ (* h (pow (* (/ D d) (/ M 2.0)) 2.0)) l)
6.2b	(* h (pow (* (/ D d) (/ M 2.0)) 2.0))
6.7b	(* (/ D d) (/ M 2.0))

rewrite34.0ms

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:

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

series388.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify36.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5304	1740

prune245.0ms

Filtered

93 candidates to 132 candidates (-41.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	131	1	132
Fresh	0	7	7
Picked	1	0	1
Done	0	1	1
Total	132	9	141

Merged error: 7.7b

Counts

141 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

4.0b	(sqrt (- 1.0 (/ (* (* h (pow (* (/ D d) (/ M 2.0)) (/ 2.0 2))) (pow (* (/ D d) (/ M 2.0)) (/ 2.0 2))) l)))
4.2b	(/ (* (* h (pow (* (/ D d) (/ M 2.0)) (/ 2.0 2))) (pow (* (/ D d) (/ M 2.0)) (/ 2.0 2))) l)
6.7b	(* (/ D d) (/ M 2.0))
6.7b	(* (/ D d) (/ M 2.0))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

352×	`add-exp-log`
173×	`prod-exp`
125×	`div-exp`
75×	`pow-exp`
62×	`add-sqr-sqrt`
47×	`times-frac`
37×	`*-un-lft-identity` `add-cbrt-cube`
35×	`add-cube-cbrt`
26×	`associate-r` `associate-l`
15×	`pow-to-exp`
11×	`cbrt-undiv` `cbrt-unprod`
9×	`pow1`
8×	`unswap-sqr`
5×	`sqrt-prod` `div-inv`
4×	`add-log-exp`
3×	`associate-/r*`
2×	`frac-times` `sqrt-div` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative`
1×	`rem-sqrt-square` `flip3--` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `flip--` `associate-/l*` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 194

Calls

4 calls:

9.0ms	(sqrt (- 1.0 (/ (* (* h (pow (* (/ D d) (/ M 2.0)) (/ 2.0 2))) (pow (* (/ D d) (/ M 2.0)) (/ 2.0 2))) l)))
14.0ms	(/ (* (* h (pow (* (/ D d) (/ M 2.0)) (/ 2.0 2))) (pow (* (/ D d) (/ M 2.0)) (/ 2.0 2))) l)
10.0ms	(* (/ D d) (/ M 2.0))
10.0ms	(* (/ D d) (/ M 2.0))

series300.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(sqrt (- 1.0 (/ (* (* h (pow (* (/ D d) (/ M 2.0)) (/ 2.0 2))) (pow (* (/ D d) (/ M 2.0)) (/ 2.0 2))) l)))
177.0ms	(/ (* (* h (pow (* (/ D d) (/ M 2.0)) (/ 2.0 2))) (pow (* (/ D d) (/ M 2.0)) (/ 2.0 2))) l)
6.0ms	(* (/ D d) (/ M 2.0))
6.0ms	(* (/ D d) (/ M 2.0))

simplify80.0ms

Algorithm

egg-herbie

Counts

206 → 206

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4982	2916
1	4982	2916

prune345.0ms

Filtered

114 candidates to 206 candidates (-80.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	204	2	206
Fresh	1	6	7
Picked	1	0	1
Done	0	1	1
Total	206	9	215

Merged error: 7.5b

Counts

215 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

4.0b	(sqrt (- 1.0 (* (* h (pow (* (/ D d) (/ M 2.0)) (/ 2.0 2))) (/ (pow (* (/ D d) (/ M 2.0)) (/ 2.0 2)) l))))
5.4b	(/ (pow (* (/ D d) (/ M 2.0)) (/ 2.0 2)) l)
6.7b	(* (/ D d) (/ M 2.0))
6.7b	(* (/ D d) (/ M 2.0))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

68×	`add-sqr-sqrt`
59×	`times-frac`
49×	`add-exp-log`
43×	`add-cube-cbrt` `*-un-lft-identity`
30×	`add-cbrt-cube`
26×	`associate-r` `associate-l`
19×	`div-exp`
12×	`prod-exp`
9×	`pow1` `cbrt-undiv`
8×	`cbrt-unprod` `unswap-sqr`
5×	`pow-exp` `div-inv` `associate-/l*`
4×	`unpow-prod-down` `add-log-exp` `sqr-pow`
3×	`associate-/r*` `sqrt-prod`
2×	`frac-times` `sqrt-div` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative`
1×	`pow-to-exp` `rem-sqrt-square` `flip3--` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `flip--`

Counts

4 → 156

Calls

4 calls:

6.0ms	(sqrt (- 1.0 (* (* h (pow (* (/ D d) (/ M 2.0)) (/ 2.0 2))) (/ (pow (* (/ D d) (/ M 2.0)) (/ 2.0 2)) l))))
7.0ms	(/ (pow (* (/ D d) (/ M 2.0)) (/ 2.0 2)) l)
10.0ms	(* (/ D d) (/ M 2.0))
10.0ms	(* (/ D d) (/ M 2.0))

series306.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(sqrt (- 1.0 (* (* h (pow (* (/ D d) (/ M 2.0)) (/ 2.0 2))) (/ (pow (* (/ D d) (/ M 2.0)) (/ 2.0 2)) l))))
182.0ms	(/ (pow (* (/ D d) (/ M 2.0)) (/ 2.0 2)) l)
6.0ms	(* (/ D d) (/ M 2.0))
7.0ms	(* (/ D d) (/ M 2.0))

simplify63.0ms

Algorithm

egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4978	2211
1	4978	2211

prune347.0ms

Filtered

126 candidates to 168 candidates (-33.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	167	1	168
Fresh	3	4	7
Picked	0	1	1
Done	0	1	1
Total	170	7	177

Merged error: 7.5b

Counts

177 → 7

regimes2.1s

Accuracy

64.7% (0.5b remaining)

Error of 7.8b against oracle of 7.3b and baseline of 8.6b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	151	118
1	151	118

end0.0ms

sample1.5s

Algorithm

intervals

Results

627.0ms	8000×	body	80	valid
256.0ms	3174×	body	80	nan
114.0ms	1418×	body	80	invalid

Details

analyze2.5s

sample50.0ms

simplify44.0ms

prune20.0ms

localize14.0ms

rewrite30.0ms

series562.0ms

simplify33.0ms

prune246.0ms

localize14.0ms

rewrite34.0ms

series388.0ms

simplify36.0ms

prune245.0ms

localize16.0ms

rewrite55.0ms

series300.0ms

simplify80.0ms

prune345.0ms

localize16.0ms

rewrite39.0ms

series306.0ms

simplify63.0ms

prune347.0ms

regimes2.1s

bsearch1.0ms

simplify2.0ms

end0.0ms

sample1.5s

Profiling