Details

analyze6.7s

Algorithm

sampling

Space saved by range analysis: 0.292611%

Space saved by search: 0.901177%

Guaranteed chance to sample good point: 12.552198%

sample51.0ms

Algorithm

intervals

Results

20.0ms	256×	body	80	valid
8.0ms	96×	body	80	nan
3.0ms	36×	body	80	invalid

simplify53.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	36	9
1	81	9
2	178	9
3	446	9
4	1530	9
5	5001	9

prune6.0ms

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: 14.1b

Counts

2 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

2.7b	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
3.5b	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
5.1b	(/ (* M D) (* 2.0 d))
12.0b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite27.0ms

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:

5.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
2.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
5.0ms	(/ (* M D) (* 2.0 d))
10.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series536.0ms

Counts

4 → 12

Calls

4 calls:

174.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
147.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
6.0ms	(/ (* M D) (* 2.0 d))
209.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify74.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	738	1124
1	2959	1046
2	5001	1043

prune263.0ms

Filtered

81 candidates to 125 candidates (-54.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	116	9	125
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	117	9	126

Merged error: 7.6b

Counts

126 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

3.5b	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
5.1b	(/ (* M D) (* 2.0 d))
5.7b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
7.1b	(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 96

Calls

4 calls:

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

series571.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
6.0ms	(/ (* M D) (* 2.0 d))
200.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
218.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)

simplify65.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	693	924
1	2737	841
2	5002	839

prune214.0ms

Filtered

69 candidates to 108 candidates (-56.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	106	2	108
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	109	8	117

Merged error: 7.5b

Counts

117 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

3.5b	(sqrt (- 1.0 (/ (* (pow (* (/ M 2.0) (/ D d)) 2.0) h) l)))
5.7b	(* (pow (* (/ M 2.0) (/ D d)) 2.0) h)
6.3b	(* (/ M 2.0) (/ D d))
7.1b	(/ (* (pow (* (/ M 2.0) (/ D d)) 2.0) h) l)

rewrite31.0ms

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-l`
16×	`associate-r`
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:

4.0ms	(sqrt (- 1.0 (/ (* (pow (* (/ M 2.0) (/ D d)) 2.0) h) l)))
5.0ms	(* (pow (* (/ M 2.0) (/ D d)) 2.0) h)
10.0ms	(* (/ M 2.0) (/ D d))
8.0ms	(/ (* (pow (* (/ M 2.0) (/ D d)) 2.0) h) l)

series567.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(sqrt (- 1.0 (/ (* (pow (* (/ M 2.0) (/ D d)) 2.0) h) l)))
202.0ms	(* (pow (* (/ M 2.0) (/ D d)) 2.0) h)
6.0ms	(* (/ M 2.0) (/ D d))
209.0ms	(/ (* (pow (* (/ M 2.0) (/ D d)) 2.0) h) l)

simplify72.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	832	1043
1	3170	960
2	5001	958

prune249.0ms

Filtered

90 candidates to 132 candidates (-46.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	131	1	132
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	131	9	140

Merged error: 7.3b

Counts

140 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

5.5b	(* (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2)) h)
6.3b	(* (/ M 2.0) (/ D d))
6.3b	(* (/ M 2.0) (/ D d))
7.1b	(/ (* (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2)) (* (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2)) h)) l)

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

373×	`add-exp-log`
184×	`prod-exp`
129×	`div-exp`
80×	`pow-exp`
63×	`add-sqr-sqrt`
47×	`times-frac`
39×	`add-cbrt-cube`
36×	`add-cube-cbrt` `*-un-lft-identity`
31×	`associate-l`
29×	`associate-r`
16×	`pow-to-exp`
12×	`cbrt-unprod`
11×	`cbrt-undiv`
10×	`unswap-sqr`
8×	`pow1`
5×	`div-inv`
4×	`add-log-exp`
3×	`associate-/r` `-commutative`
2×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/` `sqr-pow`
1×	`unpow-prod-down` `frac-2neg` `clear-num` `associate-/l*`

Counts

4 → 203

Calls

4 calls:

5.0ms	(* (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2)) h)
12.0ms	(* (/ M 2.0) (/ D d))
10.0ms	(* (/ M 2.0) (/ D d))
12.0ms	(/ (* (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2)) (* (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2)) h)) l)

series421.0ms

Counts

4 → 12

Calls

4 calls:

197.0ms	(* (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2)) h)
6.0ms	(* (/ M 2.0) (/ D d))
6.0ms	(* (/ M 2.0) (/ D d))
212.0ms	(/ (* (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2)) (* (pow (* (/ M 2.0) (/ D d)) (/ 2.0 2)) h)) l)

simplify92.0ms

Algorithm

egg-herbie

Counts

215 → 215

Iterations

Useful iterations: 2 (72.0ms)

Iter	Nodes	Cost
0	1187	2066
1	3926	1642
2	5003	1638

prune362.0ms

Filtered

117 candidates to 215 candidates (-83.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	213	2	215
Fresh	0	7	7
Picked	1	0	1
Done	0	1	1
Total	214	10	224

Merged error: 6.6b

Counts

224 → 10

regimes2.4s

Accuracy

0% (1.7b remaining)

Error of 8.7b against oracle of 6.9b and baseline of 8.7b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	16
1	24	16

end0.0ms

analyze6.6s

Algorithm

sampling

Space saved by range analysis: 0.292611%

Space saved by search: 0.901177%

Guaranteed chance to sample good point: 12.552198%

sample1.5s

Algorithm

intervals

Results

654.0ms	8000×	body	80	valid
258.0ms	3035×	body	80	nan
108.0ms	1267×	body	80	invalid

Details

analyze6.7s

sample51.0ms

simplify53.0ms

prune6.0ms

localize17.0ms

rewrite27.0ms

series536.0ms

simplify74.0ms

prune263.0ms

localize17.0ms

rewrite26.0ms

series571.0ms

simplify65.0ms

prune214.0ms

localize14.0ms

rewrite31.0ms

series567.0ms

simplify72.0ms

prune249.0ms

localize17.0ms

rewrite51.0ms

series421.0ms

simplify92.0ms

prune362.0ms

regimes2.4s

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze6.6s

sample1.5s

Profiling