Details

sample7.8s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0.402832%

Guaranteed chance to sample good point: 14.229685%

Results

23.0ms	256×	body	80	valid
9.0ms	116×	body	80	nan
2.0ms	30×	body	80	invalid

simplify54.0ms

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

prune5.0ms

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: 16.6b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

4.2b	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
4.2b	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
6.3b	(/ (* M D) (* 2.0 d))
11.9b	(* (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:

6.0ms	(* 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))))
6.0ms	(/ (* M D) (* 2.0 d))
10.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series535.0ms

Counts

4 → 12

Calls

4 calls:

175.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
143.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
7.0ms	(/ (* M D) (* 2.0 d))
210.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify72.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 2 (59.0ms)

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

prune254.0ms

Filtered

81 candidates to 125 candidates (-54.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	117	8	125
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	118	8	126

Merged error: 9.4b

Counts

126 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

4.2b	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l)))))
6.3b	(/ (* M D) (* 2.0 d))
6.3b	(/ (* M D) (* 2.0 d))
11.0b	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

77×	`add-exp-log`
33×	`add-cbrt-cube`
30×	`prod-exp`
28×	`add-sqr-sqrt`
23×	`div-exp`
15×	`times-frac`
14×	`add-cube-cbrt` `*-un-lft-identity`
13×	`associate-r`
10×	`pow-exp` `cbrt-unprod`
9×	`cbrt-undiv` `associate-l`
7×	`unpow-prod-down`
6×	`unswap-sqr`
5×	`pow1`
4×	`div-inv` `add-log-exp`
3×	`sqrt-prod` `sqr-pow`
2×	`pow-to-exp` `frac-2neg` `sqrt-div` `clear-num` `associate-/r` `associate-/l`
1×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `associate-r/` `-commutative` `flip--`

Counts

4 → 110

Calls

4 calls:

2.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l)))))
5.0ms	(/ (* M D) (* 2.0 d))
5.0ms	(/ (* M D) (* 2.0 d))
10.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l))

series364.0ms

Counts

4 → 12

Calls

4 calls:

145.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l)))))
6.0ms	(/ (* M D) (* 2.0 d))
6.0ms	(/ (* M D) (* 2.0 d))
208.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l))

simplify71.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	702	1185
1	2817	1065
2	5001	1064

prune273.0ms

Filtered

77 candidates to 122 candidates (-58.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	120	2	122
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	122	8	130

Merged error: 9.0b

Counts

130 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

5.4b	(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l)
6.1b	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
6.3b	(/ (* M D) (* 2.0 d))
6.3b	(/ (* M D) (* 2.0 d))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-exp-log`
35×	`add-cbrt-cube`
30×	`prod-exp`
24×	`div-exp`
14×	`add-sqr-sqrt`
10×	`cbrt-undiv` `pow-exp` `cbrt-unprod`
9×	`add-cube-cbrt` `-un-lft-identity` `associate-l*`
6×	`unpow-prod-down` `times-frac`
5×	`associate-/r*`
4×	`pow1` `div-inv` `add-log-exp`
3×	`frac-2neg` `associate-r` `clear-num` `associate-/l*` `unswap-sqr`
2×	`pow-to-exp` `sqr-pow`
1×	`*-commutative`

Counts

4 → 100

Calls

4 calls:

7.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l)
7.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
6.0ms	(/ (* M D) (* 2.0 d))
6.0ms	(/ (* M D) (* 2.0 d))

series420.0ms

Counts

4 → 12

Calls

4 calls:

208.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l)
200.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
5.0ms	(/ (* M D) (* 2.0 d))
6.0ms	(/ (* M D) (* 2.0 d))

simplify62.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	639	914
1	2609	782
2	5002	782

prune246.0ms

Filtered

71 candidates to 112 candidates (-57.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	111	1	112
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	112	8	120

Merged error: 9.0b

Counts

120 → 8

localize20.0ms

Local error

Found 4 expressions with local error:

5.4b	(/ (* (pow (/ 1 (/ (* 2.0 d) (* M D))) (/ 2.0 2)) h) l)
6.1b	(* (pow (/ 1 (/ (* 2.0 d) (* M D))) (/ 2.0 2)) h)
6.3b	(/ (* 2.0 d) (* M D))
6.3b	(/ (* M D) (* 2.0 d))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

176×	`add-exp-log`
71×	`div-exp`
68×	`prod-exp`
35×	`add-cbrt-cube`
32×	`pow-exp`
27×	`add-sqr-sqrt`
25×	`times-frac`
24×	`associate-l`
23×	`unpow-prod-down`
18×	`*-un-lft-identity`
17×	`add-cube-cbrt`
10×	`cbrt-undiv` `rec-exp` `1-exp` `cbrt-unprod`
7×	`div-inv`
5×	`associate-/r*` `unswap-sqr`
4×	`pow1` `add-log-exp`
3×	`frac-2neg` `associate-r` `clear-num` `associate-/l*`
2×	`pow-to-exp` `sqr-pow`
1×	`associate-/r/` `*-commutative`

Counts

4 → 139

Calls

4 calls:

14.0ms	(/ (* (pow (/ 1 (/ (* 2.0 d) (* M D))) (/ 2.0 2)) h) l)
12.0ms	(* (pow (/ 1 (/ (* 2.0 d) (* M D))) (/ 2.0 2)) h)
6.0ms	(/ (* 2.0 d) (* M D))
6.0ms	(/ (* M D) (* 2.0 d))

series419.0ms

Counts

4 → 12

Calls

4 calls:

207.0ms	(/ (* (pow (/ 1 (/ (* 2.0 d) (* M D))) (/ 2.0 2)) h) l)
201.0ms	(* (pow (/ 1 (/ (* 2.0 d) (* M D))) (/ 2.0 2)) h)
6.0ms	(/ (* 2.0 d) (* M D))
6.0ms	(/ (* M D) (* 2.0 d))

simplify95.0ms

Algorithm

egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 2 (80.0ms)

Iter	Nodes	Cost
0	962	1317
1	3958	1177
2	5001	1168

prune259.0ms

Filtered

84 candidates to 151 candidates (-79.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	151	0	151
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	151	8	159

Merged error: 9.0b

Counts

159 → 8

regimes2.1s

Accuracy

0% (1.0b remaining)

Error of 8.5b against oracle of 7.5b and baseline of 8.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	17
1	31	17

end0.0ms

sample9.1s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0.402832%

Guaranteed chance to sample good point: 14.229685%

Results

616.0ms	8000×	body	80	valid
252.0ms	3127×	body	80	nan
101.0ms	1255×	body	80	invalid

Details

sample7.8s

simplify54.0ms

prune5.0ms

localize14.0ms

rewrite27.0ms

series535.0ms

simplify72.0ms

prune254.0ms

localize16.0ms

rewrite27.0ms

series364.0ms

simplify71.0ms

prune273.0ms

localize16.0ms

rewrite28.0ms

series420.0ms

simplify62.0ms

prune246.0ms

localize20.0ms

rewrite43.0ms

series419.0ms

simplify95.0ms

prune259.0ms

regimes2.1s

bsearch0.0ms

simplify1.0ms

end0.0ms

sample9.1s

Profiling