Details

sample26.3s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 11.364746%

Guaranteed chance to sample good point: 13.028508%

Results

19.0ms	256×	body	80	valid
7.0ms	88×	body	80	nan
3.0ms	44×	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: 12.6b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

2.2b	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
3.8b	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
5.0b	(/ (* M D) (* 2.0 d))
10.8b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite29.0ms

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

series525.0ms

Counts

4 → 12

Calls

4 calls:

173.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
142.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
6.0ms	(/ (* M D) (* 2.0 d))
205.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify73.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 2 (61.0ms)

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

prune246.0ms

Filtered

81 candidates to 125 candidates (-54.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	118	7	125
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	119	7	126

Merged error: 7.9b

Counts

126 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

3.8b	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l)))))
5.0b	(/ (* M D) (* 2.0 d))
5.0b	(/ (* M D) (* 2.0 d))
8.6b	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l))

rewrite29.0ms

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))
6.0ms	(/ (* M D) (* 2.0 d))
10.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l))

series360.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(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))
6.0ms	(/ (* M D) (* 2.0 d))
206.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l))

simplify74.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	702	1184
1	2817	1065
2	5001	1064

prune271.0ms

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	0	6	6
Picked	1	0	1
Done	0	0	0
Total	121	8	129

Merged error: 7.3b

Counts

129 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

4.0b	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
4.1b	(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l)
5.0b	(/ (* M D) (* 2.0 d))
5.0b	(/ (* M D) (* 2.0 d))

rewrite31.0ms

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)
7.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l)
6.0ms	(/ (* M D) (* 2.0 d))
8.0ms	(/ (* M D) (* 2.0 d))

series417.0ms

Counts

4 → 12

Calls

4 calls:

198.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
207.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l)
5.0ms	(/ (* M D) (* 2.0 d))
6.0ms	(/ (* M D) (* 2.0 d))

simplify64.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	639	914
1	2609	782
2	5001	782

prune231.0ms

Filtered

71 candidates to 112 candidates (-57.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	111	1	112
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	112	8	120

Merged error: 7.3b

Counts

120 → 8

localize23.0ms

Local error

Found 4 expressions with local error:

3.9b	(/ M (/ (* 2.0 d) D))
4.0b	(* (pow (/ M (/ (* 2.0 d) D)) (/ 2.0 2)) h)
4.1b	(/ (* (pow (/ M (/ (* 2.0 d) D)) (/ 2.0 2)) h) l)
5.0b	(/ (* M D) (* 2.0 d))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

68×	`times-frac`
67×	`add-exp-log`
46×	`add-sqr-sqrt`
38×	`add-cube-cbrt` `*-un-lft-identity`
32×	`add-cbrt-cube`
30×	`associate-l`
28×	`unpow-prod-down`
26×	`div-exp`
19×	`prod-exp`
11×	`cbrt-undiv` `associate-/r*` `div-inv`
8×	`pow-exp`
7×	`cbrt-unprod`
5×	`associate-/l*`
4×	`pow1` `add-log-exp` `unswap-sqr`
3×	`frac-2neg` `associate-r` `clear-num`
2×	`pow-to-exp` `associate-/r/` `sqr-pow`
1×	`*-commutative`

Counts

4 → 147

Calls

4 calls:

6.0ms	(/ M (/ (* 2.0 d) D))
11.0ms	(* (pow (/ M (/ (* 2.0 d) D)) (/ 2.0 2)) h)
10.0ms	(/ (* (pow (/ M (/ (* 2.0 d) D)) (/ 2.0 2)) h) l)
6.0ms	(/ (* M D) (* 2.0 d))

series418.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(/ M (/ (* 2.0 d) D))
199.0ms	(* (pow (/ M (/ (* 2.0 d) D)) (/ 2.0 2)) h)
207.0ms	(/ (* (pow (/ M (/ (* 2.0 d) D)) (/ 2.0 2)) h) l)
6.0ms	(/ (* M D) (* 2.0 d))

simplify89.0ms

Algorithm

egg-herbie

Counts

159 → 159

Iterations

Useful iterations: 1 (21.0ms)

Iter	Nodes	Cost
0	932	1245
1	3912	1119
2	5003	1119

prune340.0ms

Filtered

120 candidates to 159 candidates (-32.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	157	2	159
Fresh	2	4	6
Picked	1	0	1
Done	0	1	1
Total	160	7	167

Merged error: 6.8b

Counts

167 → 7

regimes1.7s

Accuracy

0% (1.4b remaining)

Error of 8.5b against oracle of 7.2b and baseline of 8.5b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	27
1	29	27

end0.0ms

sample28.5s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 11.364746%

Guaranteed chance to sample good point: 13.028508%

Results

615.0ms	8000×	body	80	valid
243.0ms	3127×	body	80	nan
105.0ms	1277×	body	80	invalid

Details

sample26.3s

simplify54.0ms

prune5.0ms

localize14.0ms

rewrite29.0ms

series525.0ms

simplify73.0ms

prune246.0ms

localize16.0ms

rewrite29.0ms

series360.0ms

simplify74.0ms

prune271.0ms

localize16.0ms

rewrite31.0ms

series417.0ms

simplify64.0ms

prune231.0ms

localize23.0ms

rewrite38.0ms

series418.0ms

simplify89.0ms

prune340.0ms

regimes1.7s

bsearch0.0ms

simplify2.0ms

end0.0ms

sample28.5s

Profiling