Details

sample7.8s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0.402832%

Guaranteed chance to sample good point: 16.092658%

Results

20.0ms	256×	body	80	valid
9.0ms	116×	body	80	nan
3.0ms	31×	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

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: 16.4b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

3.5b	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
4.5b	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
6.8b	(/ (* M D) (* 2.0 d))
11.7b	(* (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:

2.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
5.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
8.0ms	(/ (* M D) (* 2.0 d))
10.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series539.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
176.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
6.0ms	(/ (* M D) (* 2.0 d))
211.0ms	(* (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

prune244.0ms

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: 9.0b

Counts

126 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

4.5b	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l))))))
6.8b	(/ (* M D) (* 2.0 d))
6.8b	(/ (* M D) (* 2.0 d))
10.8b	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-exp-log`
35×	`add-cbrt-cube`
33×	`add-sqr-sqrt`
31×	`prod-exp`
23×	`div-exp`
19×	`associate-r`
16×	`add-cube-cbrt` `*-un-lft-identity`
15×	`times-frac`
12×	`associate-l`
11×	`cbrt-unprod`
10×	`pow-exp`
9×	`cbrt-undiv`
8×	`unswap-sqr`
7×	`unpow-prod-down`
6×	`pow1`
4×	`sqrt-prod` `div-inv` `add-log-exp`
3×	`associate-*r/` `sqr-pow`
2×	`pow-to-exp` `frac-2neg` `sqrt-div` `clear-num` `associate-/r` `-commutative` `associate-/l*`
1×	`flip3--` `pow-prod-down` `flip--`

Counts

4 → 119

Calls

4 calls:

5.0ms	(* w0 (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))
10.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l))

series400.0ms

Counts

4 → 12

Calls

4 calls:

178.0ms	(* w0 (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))
211.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l))

simplify78.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	743	1334
1	3019	1197
2	5002	1195

prune271.0ms

Filtered

81 candidates to 131 candidates (-61.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	129	2	131
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	132	7	139

Merged error: 8.7b

Counts

139 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

4.7b	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
5.4b	(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) l)
6.8b	(/ (* M D) (* 2.0 d))
6.8b	(/ (* 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:

6.0ms	(* (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))
6.0ms	(/ (* M D) (* 2.0 d))

series429.0ms

Counts

4 → 12

Calls

4 calls:

206.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
212.0ms	(/ (* (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))

simplify71.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 1 (17.0ms)

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

prune230.0ms

Filtered

71 candidates to 112 candidates (-57.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	111	1	112
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	112	7	119

Merged error: 8.7b

Counts

119 → 7

localize20.0ms

Local error

Found 4 expressions with local error:

4.7b	(* (pow (/ 1 (/ (* 2.0 d) (* M D))) (/ 2.0 2)) h)
5.4b	(/ (* (pow (/ 1 (/ (* 2.0 d) (* M D))) (/ 2.0 2)) h) l)
6.7b	(/ (* 2.0 d) (* M D))
6.8b	(/ (* M D) (* 2.0 d))

rewrite40.0ms

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:

11.0ms	(* (pow (/ 1 (/ (* 2.0 d) (* M D))) (/ 2.0 2)) h)
11.0ms	(/ (* (pow (/ 1 (/ (* 2.0 d) (* M D))) (/ 2.0 2)) h) l)
6.0ms	(/ (* 2.0 d) (* M D))
5.0ms	(/ (* M D) (* 2.0 d))

series425.0ms

Counts

4 → 12

Calls

4 calls:

200.0ms	(* (pow (/ 1 (/ (* 2.0 d) (* M D))) (/ 2.0 2)) h)
210.0ms	(/ (* (pow (/ 1 (/ (* 2.0 d) (* M D))) (/ 2.0 2)) h) l)
6.0ms	(/ (* 2.0 d) (* M D))
9.0ms	(/ (* M D) (* 2.0 d))

simplify94.0ms

Algorithm

egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 2 (80.0ms)

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

prune245.0ms

Filtered

84 candidates to 151 candidates (-79.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	151	0	151
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	151	7	158

Merged error: 8.7b

Counts

158 → 7

regimes1.9s

Accuracy

-54.8% (1.9b remaining)

Error of 9.5b against oracle of 7.5b and baseline of 8.8b

bsearch83.0ms

Steps

Iters	Range		Point
10	-1.0110103823184768e-282	-4.9308936942515913e-293	-4.1185701497347385e-290
8	-inf.0	-9.43509941323196e+304	-1.7785134383207947e+308

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	39
1	41	39

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: 16.092658%

Results

628.0ms	8000×	body	80	valid
249.0ms	3118×	body	80	nan
110.0ms	1237×	body	80	invalid

Details

sample7.8s

simplify53.0ms

prune5.0ms

localize14.0ms

rewrite29.0ms

series539.0ms

simplify73.0ms

prune244.0ms

localize16.0ms

rewrite32.0ms

series400.0ms

simplify78.0ms

prune271.0ms

localize16.0ms

rewrite28.0ms

series429.0ms

simplify71.0ms

prune230.0ms

localize20.0ms

rewrite40.0ms

series425.0ms

simplify94.0ms

prune245.0ms

regimes1.9s

bsearch83.0ms

simplify2.0ms

end0.0ms

sample9.1s

Profiling