Details

sample64.0ms

Algorithm

intervals

Results

22.0ms	291×	body	80	valid
7.0ms	95×	body	80	nan

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: 12.3b

Counts

2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

1.7b	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
3.3b	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
4.9b	(/ (* M D) (* 2.0 d))
10.4b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite28.0ms

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))

series548.0ms

Counts

4 → 12

Calls

4 calls:

180.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
149.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
6.0ms	(/ (* M D) (* 2.0 d))
213.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify71.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 2 (58.0ms)

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

prune291.0ms

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: 6.2b

Counts

126 → 9

localize18.0ms

Local error

Found 4 expressions with local error:

3.3b	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
3.8b	(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
4.9b	(/ (* M D) (* 2.0 d))
5.5b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

rewrite27.0ms

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

series586.0ms

Counts

4 → 12

Calls

4 calls:

155.0ms	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
217.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)
6.0ms	(/ (* M D) (* 2.0 d))
208.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

simplify66.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (55.0ms)

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

prune225.0ms

Filtered

70 candidates to 108 candidates (-54.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	106	2	108
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	108	9	117

Merged error: 5.3b

Counts

117 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

3.8b	(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)
4.3b	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
4.9b	(/ (* M D) (* 2.0 d))
4.9b	(/ (* M D) (* 2.0 d))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

373×	`add-exp-log`
184×	`prod-exp`
129×	`div-exp`
80×	`pow-exp`
39×	`add-cbrt-cube`
16×	`pow-to-exp`
14×	`add-sqr-sqrt`
12×	`cbrt-unprod`
11×	`cbrt-undiv`
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×	`sqr-pow`
1×	`*-commutative`

Counts

4 → 150

Calls

4 calls:

14.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (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))

series448.0ms

Counts

4 → 12

Calls

4 calls:

220.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)
211.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
7.0ms	(/ (* M D) (* 2.0 d))
10.0ms	(/ (* M D) (* 2.0 d))

simplify88.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	1048	1799
1	3497	1375
2	5002	1371

prune270.0ms

Filtered

72 candidates to 162 candidates (-125.0%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	161	1	162
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	161	10	171

Merged error: 5.3b

Counts

171 → 10

localize27.0ms

Local error

Found 4 expressions with local error:

4.9b	(/ (* M D) (* 2.0 d))
17.2b	(cbrt (/ (* M D) (* 2.0 d)))
17.2b	(cbrt (/ (* M D) (* 2.0 d)))
17.2b	(cbrt (/ (* M D) (* 2.0 d)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-exp-log` `add-cbrt-cube`
15×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `cbrt-undiv` `times-frac` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `add-log-exp`
3×	`cbrt-div` `pow1/3`
1×	`frac-2neg` `clear-num` `associate-/r` `associate-/l`

Counts

4 → 63

Calls

4 calls:

6.0ms	(/ (* M D) (* 2.0 d))
4.0ms	(cbrt (/ (* M D) (* 2.0 d)))
4.0ms	(cbrt (/ (* M D) (* 2.0 d)))
4.0ms	(cbrt (/ (* M D) (* 2.0 d)))

series77.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(/ (* M D) (* 2.0 d))
23.0ms	(cbrt (/ (* M D) (* 2.0 d)))
23.0ms	(cbrt (/ (* M D) (* 2.0 d)))
23.0ms	(cbrt (/ (* M D) (* 2.0 d)))

simplify36.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	258	520
1	1204	458
2	5002	452

prune239.0ms

Filtered

62 candidates to 75 candidates (-21.0%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	75	0	75
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	75	10	85

Merged error: 5.3b

Counts

85 → 10

regimes2.1s

Accuracy

0% (2.2b remaining)

Error of 9.2b against oracle of 7.0b and baseline of 9.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	16
1	25	16

end0.0ms

sample1.8s

Algorithm

intervals

Results

722.0ms	9334×	body	80	valid
248.0ms	3111×	body	80	nan

Details

sample64.0ms

simplify54.0ms

prune5.0ms

localize15.0ms

rewrite28.0ms

series548.0ms

simplify71.0ms

prune291.0ms

localize18.0ms

rewrite27.0ms

series586.0ms

simplify66.0ms

prune225.0ms

localize17.0ms

rewrite44.0ms

series448.0ms

simplify88.0ms

prune270.0ms

localize27.0ms

rewrite21.0ms

series77.0ms

simplify36.0ms

prune239.0ms

regimes2.1s

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.8s

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