Details

sample62.0ms

Algorithm

intervals

Results

23.0ms	299×	body	80	valid
7.0ms	89×	body	80	nan

simplify51.0ms

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: 13.3b

Counts

2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

1.9b	(* 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))))
5.1b	(/ (* M D) (* 2.0 d))
10.8b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite32.0ms

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))
13.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series556.0ms

Counts

4 → 12

Calls

4 calls:

183.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
151.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
6.0ms	(/ (* M D) (* 2.0 d))
216.0ms	(* (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	1125
1	2959	1046
2	5001	1043

prune242.0ms

Filtered

81 candidates to 125 candidates (-54.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	119	6	125
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	120	6	126

Merged error: 7.0b

Counts

126 → 6

localize15.0ms

Local error

Found 4 expressions with local error:

3.3b	(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))
5.1b	(/ (* M D) (* 2.0 d))
5.2b	(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))
5.2b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

165×	`add-exp-log`
91×	`prod-exp`
40×	`div-exp`
30×	`add-cbrt-cube`
25×	`pow-exp`
21×	`add-sqr-sqrt`
16×	`associate-r`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`times-frac` `cbrt-unprod`
10×	`associate-l`
8×	`rec-exp` `1-exp`
7×	`pow1`
6×	`cbrt-undiv` `unpow-prod-down`
5×	`pow-to-exp`
4×	`add-log-exp`
3×	`sqrt-prod` `div-inv` `unswap-sqr`
2×	`sqrt-div` `*-commutative` `sqr-pow`
1×	`rem-sqrt-square` `flip3--` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `clear-num` `associate-/r` `un-div-inv` `flip--` `associate-/l*`

Counts

4 → 128

Calls

4 calls:

2.0ms	(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))
6.0ms	(/ (* M D) (* 2.0 d))
11.0ms	(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))
7.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

series577.0ms

Counts

4 → 12

Calls

4 calls:

151.0ms	(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))
6.0ms	(/ (* M D) (* 2.0 d))
216.0ms	(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))
205.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

simplify85.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	885	1232
1	3626	1109
2	5002	1096

prune223.0ms

Filtered

74 candidates to 140 candidates (-89.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	138	2	140
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	138	8	146

Merged error: 6.1b

Counts

146 → 8

localize18.0ms

Local error

Found 4 expressions with local error:

5.1b	(/ (* M D) (* 2.0 d))
5.1b	(/ (* M D) (* 2.0 d))
5.2b	(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))
6.7b	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

1402×	`add-exp-log`
907×	`prod-exp`
366×	`div-exp`
305×	`pow-exp`
61×	`pow-to-exp`
57×	`rec-exp` `1-exp`
51×	`add-cbrt-cube`
21×	`cbrt-unprod`
19×	`add-sqr-sqrt`
16×	`associate-r`
14×	`add-cube-cbrt` `*-un-lft-identity`
12×	`times-frac`
11×	`cbrt-undiv`
10×	`associate-l`
6×	`pow1` `unpow-prod-down`
4×	`div-inv` `add-log-exp`
3×	`unswap-sqr`
2×	`frac-2neg` `clear-num` `associate-/r` `-commutative` `associate-/l*` `sqr-pow`
1×	`associate-*r/` `pow-prod-down` `un-div-inv`

Counts

4 → 332

Calls

4 calls:

6.0ms	(/ (* M D) (* 2.0 d))
6.0ms	(/ (* M D) (* 2.0 d))
22.0ms	(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))
7.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

series440.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(/ (* M D) (* 2.0 d))
6.0ms	(/ (* M D) (* 2.0 d))
215.0ms	(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))
212.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

simplify126.0ms

Algorithm

egg-herbie

Counts

344 → 344

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1770	4589
1	4940	3162
2	5001	3162

prune279.0ms

Filtered

78 candidates to 344 candidates (-341.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	342	2	344
Fresh	0	6	6
Picked	1	0	1
Done	1	0	1
Total	344	8	352

Merged error: 6.1b

Counts

352 → 8

localize21.0ms

Local error

Found 4 expressions with local error:

5.1b	(/ (* M D) (* 2.0 d))
5.1b	(* (* M D) (/ 1 (* 2.0 d)))
5.2b	(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (* (* M D) (/ 1 (* 2.0 d))) (/ 2.0 2)) h)) (/ 1 l))
6.7b	(* (pow (* (* M D) (/ 1 (* 2.0 d))) (/ 2.0 2)) h)

rewrite146.0ms

Algorithm

rewrite-expression-head

Rules

3592×	`add-exp-log`
2607×	`prod-exp`
795×	`pow-exp`
786×	`div-exp`
247×	`rec-exp` `1-exp`
101×	`pow-to-exp`
60×	`add-cbrt-cube`
28×	`cbrt-unprod`
23×	`associate-r`
18×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
13×	`times-frac`
11×	`pow1` `cbrt-undiv`
7×	`associate-l`
4×	`pow-prod-down` `add-log-exp`
3×	`*-commutative` `div-inv`
2×	`associate-*r/` `un-div-inv` `unswap-sqr` `sqr-pow`
1×	`unpow-prod-down` `frac-2neg` `clear-num` `associate-/r` `associate-/l`

Counts

4 → 636

Calls

4 calls:

6.0ms	(/ (* M D) (* 2.0 d))
12.0ms	(* (* M D) (/ 1 (* 2.0 d)))
26.0ms	(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (* (* M D) (/ 1 (* 2.0 d))) (/ 2.0 2)) h)) (/ 1 l))
7.0ms	(* (pow (* (* M D) (/ 1 (* 2.0 d))) (/ 2.0 2)) h)

series444.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(/ (* M D) (* 2.0 d))
6.0ms	(* (* M D) (/ 1 (* 2.0 d)))
217.0ms	(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (* (* M D) (/ 1 (* 2.0 d))) (/ 2.0 2)) h)) (/ 1 l))
214.0ms	(* (pow (* (* M D) (/ 1 (* 2.0 d))) (/ 2.0 2)) h)

simplify121.0ms

Algorithm

egg-herbie

Counts

648 → 648

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	3328	9608
1	5001	6699

prune276.0ms

Filtered

87 candidates to 648 candidates (-644.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	648	0	648
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	648	8	656

Merged error: 6.1b

Counts

656 → 8

regimes1.9s

Accuracy

0% (2.0b remaining)

Error of 9.3b against oracle of 7.3b and baseline of 9.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	18
1	34	18

end0.0ms

sample1.8s

Algorithm

intervals

Results

694.0ms	9320×	body	80	valid
253.0ms	3226×	body	80	nan

Details

sample62.0ms

simplify51.0ms

prune6.0ms

localize15.0ms

rewrite32.0ms

series556.0ms

simplify72.0ms

prune242.0ms

localize15.0ms

rewrite31.0ms

series577.0ms

simplify85.0ms

prune223.0ms

localize18.0ms

rewrite74.0ms

series440.0ms

simplify126.0ms

prune279.0ms

localize21.0ms

rewrite146.0ms

series444.0ms

simplify121.0ms

prune276.0ms

regimes1.9s

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.8s

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