Details

sample48.0ms

Algorithm

intervals

Results

21.0ms	288×	body	80	valid
7.0ms	90×	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

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 13.0b

Counts

2 → 1

localize18.0ms

Local error

Found 4 expressions with local error:

1.7b	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
2.8b	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
5.1b	(/ (* M D) (* 2.0 d))
10.5b	(* (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))))
6.0ms	(/ (* M D) (* 2.0 d))
11.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series1.4s

Counts

4 → 12

Calls

4 calls:

390.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
355.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
30.0ms	(/ (* M D) (* 2.0 d))
660.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify71.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	609	1075
1	2742	997
2	5003	994

prune336.0ms

Filtered

125 candidates to 81 candidates (64.8%)

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: 6.2b

Counts

126 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

2.8b	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
3.8b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
5.1b	(/ (* M D) (* 2.0 d))
7.3b	(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)

rewrite30.0ms

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

series1.8s

Counts

4 → 12

Calls

4 calls:

358.0ms	(sqrt (- 1.0 (/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)))
748.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)
27.0ms	(/ (* M D) (* 2.0 d))
689.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) l)

simplify65.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	560	828
1	2559	746
2	5001	744

prune300.0ms

Filtered

108 candidates to 70 candidates (64.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	105	3	108
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	107	9	116

Merged error: 5.4b

Counts

116 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

5.1b	(/ (* M D) (* 2.0 d))
5.1b	(/ (* M D) (* 2.0 d))
6.6b	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
7.3b	(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)

rewrite50.0ms

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:

6.0ms	(/ (* M D) (* 2.0 d))
6.0ms	(/ (* M D) (* 2.0 d))
7.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
20.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)

series1.5s

Counts

4 → 12

Calls

4 calls:

28.0ms	(/ (* M D) (* 2.0 d))
34.0ms	(/ (* M D) (* 2.0 d))
734.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)
689.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) l)

simplify85.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	836	1701
1	3118	1278
2	5002	1274

prune334.0ms

Filtered

162 candidates to 72 candidates (44.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	160	2	162
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	163	8	171

Merged error: 5.1b

Counts

171 → 8

localize25.0ms

Local error

Found 4 expressions with local error:

2.9b	(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) (cbrt l))
5.1b	(/ (* M D) (* 2.0 d))
5.1b	(/ (* M D) (* 2.0 d))
6.6b	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-exp-log`
33×	`add-cbrt-cube`
30×	`prod-exp`
24×	`div-exp`
16×	`add-sqr-sqrt`
11×	`add-cube-cbrt` `*-un-lft-identity`
10×	`cbrt-undiv` `pow-exp` `cbrt-unprod`
9×	`times-frac` `associate-l`
8×	`associate-/r*`
6×	`cbrt-prod` `unpow-prod-down`
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 → 106

Calls

4 calls:

9.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) (cbrt l))
6.0ms	(/ (* M D) (* 2.0 d))
6.0ms	(/ (* M D) (* 2.0 d))
7.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

series1.5s

Counts

4 → 12

Calls

4 calls:

719.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h) (cbrt l))
33.0ms	(/ (* M D) (* 2.0 d))
27.0ms	(/ (* M D) (* 2.0 d))
713.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)

simplify64.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	520	914
1	2353	787
2	5001	787

prune388.0ms

Filtered

118 candidates to 78 candidates (66.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	118	0	118
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	118	8	126

Merged error: 5.1b

Counts

126 → 8

regimes823.0ms

Accuracy

0% (1.3b remaining)

Error of 8.4b against oracle of 7.1b and baseline of 8.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	21
1	28	21

end0.0ms

sample1.4s

Algorithm

intervals

Results

717.0ms	9385×	body	80	valid
250.0ms	3138×	body	80	nan

Details

sample48.0ms

simplify54.0ms

prune3.0ms

localize18.0ms

rewrite29.0ms

series1.4s

simplify71.0ms

prune336.0ms

localize13.0ms

rewrite30.0ms

series1.8s

simplify65.0ms

prune300.0ms

localize16.0ms

rewrite50.0ms

series1.5s

simplify85.0ms

prune334.0ms

localize25.0ms

rewrite32.0ms

series1.5s

simplify64.0ms

prune388.0ms

regimes823.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.4s

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