Details

sample271.0ms

Algorithm

intervals

Results

143.0ms	1308×	body	80	nan
60.0ms	418×	body	80	valid

simplify208.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	54	17
1	174	17
2	710	17
3	4940	17
4	5002	17

prune4.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 25.3b

Counts

2 → 1

localize28.0ms

Local error

Found 4 expressions with local error:

5.6b	(* (* (pow (/ d h) (/ 1.0 2.0)) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
10.0b	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
11.1b	(pow (/ d h) (/ 1.0 2.0))
11.5b	(pow (/ d l) (/ 1.0 2.0))

rewrite409.0ms

Algorithm

rewrite-expression-head

Rules

680×	`add-sqr-sqrt`
344×	`associate-l`
337×	`times-frac`
291×	`associate-r`
282×	`unpow-prod-down`
243×	`unswap-sqr`
205×	`add-exp-log`
186×	`*-un-lft-identity`
179×	`add-cube-cbrt`
107×	`prod-exp`
99×	`associate-*l/`
81×	`frac-times`
61×	`associate-/l*`
60×	`associate-/r*`
55×	`div-exp`
40×	`pow-exp`
31×	`difference-of-squares` `sqr-pow`
30×	`add-cbrt-cube`
28×	`*-commutative`
26×	`pow-unpow`
21×	`clear-num`
20×	`frac-2neg`
16×	`pow1`
14×	`pow-to-exp`
13×	`cbrt-unprod`
11×	`associate-*r/`
9×	`div-inv`
6×	`pow-prod-down`
5×	`cbrt-undiv`
4×	`add-log-exp`
3×	`distribute-lft-out--`
2×	`distribute-rgt-in` `sub-neg` `pow-pow` `distribute-lft-in` `un-div-inv`
1×	`flip3--` `flip--`

Counts

4 → 594

Calls

4 calls:

222.0ms	(* (* (pow (/ d h) (/ 1.0 2.0)) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
124.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
5.0ms	(pow (/ d h) (/ 1.0 2.0))
5.0ms	(pow (/ d l) (/ 1.0 2.0))

series1.5s

Counts

4 → 12

Calls

4 calls:

658.0ms	(* (* (pow (/ d h) (/ 1.0 2.0)) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
751.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
67.0ms	(pow (/ d h) (/ 1.0 2.0))
65.0ms	(pow (/ d l) (/ 1.0 2.0))

simplify150.0ms

Algorithm

egg-herbie

Counts

606 → 606

Iterations

Useful iterations: 1 (68.0ms)

Iter	Nodes	Cost
0	3591	7501
1	5001	7398

prune2.6s

Filtered

606 candidates to 461 candidates (23.9%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	584	22	606
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	585	22	607

Merged error: 6.0b

Counts

607 → 22

localize43.0ms

Local error

Found 4 expressions with local error:

4.5b	(/ (* M D) (* 2.0 d))
5.0b	(* (* (pow (/ d (cbrt h)) (/ 1.0 2.0)) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
10.0b	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
11.5b	(pow (/ d l) (/ 1.0 2.0))

rewrite435.0ms

Algorithm

rewrite-expression-head

Rules

830×	`add-sqr-sqrt`
482×	`times-frac`
444×	`associate-l`
369×	`associate-r`
290×	`unpow-prod-down`
281×	`unswap-sqr`
256×	`*-un-lft-identity`
249×	`add-cube-cbrt`
214×	`add-exp-log`
111×	`prod-exp`
99×	`associate-*l/`
81×	`frac-times`
73×	`associate-/l*`
72×	`associate-/r*`
58×	`div-exp`
54×	`*-commutative`
42×	`add-cbrt-cube`
38×	`pow-exp`
32×	`sqr-pow`
31×	`difference-of-squares`
22×	`clear-num`
21×	`frac-2neg`
17×	`cbrt-prod` `cbrt-unprod`
15×	`pow1`
13×	`pow-to-exp` `pow-unpow`
11×	`associate-*r/`
9×	`cbrt-undiv`
8×	`div-inv`
6×	`pow-prod-down`
4×	`add-log-exp`
3×	`distribute-lft-out--`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `un-div-inv`
1×	`flip3--` `pow-pow` `flip--`

Counts

4 → 759

Calls

4 calls:

13.0ms	(/ (* M D) (* 2.0 d))
229.0ms	(* (* (pow (/ d (cbrt h)) (/ 1.0 2.0)) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
125.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
5.0ms	(pow (/ d l) (/ 1.0 2.0))

series1.9s

Counts

4 → 12

Calls

4 calls:

30.0ms	(/ (* M D) (* 2.0 d))
1.1s	(* (* (pow (/ d (cbrt h)) (/ 1.0 2.0)) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
749.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
69.0ms	(pow (/ d l) (/ 1.0 2.0))

simplify191.0ms

Algorithm

egg-herbie

Counts

771 → 771

Iterations

Useful iterations: 1 (78.0ms)

Iter	Nodes	Cost
0	4138	9159
1	5001	9080

prune3.5s

Filtered

771 candidates to 582 candidates (24.5%)

Pruning

25 alts after pruning (25 fresh and 0 done)

	Pruned	Kept	Total
New	764	7	771
Fresh	3	18	21
Picked	1	0	1
Done	0	0	0
Total	768	25	793

Merged error: 5.1b

Counts

793 → 25

localize53.0ms

Local error

Found 4 expressions with local error:

4.5b	(/ (* M D) (* 2.0 d))
11.5b	(pow (/ d l) (/ 1.0 2.0))
14.4b	(sqrt (/ h l))
14.4b	(sqrt (/ h l))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

182×	`times-frac`
172×	`add-sqr-sqrt`
114×	`add-cube-cbrt` `*-un-lft-identity`
78×	`associate-r` `associate-l`
26×	`sqrt-prod` `*-commutative` `unswap-sqr`
19×	`add-exp-log`
18×	`sqrt-div` `associate-/r` `associate-/l`
16×	`add-cbrt-cube`
13×	`unpow-prod-down` `pow-unpow`
7×	`pow1`
5×	`div-exp` `div-inv`
4×	`cbrt-undiv` `rem-sqrt-square` `prod-exp` `cbrt-unprod` `add-log-exp`
3×	`frac-2neg` `clear-num`
2×	`sqrt-pow1` `pow1/2` `pow-exp`
1×	`pow-to-exp` `pow-pow` `sqr-pow`

Counts

4 → 290

Calls

4 calls:

13.0ms	(/ (* M D) (* 2.0 d))
5.0ms	(pow (/ d l) (/ 1.0 2.0))
4.0ms	(sqrt (/ h l))
4.0ms	(sqrt (/ h l))

series200.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(/ (* M D) (* 2.0 d))
68.0ms	(pow (/ d l) (/ 1.0 2.0))
51.0ms	(sqrt (/ h l))
51.0ms	(sqrt (/ h l))

simplify64.0ms

Algorithm

egg-herbie

Counts

302 → 302

Iterations

Useful iterations: 1 (36.0ms)

Iter	Nodes	Cost
0	1219	1918
1	5001	1851

prune2.2s

Filtered

302 candidates to 220 candidates (27.2%)

Pruning

26 alts after pruning (26 fresh and 0 done)

	Pruned	Kept	Total
New	297	5	302
Fresh	3	21	24
Picked	1	0	1
Done	0	0	0
Total	301	26	327

Merged error: 5.1b

Counts

327 → 26

localize78.0ms

Local error

Found 4 expressions with local error:

4.5b	(/ (* M D) (* 2.0 d))
4.5b	(/ (* M D) (* 2.0 d))
14.4b	(sqrt (/ h l))
14.4b	(sqrt (/ h l))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

308×	`times-frac`
288×	`add-sqr-sqrt`
178×	`add-cube-cbrt` `*-un-lft-identity`
156×	`associate-r` `associate-l`
52×	`*-commutative` `unswap-sqr`
30×	`associate-/r` `associate-/l`
28×	`add-exp-log` `add-cbrt-cube`
26×	`sqrt-prod`
18×	`sqrt-div`
8×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
6×	`pow1`
4×	`rem-sqrt-square` `frac-2neg` `clear-num` `div-inv` `add-log-exp`
2×	`sqrt-pow1` `pow1/2`

Counts

4 → 438

Calls

4 calls:

16.0ms	(/ (* M D) (* 2.0 d))
16.0ms	(/ (* M D) (* 2.0 d))
4.0ms	(sqrt (/ h l))
5.0ms	(sqrt (/ h l))

series201.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(/ (* M D) (* 2.0 d))
35.0ms	(/ (* M D) (* 2.0 d))
65.0ms	(sqrt (/ h l))
61.0ms	(sqrt (/ h l))

simplify189.0ms

Algorithm

egg-herbie

Counts

450 → 450

Iterations

Useful iterations: 1 (37.0ms)

Iter	Nodes	Cost
0	979	2968
1	4803	2872
2	5001	2872

prune3.3s

Filtered

450 candidates to 318 candidates (29.3%)

Pruning

24 alts after pruning (24 fresh and 0 done)

	Pruned	Kept	Total
New	447	3	450
Fresh	4	21	25
Picked	1	0	1
Done	0	0	0
Total	452	24	476

Merged error: 5.1b

Counts

476 → 24

regimes1.1s

Accuracy

-4.6% (7.3b remaining)

Error of 14.7b against oracle of 7.4b and baseline of 14.4b

bsearch196.0ms

Steps

Iters	Range		Point
7	3.1421519422282683e+262	3.3641440571041635e+264	3.3116082153282765e+264

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	76	66
1	76	66

end0.0ms

sample8.2s

Algorithm

intervals

Results

4.4s	38727×	body	80	nan
2.0s	12927×	body	80	valid