Details

sample254.0ms

Algorithm

intervals

Results

132.0ms	1244×	body	80	nan
59.0ms	410×	body	80	valid

simplify204.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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 (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: 27.1b

Counts

2 → 1

localize29.0ms

Local error

Found 4 expressions with local error:

6.9b	(* (* (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))
10.5b	(pow (/ d h) (/ 1.0 2.0))
10.9b	(pow (/ d l) (/ 1.0 2.0))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

19×	`associate-l`
15×	`associate-*l/`
9×	`frac-times` `unpow-prod-down` `associate-r` `clear-num` `div-inv`
8×	`frac-2neg` `*-commutative`
7×	`sqr-pow`
5×	`associate-*r/`
4×	`times-frac`
2×	`distribute-rgt-in` `pow-to-exp` `sub-neg` `pow-unpow` `distribute-lft-in`
1×	`flip3--` `un-div-inv` `flip--` `unswap-sqr`

Counts

4 → 49

Calls

4 calls:

10.0ms	(* (* (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))))
10.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
2.0ms	(pow (/ d h) (/ 1.0 2.0))
2.0ms	(pow (/ d l) (/ 1.0 2.0))

series1.7s

Counts

4 → 12

Calls

4 calls:

635.0ms	(* (* (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))))
741.0ms	(* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))
255.0ms	(pow (/ d h) (/ 1.0 2.0))
67.0ms	(pow (/ d l) (/ 1.0 2.0))

simplify60.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	551	575
1	2099	559
2	5001	557

prune364.0ms

Filtered

61 candidates to 53 candidates (86.9%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	42	19	61
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	43	19	62

Merged error: 10.1b

Counts

62 → 19

localize37.0ms

Local error

Found 4 expressions with local error:

6.9b	(* (* (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 2))) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l)))))
9.4b	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l))
10.5b	(pow (/ d h) (/ 1.0 2.0))
10.9b	(pow (/ d l) (/ 1.0 2.0))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

15×	`associate-l`
9×	`unpow-prod-down`
8×	`div-inv`
7×	`*-commutative` `sqr-pow`
5×	`associate-*r/`
4×	`times-frac`
3×	`associate-r`
2×	`distribute-rgt-in` `pow-to-exp` `sub-neg` `pow-unpow` `distribute-lft-in` `clear-num`
1×	`flip3--` `frac-2neg` `un-div-inv` `flip--` `unswap-sqr`

Counts

4 → 34

Calls

4 calls:

9.0ms	(* (* (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 2))) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l)))))
8.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l))
2.0ms	(pow (/ d h) (/ 1.0 2.0))
2.0ms	(pow (/ d l) (/ 1.0 2.0))

series1.5s

Counts

4 → 12

Calls

4 calls:

651.0ms	(* (* (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 2))) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l)))))
708.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l))
67.0ms	(pow (/ d h) (/ 1.0 2.0))
62.0ms	(pow (/ d l) (/ 1.0 2.0))

simplify52.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	457	559
1	1762	545
2	5001	525

prune289.0ms

Filtered

46 candidates to 38 candidates (82.6%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	31	15	46
Fresh	14	4	18
Picked	1	0	1
Done	0	0	0
Total	46	19	65

Merged error: 9.6b

Counts

65 → 19

localize33.0ms

Local error

Found 4 expressions with local error:

6.2b	(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (- h)) (- l))
6.9b	(* (* (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 2))) (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (- h)) (- l)))))
10.5b	(pow (/ d h) (/ 1.0 2.0))
10.9b	(pow (/ d l) (/ 1.0 2.0))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

21×	`associate-l`
17×	`times-frac`
14×	`unpow-prod-down`
12×	`neg-mul-1` `*-commutative`
9×	`div-inv` `associate-/l*`
8×	`sqr-pow`
4×	`associate-r`
2×	`distribute-rgt-in` `pow-to-exp` `sub-neg` `pow-unpow` `distribute-lft-in` `associate-*r/`
1×	`flip3--` `frac-2neg` `distribute-frac-neg` `clear-num` `associate-/r*` `distribute-rgt-neg-out` `flip--` `unswap-sqr`

Counts

4 → 45

Calls

4 calls:

10.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (- h)) (- l))
13.0ms	(* (* (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 2))) (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (- h)) (- l)))))
2.0ms	(pow (/ d h) (/ 1.0 2.0))
2.0ms	(pow (/ d l) (/ 1.0 2.0))

series1.4s

Counts

4 → 12

Calls

4 calls:

683.0ms	(/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (- h)) (- l))
620.0ms	(* (* (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 2))) (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (- h)) (- l)))))
65.0ms	(pow (/ d h) (/ 1.0 2.0))
60.0ms	(pow (/ d l) (/ 1.0 2.0))

simplify54.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	543	712
1	2001	687
2	5002	687

prune364.0ms

Filtered

57 candidates to 49 candidates (86.0%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	45	12	57
Fresh	12	6	18
Picked	1	0	1
Done	0	0	0
Total	58	18	76

Merged error: 7.6b

Counts

76 → 18

localize38.0ms

Local error

Found 4 expressions with local error:

10.5b	(pow (/ d h) (/ 1.0 2.0))
10.5b	(pow (/ d h) (/ 1.0 2.0))
10.9b	(pow (/ d l) (/ 1.0 2.0))
10.9b	(pow (/ d l) (/ 1.0 2.0))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

8×	`div-inv`
4×	`pow-to-exp` `unpow-prod-down` `pow-unpow` `sqr-pow`

Counts

4 → 16

Calls

4 calls:

2.0ms	(pow (/ d h) (/ 1.0 2.0))
3.0ms	(pow (/ d h) (/ 1.0 2.0))
2.0ms	(pow (/ d l) (/ 1.0 2.0))
2.0ms	(pow (/ d l) (/ 1.0 2.0))

series254.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(pow (/ d h) (/ 1.0 2.0))
65.0ms	(pow (/ d h) (/ 1.0 2.0))
65.0ms	(pow (/ d l) (/ 1.0 2.0))
59.0ms	(pow (/ d l) (/ 1.0 2.0))

simplify53.0ms

Algorithm

egg-herbie

Counts

28 → 28

Iterations

Useful iterations: 4 (50.0ms)

Iter	Nodes	Cost
0	115	148
1	269	120
2	804	120
3	2349	120
4	5002	100

prune117.0ms

Filtered

28 candidates to 20 candidates (71.4%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	25	3	28
Fresh	3	14	17
Picked	1	0	1
Done	0	0	0
Total	29	17	46

Merged error: 7.6b

Counts

46 → 17

regimes728.0ms

Accuracy

37.5% (9.1b remaining)

Error of 16.6b against oracle of 7.5b and baseline of 22.1b

bsearch780.0ms

Steps

Iters	Range		Point
7	7.94742693071978e+186	8.718640230163806e+188	1.7042909891776182e+187
4	3.631715492995854e+82	6.027276772227959e+82	3.706576782971857e+82
11	-2.1991128365843992e-299	5.554464097013436e-298	-1.86853407285333e-310
3	-1.2333817938772057e+129	-8.987021278480719e+128	-9.614545652285346e+128

simplify6.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	106	125
1	112	125
2	117	125
3	120	125
4	125	125
5	127	125
6	127	125

end0.0ms

sample7.5s

Algorithm

intervals

Results

4.0s	38284×	body	80	nan
1.8s	12748×	body	80	valid