Details

sample29.0ms

Algorithm

intervals

Results

6.0ms	190×	body	80	valid
5.0ms	33×	body	1280	valid
4.0ms	256×	pre	80	true
3.0ms	21×	body	640	valid
1.0ms	10×	body	320	valid
0.0ms	2×	body	160	valid

simplify72.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	6
1	34	6
2	52	6
3	73	6
4	123	6
5	172	6
6	224	6
7	261	6
8	323	6
9	411	6
10	532	6
11	612	6
12	654	6
13	697	6
14	922	6
15	980	6
16	1007	6
17	1027	6
18	1035	6
19	1035	6

prune2.0ms

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: 15.6b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
0.4b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

58×	`*-un-lft-identity`
26×	`add-sqr-sqrt`
25×	`times-frac`
19×	`distribute-lft-out`
14×	`add-cube-cbrt`
6×	`distribute-lft-out--` `difference-of-squares`
5×	`associate-/r` `associate-/l`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
2×	`pow1` `flip3-+` `div-sub` `associate-/r/` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `associate-+l-` `flip3--` `frac-2neg` `div-exp` `clear-num` `sum-log` `flip--` `div-inv`

Counts

2 → 65

Calls

2 calls:

10.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
21.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series103.0ms

Counts

2 → 6

Calls

2 calls:

47.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
57.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify37.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	320	535
1	1022	510
2	5001	502

prune138.0ms

Filtered

71 candidates to 46 candidates (64.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	60	11	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	61	11	72

Merged error: 15.1b

Counts

72 → 11

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.0b	(/ beta (+ (+ alpha beta) 2.0))
0.4b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

71×	`*-un-lft-identity`
34×	`add-sqr-sqrt`
32×	`times-frac`
24×	`add-cube-cbrt` `distribute-lft-out`
11×	`add-log-exp`
10×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/l*`
4×	`pow1` `diff-log` `associate-/r/` `distribute-lft-out--` `difference-of-squares`
3×	`sub-neg` `flip3--` `flip--`
2×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `frac-sub` `flip-+` `div-inv` `associate--r+`
1×	`associate--r-`

Counts

4 → 111

Calls

4 calls:

27.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
8.0ms	(/ alpha (+ (+ alpha beta) 2.0))
7.0ms	(/ beta (+ (+ alpha beta) 2.0))
13.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series229.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
45.0ms	(/ alpha (+ (+ alpha beta) 2.0))
48.0ms	(/ beta (+ (+ alpha beta) 2.0))
76.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify52.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	450	903
1	1596	871
2	5002	859

prune238.0ms

Filtered

123 candidates to 83 candidates (67.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	115	8	123
Fresh	9	1	10
Picked	1	0	1
Done	0	0	0
Total	125	9	134

Merged error: 2.5b

Counts

134 → 9

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
0.1b	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
0.1b	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
0.4b	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

rewrite125.0ms

Algorithm

rewrite-expression-head

Rules

423×	`*-un-lft-identity`
238×	`times-frac`
189×	`add-sqr-sqrt`
162×	`distribute-lft-out`
119×	`add-cube-cbrt`
78×	`swap-sqr`
42×	`associate-r` `associate-l`
39×	`unpow-prod-down` `cube-prod`
31×	`add-exp-log` `add-cbrt-cube`
24×	`difference-of-squares`
20×	`associate-/r/`
19×	`pow1`
11×	`sqr-pow`
10×	`flip3-+` `flip-+` `div-inv`
9×	`cbrt-undiv` `div-exp`
8×	`prod-exp` `cbrt-unprod` `unswap-sqr`
6×	`add-log-exp`
5×	`distribute-lft-out--`
3×	`pow-unpow`
2×	`pow2` `frac-times` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `pow-exp` `pow-sqr` `*-commutative` `pow-prod-up` `rem-cube-cbrt`
1×	`difference-cubes` `cube-div` `cube-mult` `pow-to-exp` `sub-neg` `flip3--` `pow-pow` `diff-log` `unpow3` `flip--`

Counts

4 → 322

Calls

4 calls:

14.0ms	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
24.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
24.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
41.0ms	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

series296.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
61.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
61.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
106.0ms	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

simplify179.0ms

Algorithm

egg-herbie

Counts

334 → 334

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	835	3182
1	4729	2698
2	5001	2698

prune771.0ms

Filtered

334 candidates to 157 candidates (47.0%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	330	4	334
Fresh	5	3	8
Picked	1	0	1
Done	0	0	0
Total	336	7	343

Merged error: 2.4b

Counts

343 → 7

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
0.1b	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
0.1b	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
0.4b	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

rewrite129.0ms

Algorithm

rewrite-expression-head

Rules

423×	`*-un-lft-identity`
238×	`times-frac`
189×	`add-sqr-sqrt`
162×	`distribute-lft-out`
119×	`add-cube-cbrt`
78×	`swap-sqr`
42×	`associate-r` `associate-l`
39×	`unpow-prod-down` `cube-prod`
31×	`add-exp-log` `add-cbrt-cube`
24×	`difference-of-squares`
20×	`associate-/r/`
19×	`pow1`
11×	`sqr-pow`
10×	`flip3-+` `flip-+` `div-inv`
9×	`cbrt-undiv` `div-exp`
8×	`prod-exp` `cbrt-unprod` `unswap-sqr`
6×	`add-log-exp`
5×	`distribute-lft-out--`
3×	`pow-unpow`
2×	`pow2` `frac-times` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `pow-exp` `pow-sqr` `*-commutative` `pow-prod-up` `rem-cube-cbrt`
1×	`difference-cubes` `cube-div` `cube-mult` `pow-to-exp` `sub-neg` `flip3--` `pow-pow` `diff-log` `unpow3` `flip--`

Counts

4 → 322

Calls

4 calls:

11.0ms	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
24.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
29.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
38.0ms	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

series302.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
59.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
64.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
107.0ms	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

simplify180.0ms

Algorithm

egg-herbie

Counts

334 → 334

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	835	3182
1	4729	2698
2	5001	2698

prune879.0ms

Filtered

334 candidates to 157 candidates (47.0%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	333	1	334
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	334	7	341

Merged error: 2.4b

Counts

341 → 7

regimes114.0ms

Accuracy

71.1% (3.7b remaining)

Error of 6.7b against oracle of 3.0b and baseline of 15.8b

bsearch63.0ms

Steps

Iters	Range		Point
7	9.743550080344205e+42	5.715496464363292e+44	1.5731281446950922e+43

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	67	66
1	67	66

end0.0ms

sample745.0ms

Algorithm

intervals

Results

196.0ms	5841×	body	80	valid
129.0ms	8000×	pre	80	true
127.0ms	811×	body	1280	valid
97.0ms	760×	body	640	valid
36.0ms	385×	body	320	valid
13.0ms	203×	body	160	valid