Details

sample27.0ms

Algorithm

intervals

Results

6.0ms	197×	body	80	valid
4.0ms	256×	pre	80	true
3.0ms	22×	body	1280	valid
2.0ms	20×	body	640	valid
1.0ms	12×	body	320	valid
0.0ms	5×	body	160	valid

simplify75.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 14.1b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
1.7b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite30.0ms

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))
18.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series114.0ms

Counts

2 → 6

Calls

2 calls:

50.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
63.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify38.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (30.0ms)

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

prune145.0ms

Filtered

71 candidates to 46 candidates (64.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	59	12	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	60	12	72

Merged error: 13.5b

Counts

72 → 12

localize10.0ms

Local error

Found 3 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))
1.7b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

40×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
17×	`times-frac`
13×	`add-cube-cbrt`
12×	`distribute-lft-out`
10×	`add-log-exp`
5×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
4×	`diff-log` `distribute-lft-out--` `difference-of-squares`
3×	`pow1` `sub-neg` `flip3--` `flip--` `associate-/l*`
2×	`associate-/r/` `frac-sub` `associate--r+`
1×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `div-inv` `associate--r-`

Counts

3 → 74

Calls

3 calls:

30.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
7.0ms	(/ alpha (+ (+ alpha beta) 2.0))
13.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series184.0ms

Counts

3 → 9

Calls

3 calls:

62.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
44.0ms	(/ alpha (+ (+ alpha beta) 2.0))
78.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify41.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	388	687
1	1334	662
2	5001	648

prune169.0ms

Filtered

83 candidates to 58 candidates (69.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	78	5	83
Fresh	10	1	11
Picked	1	0	1
Done	0	0	0
Total	89	6	95

Merged error: 2.3b

Counts

95 → 6

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
0.0b	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
0.1b	(/ (- (* beta (+ (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (+ (* 1.0 1.0) (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))) (* (+ (+ alpha beta) 2.0) (- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3)))) (* (+ (* 1.0 (+ 1.0 (/ alpha (+ (+ alpha beta) 2.0)))) (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))) (+ (+ alpha beta) 2.0)))
1.7b	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

rewrite180.0ms

Algorithm

rewrite-expression-head

Rules

376×	`*-un-lft-identity`
211×	`times-frac`
172×	`add-sqr-sqrt`
144×	`distribute-lft-out`
124×	`associate-*r/`
102×	`add-cube-cbrt`
85×	`flip3-+` `flip-+`
78×	`swap-sqr`
72×	`frac-times`
66×	`frac-add` `associate-/l/`
64×	`frac-sub`
48×	`associate-*l/`
42×	`associate-r` `associate-l` `associate-/r/`
33×	`add-exp-log` `add-cbrt-cube`
26×	`flip3--` `flip--`
24×	`difference-of-squares`
18×	`pow1` `unpow-prod-down` `cube-prod`
10×	`cbrt-undiv` `div-exp` `sqr-pow`
9×	`prod-exp` `cbrt-unprod` `div-inv`
8×	`unswap-sqr`
6×	`add-log-exp`
5×	`distribute-lft-out--`
3×	`associate-/l*`
2×	`pow2` `pow-plus` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up`
1×	`difference-cubes` `sub-neg` `frac-2neg` `diff-log` `div-sub` `clear-num` `associate-/r*`

Counts

4 → 374

Calls

4 calls:

30.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
24.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
59.0ms	(/ (- (* beta (+ (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (+ (* 1.0 1.0) (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))) (* (+ (+ alpha beta) 2.0) (- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3)))) (* (+ (* 1.0 (+ 1.0 (/ alpha (+ (+ alpha beta) 2.0)))) (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))) (+ (+ alpha beta) 2.0)))
38.0ms	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

series627.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
63.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
389.0ms	(/ (- (* beta (+ (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (+ (* 1.0 1.0) (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))) (* (+ (+ alpha beta) 2.0) (- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3)))) (* (+ (* 1.0 (+ 1.0 (/ alpha (+ (+ alpha beta) 2.0)))) (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))) (+ (+ alpha beta) 2.0)))
116.0ms	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

simplify124.0ms

Algorithm

egg-herbie

Counts

386 → 386

Iterations

Useful iterations: 1 (41.0ms)

Iter	Nodes	Cost
0	1906	8492
1	5002	8140

prune1.6s

Filtered

386 candidates to 236 candidates (61.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	384	2	386
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	387	5	392

Merged error: 2.3b

Counts

392 → 5

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
0.0b	(/ alpha (+ (+ alpha beta) 2.0))
1.7b	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
1.7b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

43×	`*-un-lft-identity`
32×	`add-sqr-sqrt`
18×	`times-frac`
17×	`add-cube-cbrt`
12×	`exp-prod` `distribute-lft-out`
9×	`add-log-exp`
7×	`log-pow`
6×	`add-exp-log` `add-cbrt-cube` `difference-of-squares`
5×	`pow1` `log-prod` `associate-/r*`
4×	`exp-sum`
3×	`sub-neg` `associate-/l*` `distribute-lft-out--`
2×	`exp-diff` `diff-log` `associate-/r/` `rem-exp-log`
1×	`cbrt-undiv` `log-div` `flip3--` `frac-2neg` `flip3-+` `div-exp` `rem-log-exp` `clear-num` `flip--` `flip-+` `div-inv`

Counts

4 → 91

Calls

4 calls:

13.0ms	(exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
12.0ms	(/ alpha (+ (+ alpha beta) 2.0))
14.0ms	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
13.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series272.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
44.0ms	(/ alpha (+ (+ alpha beta) 2.0))
77.0ms	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
78.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify139.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	325	652
1	1064	606
2	4504	591
3	5001	591

prune200.0ms

Filtered

103 candidates to 72 candidates (69.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	103	0	103
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	103	5	108

Merged error: 2.3b

Counts

108 → 5

regimes130.0ms

Accuracy

98.8% (0.1b remaining)

Error of 3.1b against oracle of 2.9b and baseline of 15.3b

bsearch2.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	28
1	35	28

end0.0ms

sample746.0ms

Algorithm

intervals

Results

190.0ms	5903×	body	80	valid
133.0ms	801×	body	1280	valid
124.0ms	8000×	pre	80	true
91.0ms	696×	body	640	valid
37.0ms	394×	body	320	valid
13.0ms	206×	body	160	valid

Details

sample27.0ms

simplify75.0ms

prune2.0ms

localize8.0ms

rewrite30.0ms

series114.0ms

simplify38.0ms

prune145.0ms

localize10.0ms

rewrite53.0ms

series184.0ms

simplify41.0ms

prune169.0ms

localize24.0ms

rewrite180.0ms

series627.0ms

simplify124.0ms

prune1.6s

localize13.0ms

rewrite55.0ms

series272.0ms

simplify139.0ms

prune200.0ms

regimes130.0ms

bsearch2.0ms

simplify1.0ms

end0.0ms

sample746.0ms

Profiling