Details

sample24.0ms

Algorithm

intervals

Results

5.0ms	182×	body	80	valid
4.0ms	31×	body	1280	valid
3.0ms	256×	pre	80	true
2.0ms	24×	body	640	valid
1.0ms	13×	body	320	valid
0.0ms	6×	body	160	valid

simplify73.0ms

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: 17.3b

Counts

2 → 1

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
1.5b	(+ (/ (- 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)

series106.0ms

Counts

2 → 6

Calls

2 calls:

43.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
63.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify37.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (29.0ms)

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

prune156.0ms

Filtered

71 candidates to 46 candidates (64.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	58	13	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	59	13	72

Merged error: 16.5b

Counts

72 → 13

localize9.0ms

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))
1.5b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite62.0ms

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:

26.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
8.0ms	(/ alpha (+ (+ alpha beta) 2.0))
11.0ms	(/ beta (+ (+ alpha beta) 2.0))
13.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series231.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
49.0ms	(/ alpha (+ (+ alpha beta) 2.0))
44.0ms	(/ beta (+ (+ alpha beta) 2.0))
76.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify48.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (37.0ms)

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

prune298.0ms

Filtered

123 candidates to 84 candidates (68.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	114	9	123
Fresh	12	0	12
Picked	1	0	1
Done	0	0	0
Total	127	9	136

Merged error: 3.7b

Counts

136 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ beta (+ (+ alpha beta) 2.0))
0.0b	(exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
1.5b	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
1.5b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite54.0ms

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:

7.0ms	(/ beta (+ (+ alpha beta) 2.0))
14.0ms	(exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
17.0ms	(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:

45.0ms	(/ beta (+ (+ alpha beta) 2.0))
72.0ms	(exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
76.0ms	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
79.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify137.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	347	660
1	1103	606
2	4865	589
3	5002	589

prune269.0ms

Filtered

103 candidates to 73 candidates (70.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	98	5	103
Fresh	5	3	8
Picked	1	0	1
Done	0	0	0
Total	104	8	112

Merged error: 3.7b

Counts

112 → 8

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
0.1b	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
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)))
1.4b	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

rewrite165.0ms

Algorithm

rewrite-expression-head

Rules

245×	`*-un-lft-identity`
141×	`times-frac`
131×	`add-sqr-sqrt`
123×	`associate-*r/`
90×	`distribute-lft-out`
83×	`flip3-+` `flip-+`
73×	`add-cube-cbrt`
71×	`frac-times`
66×	`frac-add` `associate-/l/`
64×	`frac-sub`
47×	`associate-*l/`
39×	`unpow-prod-down` `cube-prod` `swap-sqr`
38×	`associate-/r/`
26×	`flip3--` `flip--`
24×	`add-exp-log` `add-cbrt-cube` `difference-of-squares`
21×	`associate-r` `associate-l`
12×	`pow1`
11×	`sqr-pow`
7×	`cbrt-undiv` `div-exp` `div-inv`
6×	`add-log-exp`
5×	`prod-exp` `cbrt-unprod` `distribute-lft-out--`
4×	`unswap-sqr`
3×	`pow-unpow` `associate-/l*`
2×	`pow-exp` `rem-cube-cbrt`
1×	`difference-cubes` `cube-div` `pow2` `cube-mult` `pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `pow-plus` `diff-log` `unpow3` `div-sub` `pow-prod-down` `clear-num` `associate-/r` `pow-sqr` `-commutative` `pow-prod-up`

Counts

4 → 327

Calls

4 calls:

24.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
10.0ms	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
61.0ms	(/ (- (* 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)))
45.0ms	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

series624.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
73.0ms	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
379.0ms	(/ (- (* 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)))
111.0ms	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

simplify116.0ms

Algorithm

egg-herbie

Counts

339 → 339

Iterations

Useful iterations: 1 (45.0ms)

Iter	Nodes	Cost
0	2085	7822
1	5002	7442

prune1.6s

Filtered

339 candidates to 212 candidates (62.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	337	2	339
Fresh	5	2	7
Picked	1	0	1
Done	0	0	0
Total	343	4	347

Merged error: 3.7b

Counts

347 → 4

regimes70.0ms

Accuracy

67.6% (4.0b remaining)

Error of 7.2b against oracle of 3.1b and baseline of 15.6b

bsearch184.0ms

Steps

Iters	Range		Point
8	5.172961417222266e+65	1.3104433616643962e+70	5.293664998180793e+65
6	1.5865537497029128e+52	2.265641445575101e+53	1.138060537537574e+53
9	4.643958454173516e+32	3.261941379769491e+39	1.6980902612943045e+38

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	79	133
1	82	133
2	82	133

end0.0ms

sample637.0ms

Algorithm

intervals

Results

167.0ms	5860×	body	80	valid
110.0ms	857×	body	1280	valid
102.0ms	8000×	pre	80	true
73.0ms	694×	body	640	valid
29.0ms	384×	body	320	valid
10.0ms	205×	body	160	valid