Details

sample23.0ms

Algorithm

intervals

Results

4.0ms	188×	body	80	valid
3.0ms	30×	body	1280	valid
3.0ms	256×	pre	80	true
2.0ms	18×	body	640	valid
1.0ms	16×	body	320	valid
0.0ms	4×	body	160	valid

simplify75.0ms

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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.8b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
1.1b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite114.0ms

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:

25.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
86.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series107.0ms

Counts

2 → 6

Calls

2 calls:

49.0ms	(/ (- 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

prune154.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 15.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.0b	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
0.0b	(/ beta (+ (+ alpha beta) 2.0))
1.1b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite354.0ms

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:

17.0ms	(/ alpha (+ (+ alpha beta) 2.0))
218.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
19.0ms	(/ beta (+ (+ alpha beta) 2.0))
95.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series231.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(/ alpha (+ (+ alpha beta) 2.0))
62.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
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

prune287.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ beta (+ (+ alpha beta) 2.0))
0.0b	(/ (- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0)) (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
0.1b	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
1.1b	(- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0))

rewrite291.0ms

Algorithm

rewrite-expression-head

Rules

234×	`*-un-lft-identity`
131×	`times-frac`
89×	`distribute-lft-out`
84×	`add-sqr-sqrt`
72×	`add-cube-cbrt`
39×	`swap-sqr`
21×	`associate-r` `associate-l`
20×	`add-exp-log` `add-cbrt-cube`
12×	`associate-/r/`
11×	`pow1`
9×	`associate-/r*`
7×	`associate-/l*`
6×	`cbrt-undiv` `flip3-+` `div-exp` `flip-+` `div-inv` `add-log-exp` `difference-of-squares`
4×	`prod-exp` `cbrt-unprod` `unswap-sqr`
2×	`flip3--` `frac-2neg` `clear-num` `flip--` `associate-/l/`
1×	`pow2` `frac-times` `sub-neg` `pow-plus` `diff-log` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `*-commutative` `pow-prod-up`

Counts

4 → 200

Calls

4 calls:

18.0ms	(/ beta (+ (+ alpha beta) 2.0))
151.0ms	(/ (- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0)) (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
84.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
26.0ms	(- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0))

series330.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(/ beta (+ (+ alpha beta) 2.0))
133.0ms	(/ (- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0)) (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
62.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
90.0ms	(- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0))

simplify119.0ms

Algorithm

egg-herbie

Counts

212 → 212

Iterations

Useful iterations: 2 (96.0ms)

Iter	Nodes	Cost
0	825	2427
1	4052	2191
2	5001	2151

prune458.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.5b

localize22.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (+ (+ alpha beta) 2.0))
0.7b	(cbrt (+ (+ alpha beta) 2.0))
0.7b	(cbrt (+ (+ alpha beta) 2.0))
1.1b	(- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
15×	`cbrt-prod`
9×	`distribute-lft-out`
7×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`cbrt-div` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`flip3-+` `pow1/3` `flip-+`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `difference-of-squares`

Counts

4 → 58

Calls

4 calls:

8.0ms	(cbrt (+ (+ alpha beta) 2.0))
11.0ms	(cbrt (+ (+ alpha beta) 2.0))
8.0ms	(cbrt (+ (+ alpha beta) 2.0))
23.0ms	(- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0))

series386.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(cbrt (+ (+ alpha beta) 2.0))
98.0ms	(cbrt (+ (+ alpha beta) 2.0))
99.0ms	(cbrt (+ (+ alpha beta) 2.0))
91.0ms	(- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0))

simplify84.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (23.0ms)

Iter	Nodes	Cost
0	293	637
1	865	587
2	3379	563
3	5002	563

prune297.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.5b

regimes109.0ms

Accuracy

70.5% (3.8b remaining)

Error of 6.8b against oracle of 3.1b and baseline of 15.8b

bsearch52.0ms

Steps

Iters	Range		Point
7	1.2675713909696286e+39	2.5917733915296634e+41	1.2077500397799626e+40

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	42
1	50	42

end0.0ms

sample571.0ms

Algorithm

intervals

Results

139.0ms	5836×	body	80	valid
97.0ms	833×	body	1280	valid
92.0ms	8000×	pre	80	true
70.0ms	725×	body	640	valid
28.0ms	424×	body	320	valid
8.0ms	182×	body	160	valid