Details

sample23.0ms

Algorithm

intervals

Results

5.0ms	194×	body	80	valid
3.0ms	27×	body	1280	valid
3.0ms	256×	pre	80	true
2.0ms	16×	body	640	valid
1.0ms	11×	body	320	valid
0.0ms	8×	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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.7b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
2.6b	(+ (/ (- 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))
17.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series115.0ms

Counts

2 → 6

Calls

2 calls:

47.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
67.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify35.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (28.0ms)

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

prune285.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 14.0b

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))
2.6b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite60.0ms

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:

8.0ms	(/ alpha (+ (+ alpha beta) 2.0))
29.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
7.0ms	(/ beta (+ (+ alpha beta) 2.0))
13.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series244.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(/ alpha (+ (+ alpha beta) 2.0))
64.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
48.0ms	(/ beta (+ (+ alpha beta) 2.0))
82.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify46.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (35.0ms)

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

prune276.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 2.8b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0)) (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
0.0b	(/ beta (+ (+ alpha beta) 2.0))
0.0b	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
2.6b	(- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0))

rewrite92.0ms

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:

31.0ms	(/ (- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0)) (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
7.0ms	(/ beta (+ (+ alpha beta) 2.0))
27.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
17.0ms	(- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0))

series347.0ms

Counts

4 → 12

Calls

4 calls:

134.0ms	(/ (- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0)) (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
52.0ms	(/ beta (+ (+ alpha beta) 2.0))
64.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
96.0ms	(- (* (/ 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

prune455.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 2.8b

localize25.0ms

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)))
0.0b	(pow (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) 3)
2.6b	(- (pow (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) 3) (pow (* 1.0 1.0) 3))

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

367×	`*-un-lft-identity`
200×	`times-frac`
144×	`distribute-lft-out`
133×	`add-sqr-sqrt`
101×	`add-cube-cbrt`
78×	`swap-sqr`
42×	`associate-r` `associate-l`
41×	`add-exp-log` `add-cbrt-cube`
26×	`pow1`
16×	`associate-/r/` `difference-of-squares`
12×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
9×	`unpow-prod-down` `cube-prod` `sqr-pow`
8×	`flip3-+` `flip-+` `div-inv` `unswap-sqr`
6×	`pow-pow` `add-log-exp`
5×	`pow-exp` `rem-cube-cbrt`
3×	`cube-div` `pow2` `frac-times` `pow-unpow` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
2×	`*-commutative`
1×	`difference-cubes` `cube-mult` `pow-to-exp` `sub-neg` `flip3--` `diff-log` `unpow3` `flip--` `distribute-lft-out--`

Counts

4 → 283

Calls

4 calls:

27.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
29.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
18.0ms	(pow (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) 3)
9.0ms	(- (pow (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) 3) (pow (* 1.0 1.0) 3))

series353.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
62.0ms	(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
109.0ms	(pow (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) 3)
118.0ms	(- (pow (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) 3) (pow (* 1.0 1.0) 3))

simplify131.0ms

Algorithm

egg-herbie

Counts

295 → 295

Iterations

Useful iterations: 2 (96.0ms)

Iter	Nodes	Cost
0	727	2938
1	3434	2656
2	5001	2568

prune909.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 2.7b

regimes94.0ms

Accuracy

77% (3.0b remaining)

Error of 6.0b against oracle of 3.1b and baseline of 16.0b

bsearch61.0ms

Steps

Iters	Range		Point
7	99314083682.35872	1732166801363.969	410714263654.7934

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	60	66
1	60	66

end0.0ms

sample615.0ms

Algorithm

intervals

Results

150.0ms	5813×	body	80	valid
109.0ms	886×	body	1280	valid
97.0ms	8000×	pre	80	true
74.0ms	704×	body	640	valid
29.0ms	395×	body	320	valid
10.0ms	202×	body	160	valid