Details

sample25.0ms

Algorithm

intervals

Results

5.0ms	192×	body	80	valid
4.0ms	32×	body	1280	valid
3.0ms	256×	pre	80	true
2.0ms	17×	body	640	valid
1.0ms	8×	body	320	valid
0.0ms	7×	body	160	valid

simplify69.0ms

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
done	1035	6

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.8b

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
2.5b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite196.0ms

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:

45.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
149.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series113.0ms

Counts

2 → 6

Calls

2 calls:

47.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
66.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify34.0ms

Counts

71 → 71

Iterations

Useful iterations: 2 (28.0ms)

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

prune147.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 14.1b

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))
2.5b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite639.0ms

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:

392.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
35.0ms	(/ alpha (+ (+ alpha beta) 2.0))
34.0ms	(/ beta (+ (+ alpha beta) 2.0))
174.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series242.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
51.0ms	(/ alpha (+ (+ alpha beta) 2.0))
52.0ms	(/ beta (+ (+ alpha beta) 2.0))
77.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify46.0ms

Counts

123 → 123

Iterations

Useful iterations: 2 (36.0ms)

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

prune291.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 2.4b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3)) (+ (* (/ alpha (+ (+ alpha beta) 2.0)) (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) (* 1.0 1.0)))
0.0b	(/ beta (+ (+ alpha beta) 2.0))
0.1b	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
2.5b	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

rewrite1.5s

Algorithm

rewrite-expression-head

Rules

301×	`add-sqr-sqrt`
184×	`times-frac`
171×	`*-un-lft-identity`
120×	`difference-of-squares`
111×	`unpow-prod-down` `cube-prod`
71×	`add-cube-cbrt`
51×	`sqr-pow`
36×	`associate-/l*`
30×	`distribute-lft-out`
25×	`distribute-lft-out--`
11×	`add-exp-log` `add-cbrt-cube`
8×	`associate-/r*` `associate-/r/`
6×	`add-log-exp`
5×	`pow1` `difference-cubes`
4×	`flip3-+` `flip-+` `div-inv`
3×	`cbrt-undiv` `pow-unpow` `div-exp`
2×	`flip3--` `frac-2neg` `pow-exp` `clear-num` `flip--` `associate-/l/` `rem-cube-cbrt`
1×	`cube-div` `cube-mult` `pow-to-exp` `sub-neg` `pow-pow` `diff-log` `unpow3` `div-sub`

Counts

4 → 293

Calls

4 calls:

973.0ms	(/ (- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3)) (+ (* (/ alpha (+ (+ alpha beta) 2.0)) (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) (* 1.0 1.0)))
36.0ms	(/ beta (+ (+ alpha beta) 2.0))
38.0ms	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
386.0ms	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

series428.0ms

Counts

4 → 12

Calls

4 calls:

185.0ms	(/ (- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3)) (+ (* (/ alpha (+ (+ alpha beta) 2.0)) (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) (* 1.0 1.0)))
51.0ms	(/ beta (+ (+ alpha beta) 2.0))
76.0ms	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
115.0ms	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

simplify157.0ms

Counts

305 → 305

Iterations

Useful iterations: 2 (107.0ms)

Iter	Nodes	Cost
0	1003	6132
1	4224	5953
2	5001	5877
done	5001	5877

prune716.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 2.4b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
0.1b	(pow (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) 3)
0.1b	(pow (/ alpha (+ (+ alpha beta) 2.0)) 6)
2.5b	(- (pow (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) 3) (pow (pow 1.0 3) 3))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

352×	`unpow-prod-down`
331×	`cube-prod`
320×	`add-sqr-sqrt`
219×	`*-un-lft-identity`
145×	`times-frac`
140×	`difference-of-squares`
77×	`sqr-pow`
72×	`add-cube-cbrt`
63×	`distribute-lft-out`
21×	`distribute-lft-out--`
14×	`add-exp-log` `associate-/r/`
10×	`pow-exp`
9×	`pow-unpow`
8×	`add-cbrt-cube`
7×	`flip3-+` `flip-+` `div-inv`
6×	`pow1` `add-log-exp`
4×	`cube-mult` `pow-to-exp` `unpow3`
3×	`cube-div` `pow-pow` `div-exp` `rem-cube-cbrt`
1×	`difference-cubes` `cbrt-undiv` `sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 389

Calls

4 calls:

39.0ms	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
78.0ms	(pow (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) 3)
38.0ms	(pow (/ alpha (+ (+ alpha beta) 2.0)) 6)
897.0ms	(- (pow (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) 3) (pow (pow 1.0 3) 3))

series428.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
124.0ms	(pow (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) 3)
98.0ms	(pow (/ alpha (+ (+ alpha beta) 2.0)) 6)
126.0ms	(- (pow (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) 3) (pow (pow 1.0 3) 3))

simplify195.0ms

Counts

401 → 401

Iterations

Useful iterations: 2 (139.0ms)

Iter	Nodes	Cost
0	1006	5047
1	4543	4796
2	5002	4704
done	5002	4704

prune934.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 2.4b

regimes164.0ms

Accuracy

97.5% (0.3b remaining)

Error of 3.4b against oracle of 3.1b and baseline of 15.2b

bsearch2.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	30
1	43	30
done	43	30

end0.0ms

sample637.0ms

Algorithm

intervals

Results

143.0ms	5909×	body	80	valid
99.0ms	775×	body	1280	valid
90.0ms	8000×	pre	80	true
74.0ms	713×	body	640	valid
29.0ms	399×	body	320	valid
10.0ms	204×	body	160	valid