Details

sample21.0ms

Algorithm

intervals

Results

5.0ms	207×	body	80	valid
3.0ms	256×	pre	80	true
2.0ms	18×	body	1280	valid
2.0ms	17×	body	640	valid
1.0ms	7×	body	320	valid
0.0ms	7×	body	160	valid

simplify71.0ms

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: 11.2b

localize8.0ms

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)

rewrite111.0ms

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:

24.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
84.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series105.0ms

Counts

2 → 6

Calls

2 calls:

48.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
57.0ms	(+ (/ (- 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

prune152.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 10.9b

localize9.0ms

Local error

Found 3 expressions with local error:

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

rewrite137.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 89

Calls

3 calls:

18.0ms	(/ alpha (+ (+ alpha beta) 2.0))
20.0ms	(/ beta (+ (+ alpha beta) 2.0))
96.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series171.0ms

Counts

3 → 9

Calls

3 calls:

49.0ms	(/ alpha (+ (+ alpha beta) 2.0))
44.0ms	(/ beta (+ (+ alpha beta) 2.0))
77.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify149.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	328	582
1	1072	553
2	4888	544
3	5001	544

prune226.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 1.4b

localize20.0ms

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

rewrite121.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

8.0ms	(cbrt (+ (+ alpha beta) 2.0))
8.0ms	(cbrt (+ (+ alpha beta) 2.0))
9.0ms	(cbrt (+ (+ alpha beta) 2.0))
94.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series373.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(cbrt (+ (+ alpha beta) 2.0))
99.0ms	(cbrt (+ (+ alpha beta) 2.0))
98.0ms	(cbrt (+ (+ alpha beta) 2.0))
76.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify67.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (60.0ms)

Iter	Nodes	Cost
0	278	567
1	708	537
2	2658	521
3	5001	512

prune260.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 1.4b

localize21.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (+ (+ alpha beta) 2.0))
0.7b	(cbrt (+ (+ alpha beta) 2.0))
1.5b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
2.5b	(pow (+ (+ alpha beta) 2.0) 1/3)

rewrite137.0ms

Algorithm

rewrite-expression-head

Rules

25×	`*-un-lft-identity`
13×	`add-sqr-sqrt`
10×	`cbrt-prod`
9×	`distribute-lft-out`
8×	`add-cube-cbrt`
6×	`add-log-exp`
5×	`pow1` `add-exp-log` `unpow-prod-down`
4×	`cbrt-div` `add-cbrt-cube`
3×	`pow-unpow`
2×	`flip3-+` `pow1/3` `flip-+` `difference-of-squares`
1×	`pow-to-exp` `sub-neg` `flip3--` `pow-pow` `times-frac` `unpow1/3` `diff-log` `pow-exp` `flip--` `distribute-lft-out--` `sqr-pow`

Counts

4 → 65

Calls

4 calls:

8.0ms	(cbrt (+ (+ alpha beta) 2.0))
8.0ms	(cbrt (+ (+ alpha beta) 2.0))
98.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
20.0ms	(pow (+ (+ alpha beta) 2.0) 1/3)

series378.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(cbrt (+ (+ alpha beta) 2.0))
100.0ms	(cbrt (+ (+ alpha beta) 2.0))
80.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
100.0ms	(pow (+ (+ alpha beta) 2.0) 1/3)

simplify105.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (26.0ms)

Iter	Nodes	Cost
0	326	549
1	971	504
2	4014	488
3	5002	488

prune281.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 1.4b

regimes67.0ms

Accuracy

72.9% (4.0b remaining)

Error of 6.7b against oracle of 2.7b and baseline of 17.3b

bsearch58.0ms

Steps

Iters	Range		Point
9	5.840411952416047	26520870.86331656	7498507.783475389

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	41
1	44	41

end0.0ms

sample610.0ms

Algorithm

intervals

Results

153.0ms	5830×	body	80	valid
110.0ms	872×	body	1280	valid
91.0ms	8000×	pre	80	true
78.0ms	706×	body	640	valid
29.0ms	394×	body	320	valid
10.0ms	198×	body	160	valid