Details

sample24.0ms

Algorithm

intervals

Results

5.0ms	181×	body	80	valid
4.0ms	31×	body	1280	valid
3.0ms	256×	pre	80	true
2.0ms	23×	body	640	valid
1.0ms	13×	body	320	valid
0.0ms	8×	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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.5b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
2.7b	(+ (/ (- 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)

series113.0ms

Counts

2 → 6

Calls

2 calls:

50.0ms	(/ (- 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 (30.0ms)

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

prune156.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 16.6b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.0b	(/ beta (+ (+ alpha beta) 2.0))
2.7b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 137

Calls

4 calls:

28.0ms	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
7.0ms	(/ alpha (+ (+ alpha beta) 2.0))
7.0ms	(/ beta (+ (+ alpha beta) 2.0))
13.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series240.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
49.0ms	(/ alpha (+ (+ alpha beta) 2.0))
52.0ms	(/ beta (+ (+ alpha beta) 2.0))
77.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify57.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	544	1336
1	1910	1268
2	5001	1268

prune369.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.6b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (+ (+ alpha beta) 2.0))
0.0b	(/ beta (+ (+ alpha beta) 2.0))
0.1b	(* alpha (/ 1 (+ (+ alpha beta) 2.0)))
5.1b	(- (* alpha (/ 1 (+ (+ alpha beta) 2.0))) 1.0)

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

90×	`*-un-lft-identity`
47×	`times-frac`
41×	`add-sqr-sqrt`
34×	`add-cube-cbrt`
33×	`distribute-lft-out`
21×	`associate-r`
19×	`add-exp-log`
13×	`add-cbrt-cube`
10×	`associate-/r*`
7×	`pow1`
6×	`associate-/r/` `associate-/l*` `add-log-exp`
5×	`div-exp`
4×	`prod-exp`
3×	`cbrt-undiv` `flip3-+` `associate-l` `flip-+` `div-inv` `unswap-sqr`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num` `cbrt-unprod`
1×	`sub-neg` `flip3--` `pow-flip` `diff-log` `associate-r/` `pow-prod-down` `un-div-inv` `-commutative` `flip--` `inv-pow`

Counts

4 → 134

Calls

4 calls:

8.0ms	(/ 1 (+ (+ alpha beta) 2.0))
7.0ms	(/ beta (+ (+ alpha beta) 2.0))
13.0ms	(* alpha (/ 1 (+ (+ alpha beta) 2.0)))
10.0ms	(- (* alpha (/ 1 (+ (+ alpha beta) 2.0))) 1.0)

series218.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(/ 1 (+ (+ alpha beta) 2.0))
45.0ms	(/ beta (+ (+ alpha beta) 2.0))
52.0ms	(* alpha (/ 1 (+ (+ alpha beta) 2.0)))
79.0ms	(- (* alpha (/ 1 (+ (+ alpha beta) 2.0))) 1.0)

simplify54.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	436	818
1	1801	737
2	5002	682

prune290.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.6b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (+ (+ alpha beta) 2.0))
0.1b	(* alpha (/ 1 (+ (+ alpha beta) 2.0)))
0.1b	(* beta (/ 1 (+ (+ alpha beta) 2.0)))
5.1b	(- (* alpha (/ 1 (+ (+ alpha beta) 2.0))) 1.0)

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

86×	`*-un-lft-identity`
49×	`times-frac`
48×	`add-sqr-sqrt`
42×	`associate-r`
34×	`add-cube-cbrt`
30×	`distribute-lft-out`
26×	`add-exp-log`
16×	`add-cbrt-cube`
9×	`pow1`
8×	`prod-exp`
6×	`div-exp` `associate-l` `associate-/r/` `add-log-exp` `unswap-sqr`
5×	`associate-/r*`
4×	`cbrt-unprod`
3×	`cbrt-undiv` `rec-exp` `flip3-+` `1-exp` `flip-+` `div-inv` `associate-/l*`
2×	`associate-r/` `pow-prod-down` `un-div-inv` `-commutative`
1×	`sub-neg` `flip3--` `pow-flip` `frac-2neg` `diff-log` `clear-num` `flip--` `inv-pow`

Counts

4 → 141

Calls

4 calls:

7.0ms	(/ 1 (+ (+ alpha beta) 2.0))
12.0ms	(* alpha (/ 1 (+ (+ alpha beta) 2.0)))
18.0ms	(* beta (/ 1 (+ (+ alpha beta) 2.0)))
11.0ms	(- (* alpha (/ 1 (+ (+ alpha beta) 2.0))) 1.0)

series213.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(/ 1 (+ (+ alpha beta) 2.0))
52.0ms	(* alpha (/ 1 (+ (+ alpha beta) 2.0)))
46.0ms	(* beta (/ 1 (+ (+ alpha beta) 2.0)))
81.0ms	(- (* alpha (/ 1 (+ (+ alpha beta) 2.0))) 1.0)

simplify65.0ms

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	484	844
1	2126	735
2	5001	665

prune280.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.6b

regimes96.0ms

Accuracy

76.9% (2.9b remaining)

Error of 6.0b against oracle of 3.1b and baseline of 15.6b

bsearch56.0ms

Steps

Iters	Range		Point
8	344508661.55183023	2634376859814.122	77515147515.86223

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	27
1	44	27

end0.0ms

sample615.0ms

Algorithm

intervals

Results

153.0ms	5870×	body	80	valid
114.0ms	861×	body	1280	valid
96.0ms	8000×	pre	80	true
70.0ms	690×	body	640	valid
30.0ms	401×	body	320	valid
9.0ms	178×	body	160	valid