Details

sample24.0ms

Algorithm

intervals

Results

5.0ms	203×	body	80	valid
4.0ms	256×	pre	80	true
3.0ms	21×	body	1280	valid
1.0ms	15×	body	640	valid
1.0ms	13×	body	320	valid
0.0ms	4×	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: 12.5b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
1.6b	(+ (/ (- 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)

series107.0ms

Counts

2 → 6

Calls

2 calls:

49.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
58.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify36.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (29.0ms)

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

prune157.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 11.9b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.0b	(/ beta (+ (+ alpha beta) 2.0))
1.6b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite134.0ms

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:

17.0ms	(/ alpha (+ (+ alpha beta) 2.0))
19.0ms	(/ beta (+ (+ alpha beta) 2.0))
94.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series175.0ms

Counts

3 → 9

Calls

3 calls:

53.0ms	(/ alpha (+ (+ alpha beta) 2.0))
44.0ms	(/ beta (+ (+ alpha beta) 2.0))
78.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify157.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (28.0ms)

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

prune370.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.6b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.0b	(/ beta (+ (+ alpha beta) 2.0))
0.1b	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
1.6b	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

rewrite294.0ms

Algorithm

rewrite-expression-head

Rules

123×	`*-un-lft-identity`
89×	`add-sqr-sqrt`
68×	`times-frac`
43×	`add-cube-cbrt`
42×	`distribute-lft-out`
39×	`unpow-prod-down` `cube-prod`
24×	`difference-of-squares`
11×	`add-exp-log` `add-cbrt-cube` `sqr-pow`
10×	`associate-/r*`
8×	`associate-/r/`
6×	`associate-/l*` `add-log-exp`
5×	`pow1` `distribute-lft-out--`
4×	`flip3-+` `flip-+` `div-inv`
3×	`cbrt-undiv` `pow-unpow` `div-exp`
2×	`frac-2neg` `pow-exp` `clear-num` `rem-cube-cbrt`
1×	`difference-cubes` `cube-div` `cube-mult` `pow-to-exp` `sub-neg` `flip3--` `pow-pow` `diff-log` `unpow3` `flip--`

Counts

4 → 178

Calls

4 calls:

19.0ms	(/ alpha (+ (+ alpha beta) 2.0))
17.0ms	(/ beta (+ (+ alpha beta) 2.0))
20.0ms	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
230.0ms	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

series289.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(/ alpha (+ (+ alpha beta) 2.0))
44.0ms	(/ beta (+ (+ alpha beta) 2.0))
92.0ms	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
107.0ms	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

simplify88.0ms

Algorithm

egg-herbie

Counts

190 → 190

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	655	1491
1	2823	1393
2	5001	1368

prune463.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 2.6b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ beta (+ (+ alpha beta) 2.0))
0.1b	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
1.2b	(log (exp (pow (/ alpha (+ (+ alpha beta) 2.0)) 3)))
1.6b	(- (log (exp (pow (/ alpha (+ (+ alpha beta) 2.0)) 3))) (pow 1.0 3))

rewrite818.0ms

Algorithm

rewrite-expression-head

Rules

137×	`*-un-lft-identity`
75×	`times-frac`
61×	`add-sqr-sqrt`
54×	`add-cube-cbrt`
50×	`log-pow`
48×	`exp-prod` `distribute-lft-out`
43×	`unpow-prod-down` `cube-prod`
10×	`associate-/r/`
9×	`add-exp-log` `add-cbrt-cube`
7×	`pow1`
6×	`log-prod`
5×	`flip3-+` `associate-/r*` `flip-+` `div-inv` `add-log-exp`
4×	`difference-of-squares`
3×	`pow-unpow` `associate--l+` `associate-/l*` `sqr-pow`
2×	`cbrt-undiv` `cube-mult` `unpow3` `div-exp` `pow-exp` `distribute-lft-out--` `rem-cube-cbrt`
1×	`cube-div` `pow-to-exp` `sub-neg` `flip3--` `pow-pow` `frac-2neg` `diff-log` `rem-log-exp` `clear-num` `flip--`

Counts

4 → 180

Calls

4 calls:

18.0ms	(/ beta (+ (+ alpha beta) 2.0))
20.0ms	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
86.0ms	(log (exp (pow (/ alpha (+ (+ alpha beta) 2.0)) 3)))
685.0ms	(- (log (exp (pow (/ alpha (+ (+ alpha beta) 2.0)) 3))) (pow 1.0 3))

series289.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(/ beta (+ (+ alpha beta) 2.0))
70.0ms	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
70.0ms	(log (exp (pow (/ alpha (+ (+ alpha beta) 2.0)) 3)))
104.0ms	(- (log (exp (pow (/ alpha (+ (+ alpha beta) 2.0)) 3))) (pow 1.0 3))

simplify84.0ms

Algorithm

egg-herbie

Counts

192 → 192

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	642	1313
1	2693	1104
2	5001	1094

prune496.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 2.6b

regimes95.0ms

Accuracy

76.5% (3.0b remaining)

Error of 6.0b against oracle of 3.0b and baseline of 15.7b

bsearch49.0ms

Steps

Iters	Range		Point
8	24737842517792.957	13792859963305502.0	1188863810682620.8

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	24
1	33	24

end0.0ms

sample613.0ms

Algorithm

intervals

Results

159.0ms	5853×	body	80	valid
101.0ms	824×	body	1280	valid
97.0ms	8000×	pre	80	true
68.0ms	709×	body	640	valid
33.0ms	416×	body	320	valid
10.0ms	198×	body	160	valid