Details

sample29.0ms

Algorithm

intervals

Results

6.0ms	190×	body	80	valid
4.0ms	24×	body	1280	valid
4.0ms	256×	pre	80	true
4.0ms	28×	body	640	valid
1.0ms	8×	body	320	valid
0.0ms	6×	body	160	valid

simplify79.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	20	6
1	34	6
2	52	6
3	73	6
4	123	6
5	184	6
6	250	6
7	287	6
8	349	6
9	437	6
10	574	6
11	654	6
12	712	6
13	785	6
14	1075	6
15	1150	6
16	1193	6
17	1213	6
18	1221	6
19	1221	6

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.4b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
1.4b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite216.0ms

Algorithm

rewrite-expression-head

Rules

104×	`*-un-lft-identity`
50×	`times-frac`
47×	`add-sqr-sqrt`
34×	`distribute-lft-out`
31×	`fma-def`
25×	`add-cube-cbrt`
11×	`distribute-lft-out--` `difference-of-squares`
5×	`associate-/r` `associate-/l`
4×	`add-exp-log` `associate-/r/` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `flip-+`
2×	`pow1` `expm1-log1p-u` `div-sub` `log1p-expm1-u` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `associate-+l-` `flip3--` `frac-2neg` `div-exp` `clear-num` `sum-log` `flip--`

Counts

2 → 100

Calls

2 calls:

45.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
166.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series98.0ms

Counts

2 → 6

Calls

2 calls:

45.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
53.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify39.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	335	555
1	1087	529
2	5002	525

prune369.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 14.8b

localize10.0ms

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	(/ beta (+ (+ alpha beta) 2.0))
0.0b	(/ alpha (+ (+ alpha beta) 2.0))
1.4b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite1.4s

Algorithm

rewrite-expression-head

Rules

215×	`*-un-lft-identity`
118×	`add-sqr-sqrt`
116×	`times-frac`
93×	`add-cube-cbrt`
63×	`prod-diff`
60×	`distribute-lft-out`
21×	`fma-neg`
13×	`associate-/r` `associate-/l` `distribute-lft-out--`
12×	`associate-/r/`
10×	`add-exp-log` `add-cbrt-cube` `difference-of-squares`
7×	`div-inv`
6×	`flip3-+` `flip-+` `add-log-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `associate-/l/`
3×	`cbrt-undiv` `flip3--` `frac-2neg` `div-exp` `clear-num` `flip--`
2×	`frac-sub`
1×	`sub-neg` `diff-log` `div-sub`

Counts

4 → 229

Calls

4 calls:

1.1s	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
33.0ms	(/ beta (+ (+ alpha beta) 2.0))
33.0ms	(/ alpha (+ (+ alpha beta) 2.0))
201.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series217.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
46.0ms	(/ beta (+ (+ alpha beta) 2.0))
41.0ms	(/ alpha (+ (+ alpha beta) 2.0))
72.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify88.0ms

Algorithm

egg-herbie

Counts

241 → 241

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	714	2537
1	2533	2035
2	5001	2004

prune874.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.9b

localize17.0ms

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))
1.4b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite254.0ms

Algorithm

rewrite-expression-head

Rules

141×	`*-un-lft-identity`
69×	`add-sqr-sqrt`
64×	`add-cube-cbrt`
63×	`prod-diff`
61×	`times-frac`
45×	`distribute-lft-out`
21×	`fma-neg`
15×	`cbrt-prod`
8×	`associate-/r/`
7×	`flip3-+` `flip-+`
6×	`cbrt-div` `add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `div-inv`
3×	`pow1/3`
2×	`difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 152

Calls

4 calls:

15.0ms	(cbrt (+ (+ alpha beta) 2.0))
15.0ms	(cbrt (+ (+ alpha beta) 2.0))
15.0ms	(cbrt (+ (+ alpha beta) 2.0))
202.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series348.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(cbrt (+ (+ alpha beta) 2.0))
91.0ms	(cbrt (+ (+ alpha beta) 2.0))
92.0ms	(cbrt (+ (+ alpha beta) 2.0))
73.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify53.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	460	1755
1	1302	1290
2	5001	1240

prune1.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 2.9b

localize26.0ms

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))
1.4b	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

rewrite564.0ms

Algorithm

rewrite-expression-head

Rules

813×	`*-un-lft-identity`
576×	`prod-diff`
444×	`add-sqr-sqrt`
435×	`unpow-prod-down` `cube-prod`
398×	`add-cube-cbrt` `times-frac`
243×	`distribute-lft-out`
71×	`sqr-pow`
61×	`cube-mult` `unpow3`
52×	`associate-/r/`
48×	`fma-neg`
29×	`flip3-+` `flip-+`
26×	`div-inv`
24×	`difference-of-squares`
15×	`cbrt-prod`
6×	`cbrt-div` `add-log-exp`
5×	`distribute-lft-out--`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`pow1/3`
1×	`difference-cubes` `sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 719

Calls

4 calls:

15.0ms	(cbrt (+ (+ alpha beta) 2.0))
16.0ms	(cbrt (+ (+ alpha beta) 2.0))
15.0ms	(cbrt (+ (+ alpha beta) 2.0))
456.0ms	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

series370.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(cbrt (+ (+ alpha beta) 2.0))
90.0ms	(cbrt (+ (+ alpha beta) 2.0))
89.0ms	(cbrt (+ (+ alpha beta) 2.0))
101.0ms	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

simplify239.0ms

Algorithm

egg-herbie

Counts

731 → 731

Iterations

Useful iterations: 2 (111.0ms)

Iter	Nodes	Cost
0	1079	12205
1	3449	8551
2	5002	8510

prune2.0s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 2.9b

regimes167.0ms

Accuracy

73.6% (3.5b remaining)

Error of 6.6b against oracle of 3.0b and baseline of 16.4b

bsearch91.0ms

Steps

Iters	Range		Point
6	3.164613017666376e+27	2.9042202766263138e+28	3.596278001625763e+27

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	47
1	48	47

end0.0ms

sample725.0ms

Algorithm

intervals

Results

186.0ms	5856×	body	80	valid
131.0ms	833×	body	1280	valid
114.0ms	8000×	pre	80	true
92.0ms	701×	body	640	valid
37.0ms	398×	body	320	valid
13.0ms	212×	body	160	valid