Details

sample23.0ms

Algorithm

intervals

Results

5.0ms	194×	body	80	valid
3.0ms	256×	pre	80	true
3.0ms	22×	body	1280	valid
2.0ms	16×	body	640	valid
1.0ms	15×	body	320	valid
0.0ms	9×	body	160	valid

simplify77.0ms

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	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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.5b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
2.1b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite39.0ms

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:

11.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
22.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series112.0ms

Counts

2 → 6

Calls

2 calls:

46.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
66.0ms	(+ (/ (- 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

prune261.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 13.9b

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))
2.1b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

512×	`*-un-lft-identity`
328×	`add-sqr-sqrt`
263×	`times-frac`
252×	`prod-diff`
213×	`add-cube-cbrt`
150×	`distribute-lft-out`
65×	`associate--r+`
46×	`difference-of-squares`
42×	`fma-neg`
32×	`associate-/r/`
25×	`distribute-lft-out--`
16×	`flip3-+` `flip-+` `div-inv`
11×	`add-log-exp`
10×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/l*`
4×	`pow1` `expm1-log1p-u` `diff-log` `log1p-expm1-u`
3×	`sub-neg` `flip3--` `flip--`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `frac-sub`
1×	`associate--r-`

Counts

4 → 413

Calls

4 calls:

43.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
8.0ms	(/ alpha (+ (+ alpha beta) 2.0))
8.0ms	(/ beta (+ (+ alpha beta) 2.0))
17.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series248.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
46.0ms	(/ alpha (+ (+ alpha beta) 2.0))
52.0ms	(/ beta (+ (+ alpha beta) 2.0))
84.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify144.0ms

Algorithm

egg-herbie

Counts

425 → 425

Iterations

Useful iterations: 2 (74.0ms)

Iter	Nodes	Cost
0	977	8429
1	3143	6259
2	5002	6131

prune965.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 2.3b

localize23.0ms

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))
2.1b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite44.0ms

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:

6.0ms	(cbrt (+ (+ alpha beta) 2.0))
6.0ms	(cbrt (+ (+ alpha beta) 2.0))
6.0ms	(cbrt (+ (+ alpha beta) 2.0))
18.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series376.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(cbrt (+ (+ alpha beta) 2.0))
98.0ms	(cbrt (+ (+ alpha beta) 2.0))
98.0ms	(cbrt (+ (+ alpha beta) 2.0))
80.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify56.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 2 (38.0ms)

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

prune479.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 2.3b

localize14.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt beta)
0.6b	(cbrt beta)
0.6b	(cbrt beta)
2.1b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 140

Calls

4 calls:

1.0ms	(cbrt beta)
2.0ms	(cbrt beta)
1.0ms	(cbrt beta)
20.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series610.0ms

Counts

4 → 12

Calls

4 calls:

177.0ms	(cbrt beta)
174.0ms	(cbrt beta)
179.0ms	(cbrt beta)
79.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify56.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	386	1443
1	1119	993
2	5001	940

prune314.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 2.3b

regimes87.0ms

Accuracy

76.4% (3.1b remaining)

Error of 6.2b against oracle of 3.1b and baseline of 16.2b

bsearch49.0ms

Steps

Iters	Range		Point
8	13.202733199564877	775728.8687199388	759519.7231227644

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	29
1	41	29

end0.0ms

sample630.0ms

Algorithm

intervals

Results

153.0ms	5806×	body	80	valid
112.0ms	847×	body	1280	valid
99.0ms	8000×	pre	80	true
78.0ms	750×	body	640	valid
32.0ms	384×	body	320	valid
11.0ms	213×	body	160	valid