Details

sample25.0ms

Algorithm

intervals

Results

4.0ms	178×	body	80	valid
4.0ms	34×	body	1280	valid
3.0ms	256×	pre	80	true
2.0ms	19×	body	640	valid
1.0ms	15×	body	320	valid
1.0ms	10×	body	160	valid

simplify78.0ms

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: 18.0b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
2.6b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite129.0ms

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:

26.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
98.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series109.0ms

Counts

2 → 6

Calls

2 calls:

50.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
59.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify37.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (29.0ms)

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

prune226.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 17.3b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.0b	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
0.0b	(/ beta (+ (+ alpha beta) 2.0))
2.6b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite476.0ms

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:

19.0ms	(/ alpha (+ (+ alpha beta) 2.0))
294.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
17.0ms	(/ beta (+ (+ alpha beta) 2.0))
117.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series240.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(/ alpha (+ (+ alpha beta) 2.0))
58.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
50.0ms	(/ beta (+ (+ alpha beta) 2.0))
81.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify139.0ms

Algorithm

egg-herbie

Counts

425 → 425

Iterations

Useful iterations: 2 (70.0ms)

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

prune775.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.6b

localize21.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (+ (+ alpha beta) 2.0))
0.7b	(cbrt (+ (+ alpha beta) 2.0))
2.6b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
2.6b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite264.0ms

Algorithm

rewrite-expression-head

Rules

254×	`*-un-lft-identity`
130×	`add-sqr-sqrt`
126×	`prod-diff`
122×	`times-frac`
120×	`add-cube-cbrt`
78×	`distribute-lft-out`
42×	`fma-neg`
16×	`associate-/r/`
10×	`cbrt-prod` `flip3-+` `flip-+`
8×	`div-inv` `add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `cbrt-div` `add-cbrt-cube` `log1p-expm1-u` `difference-of-squares`
2×	`sub-neg` `flip3--` `pow1/3` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 236

Calls

4 calls:

8.0ms	(cbrt (+ (+ alpha beta) 2.0))
8.0ms	(cbrt (+ (+ alpha beta) 2.0))
116.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
118.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series357.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(cbrt (+ (+ alpha beta) 2.0))
100.0ms	(cbrt (+ (+ alpha beta) 2.0))
79.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
79.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify61.0ms

Algorithm

egg-herbie

Counts

248 → 248

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	460	2922
1	1302	2024
2	5001	1948

prune613.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 2.6b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ beta (+ (+ alpha beta) 2.0))
0.6b	(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
2.6b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
10.6b	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

rewrite537.0ms

Algorithm

rewrite-expression-head

Rules

166×	`*-un-lft-identity`
89×	`add-sqr-sqrt`
78×	`times-frac`
74×	`add-cube-cbrt`
63×	`prod-diff`
48×	`distribute-lft-out`
21×	`fma-neg`
14×	`log-prod`
10×	`associate-/r/`
8×	`log-div`
7×	`add-exp-log` `exp-sum` `distribute-lft-out--`
6×	`pow1` `add-cbrt-cube` `add-log-exp` `difference-of-squares`
5×	`flip3--` `flip3-+` `associate-/r*` `flip--` `flip-+` `div-inv`
4×	`expm1-log1p-u` `exp-prod` `exp-diff` `frac-sub` `log1p-expm1-u`
3×	`associate-/l*`
2×	`log-pow`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `clear-num` `rem-exp-log`

Counts

4 → 187

Calls

4 calls:

19.0ms	(/ beta (+ (+ alpha beta) 2.0))
168.0ms	(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
115.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
225.0ms	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

series452.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(/ beta (+ (+ alpha beta) 2.0))
199.0ms	(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
79.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
127.0ms	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

simplify76.0ms

Algorithm

egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	666	2336
1	2236	1838
2	5002	1790

prune392.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.6b

regimes128.0ms

Accuracy

78.1% (2.8b remaining)

Error of 6.0b against oracle of 3.3b and baseline of 15.9b

bsearch41.0ms

Steps

Iters	Range		Point
5	391248603.19673574	1027443772.3458656	1015227874.2528594

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	55
1	49	55

end0.0ms

sample619.0ms

Algorithm

intervals

Results

151.0ms	5870×	body	80	valid
101.0ms	828×	body	1280	valid
95.0ms	8000×	pre	80	true
70.0ms	692×	body	640	valid
39.0ms	409×	body	320	valid
10.0ms	201×	body	160	valid