Details

sample22.0ms

Algorithm

intervals

Results

5.0ms	207×	body	80	valid
3.0ms	256×	pre	80	true
2.0ms	19×	body	1280	valid
2.0ms	17×	body	640	valid
1.0ms	10×	body	320	valid
0.0ms	3×	body	160	valid

simplify76.0ms

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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.7b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
1.1b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite127.0ms

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:

27.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
96.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series110.0ms

Counts

2 → 6

Calls

2 calls:

51.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
59.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify36.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (29.0ms)

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

prune223.0ms

Filtered

106 candidates to 68 candidates (64.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 11.2b

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))
1.1b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite475.0ms

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:

294.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
19.0ms	(/ alpha (+ (+ alpha beta) 2.0))
17.0ms	(/ beta (+ (+ alpha beta) 2.0))
116.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series243.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
45.0ms	(/ alpha (+ (+ alpha beta) 2.0))
51.0ms	(/ beta (+ (+ alpha beta) 2.0))
82.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify136.0ms

Algorithm

egg-herbie

Counts

425 → 425

Iterations

Useful iterations: 2 (71.0ms)

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

prune776.0ms

Filtered

425 candidates to 199 candidates (46.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.2b

localize21.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (+ (+ alpha beta) 2.0))
0.7b	(cbrt (+ (+ alpha beta) 2.0))
1.1b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
1.1b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite260.0ms

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))
113.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
114.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series357.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(cbrt (+ (+ alpha beta) 2.0))
104.0ms	(cbrt (+ (+ alpha beta) 2.0))
73.0ms	(- (/ 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 (36.0ms)

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

prune628.0ms

Filtered

248 candidates to 116 candidates (46.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.2b

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))))
1.1b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
9.1b	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

rewrite526.0ms

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:

17.0ms	(/ beta (+ (+ alpha beta) 2.0))
164.0ms	(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
113.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
220.0ms	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

series318.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(/ beta (+ (+ alpha beta) 2.0))
65.0ms	(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
79.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
128.0ms	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

simplify73.0ms

Algorithm

egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 2 (51.0ms)

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

prune422.0ms

Filtered

199 candidates to 109 candidates (54.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.2b

regimes109.0ms

Accuracy

73.6% (3.4b remaining)

Error of 6.7b against oracle of 3.3b and baseline of 16.3b

bsearch73.0ms

Steps

Iters	Range		Point
8	4.1727533087397775e+29	9.936283259031203e+33	2.9333956029595996e+31

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	64	56
1	71	56
2	71	56

end0.0ms

sample610.0ms

Algorithm

intervals

Results

144.0ms	5839×	body	80	valid
110.0ms	845×	body	1280	valid
105.0ms	8000×	pre	80	true
66.0ms	696×	body	640	valid
29.0ms	406×	body	320	valid
10.0ms	214×	body	160	valid