Details

sample24.0ms

Algorithm

intervals

Results

5.0ms	203×	body	80	valid
3.0ms	256×	pre	80	true
2.0ms	19×	body	1280	valid
1.0ms	16×	body	640	valid
1.0ms	13×	body	320	valid
0.0ms	5×	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: 12.6b

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)

rewrite229.0ms

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:

48.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
176.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series100.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify38.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (30.0ms)

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

prune224.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 11.9b

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite1.5s

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:

1.2s	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
35.0ms	(/ alpha (+ (+ alpha beta) 2.0))
35.0ms	(/ beta (+ (+ alpha beta) 2.0))
213.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series218.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
48.0ms	(/ alpha (+ (+ alpha beta) 2.0))
41.0ms	(/ beta (+ (+ alpha beta) 2.0))
72.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify85.0ms

Algorithm

egg-herbie

Counts

241 → 241

Iterations

Useful iterations: 2 (57.0ms)

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

prune477.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.4b

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite1.0s

Algorithm

rewrite-expression-head

Rules

346×	`*-un-lft-identity`
189×	`prod-diff`
185×	`add-sqr-sqrt`
170×	`add-cube-cbrt`
168×	`times-frac`
130×	`exp-sum`
102×	`distribute-lft-out`
68×	`log-prod`
22×	`associate-/r/`
21×	`fma-neg`
12×	`exp-prod`
11×	`flip3-+` `flip-+` `div-inv`
9×	`add-log-exp`
7×	`log-pow`
6×	`add-exp-log` `add-cbrt-cube` `difference-of-squares`
5×	`pow1` `associate-/r*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`sub-neg` `associate-/l*` `distribute-lft-out--`
2×	`exp-diff` `diff-log` `rem-exp-log`
1×	`cbrt-undiv` `log-div` `flip3--` `frac-2neg` `div-exp` `rem-log-exp` `clear-num` `flip--`

Counts

4 → 309

Calls

4 calls:

352.0ms	(exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
35.0ms	(/ beta (+ (+ alpha beta) 2.0))
211.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
395.0ms	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

series248.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
47.0ms	(/ beta (+ (+ alpha beta) 2.0))
72.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
67.0ms	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

simplify81.0ms

Algorithm

egg-herbie

Counts

321 → 321

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	638	4268
1	1854	3053
2	5002	2419

prune481.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 2.4b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite731.0ms

Algorithm

rewrite-expression-head

Rules

364×	`*-un-lft-identity`
196×	`add-sqr-sqrt`
189×	`prod-diff`
184×	`times-frac`
176×	`add-cube-cbrt`
108×	`distribute-lft-out`
63×	`fma-neg`
24×	`associate-/r/`
12×	`flip3-+` `flip-+` `div-inv`
10×	`add-log-exp`
8×	`difference-of-squares`
6×	`cbrt-prod`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `flip3--` `add-cbrt-cube` `flip--` `log1p-expm1-u` `distribute-lft-out--`
3×	`sub-neg` `diff-log`
2×	`cbrt-div`
1×	`pow1/3`

Counts

4 → 321

Calls

4 calls:

75.0ms	(cbrt (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
210.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
211.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
212.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series373.0ms

Counts

4 → 12

Calls

4 calls:

164.0ms	(cbrt (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
71.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
65.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
73.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify72.0ms

Algorithm

egg-herbie

Counts

333 → 333

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	483	4200
1	1397	2862
2	5001	2757

prune772.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 2.4b

regimes84.0ms

Accuracy

76.7% (2.9b remaining)

Error of 6.0b against oracle of 3.1b and baseline of 15.6b

bsearch50.0ms

Steps

Iters	Range		Point
8	5.407778613963265e+17	3.085216785564451e+20	3.0659731518348657e+18

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	25
1	37	25

end0.0ms

sample627.0ms

Algorithm

intervals

Results

150.0ms	5853×	body	80	valid
98.0ms	844×	body	1280	valid
86.0ms	8000×	pre	80	true
71.0ms	748×	body	640	valid
25.0ms	361×	body	320	valid
9.0ms	194×	body	160	valid