Details

sample24.0ms

Algorithm

intervals

Results

4.0ms	176×	body	80	valid
3.0ms	31×	body	1280	valid
3.0ms	256×	pre	80	true
2.0ms	21×	body	640	valid
1.0ms	18×	body	320	valid
0.0ms	10×	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: 18.7b

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)

rewrite234.0ms

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))
180.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series97.0ms

Counts

2 → 6

Calls

2 calls:

45.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
52.0ms	(+ (/ (- 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

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 17.7b

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

rewrite862.0ms

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:

542.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
36.0ms	(/ beta (+ (+ alpha beta) 2.0))
35.0ms	(/ alpha (+ (+ alpha beta) 2.0))
218.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series209.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
45.0ms	(/ beta (+ (+ alpha beta) 2.0))
40.0ms	(/ alpha (+ (+ alpha beta) 2.0))
72.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify136.0ms

Algorithm

egg-herbie

Counts

425 → 425

Iterations

Useful iterations: 2 (70.0ms)

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

prune755.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.8b

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

rewrite273.0ms

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:

16.0ms	(cbrt (+ (+ alpha beta) 2.0))
16.0ms	(cbrt (+ (+ alpha beta) 2.0))
17.0ms	(cbrt (+ (+ alpha beta) 2.0))
216.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series338.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(cbrt (+ (+ alpha beta) 2.0))
89.0ms	(cbrt (+ (+ alpha beta) 2.0))
89.0ms	(cbrt (+ (+ alpha beta) 2.0))
69.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify51.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 2 (35.0ms)

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

prune420.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.8b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.8b	(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
2.6b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
11.5b	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

rewrite977.0ms

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:

35.0ms	(/ alpha (+ (+ alpha beta) 2.0))
307.0ms	(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
216.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
408.0ms	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

series281.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(/ alpha (+ (+ alpha beta) 2.0))
57.0ms	(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
65.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
114.0ms	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

simplify71.0ms

Algorithm

egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	633	2335
1	2127	1835
2	5001	1784

prune518.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.8b

regimes194.0ms

Accuracy

76.8% (3.0b remaining)

Error of 6.0b against oracle of 3.1b and baseline of 15.9b

bsearch48.0ms

Steps

Iters	Range		Point
7	72224756.60973874	4926405641.889644	584068019.196283

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	39
1	45	39

end0.0ms

sample608.0ms

Algorithm

intervals

Results

141.0ms	5875×	body	80	valid
100.0ms	856×	body	1280	valid
83.0ms	8000×	pre	80	true
68.0ms	692×	body	640	valid
27.0ms	390×	body	320	valid
9.0ms	187×	body	160	valid