Details

sample23.0ms

Algorithm

intervals

Results

4.0ms	184×	body	80	valid
3.0ms	256×	pre	80	true
3.0ms	25×	body	1280	valid
2.0ms	22×	body	640	valid
1.0ms	15×	body	320	valid
0.0ms	10×	body	160	valid

simplify79.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 17.0b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
2.4b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite225.0ms

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:

47.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
173.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series99.0ms

Counts

2 → 6

Calls

2 calls:

42.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
57.0ms	(+ (/ (- 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

prune205.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 16.1b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ alpha (+ (+ alpha beta) 2.0))
2.4b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite253.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 140

Calls

2 calls:

34.0ms	(/ alpha (+ (+ alpha beta) 2.0))
211.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series118.0ms

Counts

2 → 6

Calls

2 calls:

45.0ms	(/ alpha (+ (+ alpha beta) 2.0))
73.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify53.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	409	1536
1	1340	1086
2	5001	1048

prune226.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 2.9b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ (+ alpha beta) 2.0))
0.3b	(/ (/ alpha (sqrt (+ (+ alpha beta) 2.0))) (sqrt (+ (+ alpha beta) 2.0)))
0.4b	(/ alpha (sqrt (+ (+ alpha beta) 2.0)))
10.0b	(- (/ (/ alpha (sqrt (+ (+ alpha beta) 2.0))) (sqrt (+ (+ alpha beta) 2.0))) 1.0)

rewrite940.0ms

Algorithm

rewrite-expression-head

Rules

2586×	`*-un-lft-identity`
2218×	`times-frac`
1400×	`sqrt-prod`
1216×	`add-sqr-sqrt`
1189×	`add-cube-cbrt`
837×	`distribute-lft-out`
738×	`prod-diff`
246×	`fma-neg`
96×	`sqrt-div`
94×	`associate-/r/`
48×	`flip3-+` `flip-+`
47×	`div-inv`
33×	`associate-/l*`
16×	`associate-/r*`
11×	`add-exp-log` `add-cbrt-cube`
7×	`difference-of-squares`
6×	`add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u`
2×	`frac-2neg` `clear-num`
1×	`sub-neg` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `diff-log` `flip--` `hypot-def` `associate-/l/` `distribute-lft-out--`

Counts

4 → 1374

Calls

4 calls:

33.0ms	(sqrt (+ (+ alpha beta) 2.0))
97.0ms	(/ (/ alpha (sqrt (+ (+ alpha beta) 2.0))) (sqrt (+ (+ alpha beta) 2.0)))
35.0ms	(/ alpha (sqrt (+ (+ alpha beta) 2.0)))
602.0ms	(- (/ (/ alpha (sqrt (+ (+ alpha beta) 2.0))) (sqrt (+ (+ alpha beta) 2.0))) 1.0)

series228.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(sqrt (+ (+ alpha beta) 2.0))
42.0ms	(/ (/ alpha (sqrt (+ (+ alpha beta) 2.0))) (sqrt (+ (+ alpha beta) 2.0)))
76.0ms	(/ alpha (sqrt (+ (+ alpha beta) 2.0)))
77.0ms	(- (/ (/ alpha (sqrt (+ (+ alpha beta) 2.0))) (sqrt (+ (+ alpha beta) 2.0))) 1.0)

simplify233.0ms

Algorithm

egg-herbie

Counts

1386 → 1386

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1668	27794
1	5001	17502

prune1.2s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 2.9b

localize16.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ alpha (sqrt (+ (+ alpha beta) 2.0)))
10.0b	(- (/ (/ alpha (sqrt (+ (+ alpha beta) 2.0))) (sqrt (+ (+ alpha beta) 2.0))) 1.0)
10.0b	(- (/ (/ alpha (sqrt (+ (+ alpha beta) 2.0))) (sqrt (+ (+ alpha beta) 2.0))) 1.0)
10.0b	(- (/ (/ alpha (sqrt (+ (+ alpha beta) 2.0))) (sqrt (+ (+ alpha beta) 2.0))) 1.0)

rewrite2.3s

Algorithm

rewrite-expression-head

Rules

6197×	`*-un-lft-identity`
5238×	`times-frac`
3275×	`sqrt-prod`
3003×	`add-sqr-sqrt`
2931×	`add-cube-cbrt`
2214×	`prod-diff`
1956×	`distribute-lft-out`
738×	`fma-neg`
218×	`sqrt-div` `associate-/r/`
109×	`flip3-+` `flip-+` `div-inv`
21×	`difference-of-squares`
10×	`add-log-exp`
8×	`associate-/r*`
6×	`add-exp-log` `add-cbrt-cube`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
3×	`sub-neg` `flip3--` `diff-log` `flip--` `associate-/l*` `distribute-lft-out--`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num`

Counts

4 → 3069

Calls

4 calls:

36.0ms	(/ alpha (sqrt (+ (+ alpha beta) 2.0)))
595.0ms	(- (/ (/ alpha (sqrt (+ (+ alpha beta) 2.0))) (sqrt (+ (+ alpha beta) 2.0))) 1.0)
604.0ms	(- (/ (/ alpha (sqrt (+ (+ alpha beta) 2.0))) (sqrt (+ (+ alpha beta) 2.0))) 1.0)
605.0ms	(- (/ (/ alpha (sqrt (+ (+ alpha beta) 2.0))) (sqrt (+ (+ alpha beta) 2.0))) 1.0)

series297.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(/ alpha (sqrt (+ (+ alpha beta) 2.0)))
68.0ms	(- (/ (/ alpha (sqrt (+ (+ alpha beta) 2.0))) (sqrt (+ (+ alpha beta) 2.0))) 1.0)
74.0ms	(- (/ (/ alpha (sqrt (+ (+ alpha beta) 2.0))) (sqrt (+ (+ alpha beta) 2.0))) 1.0)
78.0ms	(- (/ (/ alpha (sqrt (+ (+ alpha beta) 2.0))) (sqrt (+ (+ alpha beta) 2.0))) 1.0)

simplify583.0ms

Algorithm

egg-herbie

Counts

3081 → 3081

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1539	67939
1	4858	38930
2	5001	38930

prune3.4s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 2.9b

regimes72.0ms

Accuracy

76.2% (3.1b remaining)

Error of 6.4b against oracle of 3.2b and baseline of 16.4b

bsearch24.0ms

Steps

Iters	Range		Point
3	101403271.01852646	122647865.33979332	121320078.19471414

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	45
1	47	45

end0.0ms

sample612.0ms

Algorithm

intervals

Results

135.0ms	5804×	body	80	valid
108.0ms	896×	body	1280	valid
82.0ms	8000×	pre	80	true
66.0ms	696×	body	640	valid
25.0ms	376×	body	320	valid
10.0ms	228×	body	160	valid