Details

sample23.0ms

Algorithm

intervals

Results

5.0ms	200×	body	80	valid
3.0ms	256×	pre	80	true
2.0ms	19×	body	1280	valid
2.0ms	20×	body	640	valid
1.0ms	13×	body	320	valid
0.0ms	4×	body	160	valid

simplify80.0ms

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: 13.5b

localize11.0ms

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)

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:

25.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
100.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series107.0ms

Counts

2 → 6

Calls

2 calls:

46.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
60.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify39.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (31.0ms)

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

prune219.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 12.9b

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite494.0ms

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:

307.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
18.0ms	(/ beta (+ (+ alpha beta) 2.0))
18.0ms	(/ alpha (+ (+ alpha beta) 2.0))
120.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series229.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
47.0ms	(/ beta (+ (+ alpha beta) 2.0))
44.0ms	(/ alpha (+ (+ alpha beta) 2.0))
79.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify140.0ms

Algorithm

egg-herbie

Counts

425 → 425

Iterations

Useful iterations: 2 (71.0ms)

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

prune743.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.4b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ (+ alpha beta) 2.0) beta)
0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.8b	(/ 1 (/ (+ (+ alpha beta) 2.0) beta))
1.4b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite210.0ms

Algorithm

rewrite-expression-head

Rules

299×	`*-un-lft-identity`
208×	`times-frac`
142×	`add-sqr-sqrt`
137×	`add-cube-cbrt`
96×	`distribute-lft-out`
63×	`prod-diff`
27×	`associate-/r*`
21×	`fma-neg`
19×	`add-exp-log`
13×	`add-cbrt-cube`
11×	`associate-/r/` `div-inv` `associate-/l*`
9×	`div-exp`
6×	`flip3-+` `flip-+` `add-log-exp`
5×	`pow1` `cbrt-undiv`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`frac-2neg` `clear-num`
2×	`rec-exp` `1-exp` `associate-/l/` `difference-of-squares`
1×	`sub-neg` `flip3--` `pow-flip` `diff-log` `flip--` `distribute-lft-out--` `inv-pow`

Counts

4 → 281

Calls

4 calls:

34.0ms	(/ (+ (+ alpha beta) 2.0) beta)
20.0ms	(/ alpha (+ (+ alpha beta) 2.0))
22.0ms	(/ 1 (/ (+ (+ alpha beta) 2.0) beta))
120.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series206.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(/ (+ (+ alpha beta) 2.0) beta)
43.0ms	(/ alpha (+ (+ alpha beta) 2.0))
59.0ms	(/ 1 (/ (+ (+ alpha beta) 2.0) beta))
78.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify92.0ms

Algorithm

egg-herbie

Counts

293 → 293

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	739	2640
1	3031	2069
2	5001	1937

prune445.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.4b

localize15.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
4.3b	(cbrt (/ 1 (/ (+ (+ alpha beta) 2.0) beta)))
4.3b	(cbrt (/ 1 (/ (+ (+ alpha beta) 2.0) beta)))
4.3b	(cbrt (/ 1 (/ (+ (+ alpha beta) 2.0) beta)))

rewrite183.0ms

Algorithm

rewrite-expression-head

Rules

399×	`*-un-lft-identity`
367×	`times-frac`
207×	`add-sqr-sqrt`
202×	`add-cube-cbrt`
186×	`cbrt-prod`
117×	`distribute-lft-out`
63×	`prod-diff`
21×	`fma-neg`
16×	`div-inv`
11×	`associate-/r/`
6×	`add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `flip3-+` `add-cbrt-cube` `flip-+` `log1p-expm1-u`
3×	`cbrt-div` `pow1/3`
2×	`difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 320

Calls

4 calls:

120.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
14.0ms	(cbrt (/ 1 (/ (+ (+ alpha beta) 2.0) beta)))
14.0ms	(cbrt (/ 1 (/ (+ (+ alpha beta) 2.0) beta)))
14.0ms	(cbrt (/ 1 (/ (+ (+ alpha beta) 2.0) beta)))

series525.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
148.0ms	(cbrt (/ 1 (/ (+ (+ alpha beta) 2.0) beta)))
151.0ms	(cbrt (/ 1 (/ (+ (+ alpha beta) 2.0) beta)))
152.0ms	(cbrt (/ 1 (/ (+ (+ alpha beta) 2.0) beta)))

simplify104.0ms

Algorithm

egg-herbie

Counts

332 → 332

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	752	4311
1	2504	3696
2	5002	3342

prune509.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.4b

regimes83.0ms

Accuracy

78% (2.8b remaining)

Error of 5.9b against oracle of 3.2b and baseline of 15.7b

bsearch47.0ms

Steps

Iters	Range		Point
8	60.984244775781654	93455.48925387283	92108.89598052698

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	20
1	35	20

end0.0ms

sample618.0ms

Algorithm

intervals

Results

158.0ms	5846×	body	80	valid
109.0ms	855×	body	1280	valid
96.0ms	8000×	pre	80	true
68.0ms	690×	body	640	valid
30.0ms	401×	body	320	valid
13.0ms	208×	body	160	valid