Details

sample24.0ms

Algorithm

intervals

Results

5.0ms	196×	body	80	valid
3.0ms	256×	pre	80	true
3.0ms	26×	body	1280	valid
2.0ms	21×	body	640	valid
1.0ms	7×	body	320	valid
0.0ms	6×	body	160	valid

simplify79.0ms

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

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 13.9b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
1.6b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite39.0ms

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:

11.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
24.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series108.0ms

Counts

2 → 6

Calls

2 calls:

51.0ms	(/ (- 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

prune195.0ms

Filtered

106 candidates to 68 candidates (64.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	94	12	106
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	95	12	107

Merged error: 13.4b

Counts

107 → 12

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))
1.6b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite103.0ms

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:

36.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
7.0ms	(/ alpha (+ (+ alpha beta) 2.0))
11.0ms	(/ beta (+ (+ alpha beta) 2.0))
16.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series227.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
48.0ms	(/ alpha (+ (+ alpha beta) 2.0))
45.0ms	(/ beta (+ (+ alpha beta) 2.0))
78.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify146.0ms

Algorithm

egg-herbie

Counts

425 → 425

Iterations

Useful iterations: 2 (74.0ms)

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

prune601.0ms

Filtered

425 candidates to 199 candidates (46.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	420	5	425
Fresh	8	3	11
Picked	1	0	1
Done	0	0	0
Total	429	8	437

Merged error: 1.8b

Counts

437 → 8

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))
1.6b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite43.0ms

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:

5.0ms	(cbrt (+ (+ alpha beta) 2.0))
5.0ms	(cbrt (+ (+ alpha beta) 2.0))
5.0ms	(cbrt (+ (+ alpha beta) 2.0))
20.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series365.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(cbrt (+ (+ alpha beta) 2.0))
95.0ms	(cbrt (+ (+ alpha beta) 2.0))
96.0ms	(cbrt (+ (+ alpha beta) 2.0))
77.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify55.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 2 (37.0ms)

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

prune368.0ms

Filtered

164 candidates to 90 candidates (54.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	161	3	164
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	165	7	172

Merged error: 1.8b

Counts

172 → 7

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ 1 (+ (+ alpha beta) 2.0))
14.2b	(fma (- beta alpha) (/ 1 (+ (+ alpha beta) 2.0)) 1.0)

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

32×	`*-un-lft-identity`
15×	`times-frac`
12×	`add-sqr-sqrt` `add-cube-cbrt` `distribute-lft-out`
6×	`add-exp-log`
5×	`associate-/r*`
4×	`add-cbrt-cube`
3×	`pow1` `associate-/l*`
2×	`expm1-log1p-u` `div-exp` `associate-/r/` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `rec-exp` `pow-flip` `frac-2neg` `flip3-+` `1-exp` `clear-num` `flip-+` `fma-udef` `div-inv` `inv-pow`

Counts

2 → 53

Calls

2 calls:

7.0ms	(/ 1 (+ (+ alpha beta) 2.0))
1.0ms	(fma (- beta alpha) (/ 1 (+ (+ alpha beta) 2.0)) 1.0)

series85.0ms

Counts

2 → 6

Calls

2 calls:

40.0ms	(/ 1 (+ (+ alpha beta) 2.0))
45.0ms	(fma (- beta alpha) (/ 1 (+ (+ alpha beta) 2.0)) 1.0)

simplify102.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 3 (95.0ms)

Iter	Nodes	Cost
0	203	328
1	728	289
2	3595	264
3	5002	261

prune78.0ms

Filtered

59 candidates to 34 candidates (57.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	59	0	59
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	59	7	66

Merged error: 1.8b

Counts

66 → 7

regimes85.0ms

Accuracy

69% (4.2b remaining)

Error of 7.5b against oracle of 3.3b and baseline of 16.9b

bsearch47.0ms

Steps

Iters	Range		Point
7	2.3146017749477097e+64	3.0708296053197817e+66	2.423578056688418e+64

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	20
1	35	20

end0.0ms

sample613.0ms

Algorithm

intervals

Results

154.0ms	5781×	body	80	valid
108.0ms	881×	body	1280	valid
97.0ms	8000×	pre	80	true
71.0ms	732×	body	640	valid
31.0ms	419×	body	320	valid
9.0ms	187×	body	160	valid