Details

sample29.0ms

Algorithm

intervals

Results

6.0ms	184×	body	80	valid
4.0ms	256×	pre	80	true
4.0ms	25×	body	1280	valid
3.0ms	23×	body	640	valid
2.0ms	17×	body	320	valid
0.0ms	7×	body	160	valid

simplify82.0ms

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

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: 16.9b

Counts

2 → 1

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
2.9b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite36.0ms

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:

10.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
21.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series106.0ms

Counts

2 → 6

Calls

2 calls:

44.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
62.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify41.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (33.0ms)

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

prune194.0ms

Filtered

106 candidates to 68 candidates (64.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	95	11	106
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	96	11	107

Merged error: 16.2b

Counts

107 → 11

localize14.0ms

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))
2.9b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite98.0ms

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:

35.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
7.0ms	(/ alpha (+ (+ alpha beta) 2.0))
8.0ms	(/ beta (+ (+ alpha beta) 2.0))
16.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series240.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
50.0ms	(/ alpha (+ (+ alpha beta) 2.0))
45.0ms	(/ beta (+ (+ alpha beta) 2.0))
81.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify143.0ms

Algorithm

egg-herbie

Counts

425 → 425

Iterations

Useful iterations: 2 (78.0ms)

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

prune581.0ms

Filtered

425 candidates to 199 candidates (46.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	421	4	425
Fresh	7	3	10
Picked	1	0	1
Done	0	0	0
Total	429	7	436

Merged error: 2.7b

Counts

436 → 7

localize17.0ms

Local error

Found 4 expressions with local error:

2.9b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
6.6b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
6.6b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
6.6b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

195×	`*-un-lft-identity`
106×	`times-frac`
93×	`add-sqr-sqrt`
88×	`add-cube-cbrt`
63×	`cbrt-prod` `prod-diff` `distribute-lft-out`
21×	`fma-neg`
14×	`associate-/r/`
7×	`flip3-+` `flip-+` `div-inv`
6×	`add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`cbrt-div` `pow1/3`
2×	`difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 197

Calls

4 calls:

15.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
7.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
7.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
7.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

series519.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
150.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
142.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
148.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

simplify66.0ms

Algorithm

egg-herbie

Counts

209 → 209

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	509	2277
1	1447	1794
2	5001	1714

prune416.0ms

Filtered

209 candidates to 120 candidates (57.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	206	3	209
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	208	8	216

Merged error: 2.7b

Counts

216 → 8

localize14.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ 1 (+ (+ alpha beta) 2.0))
17.1b	(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:

8.0ms	(/ 1 (+ (+ alpha beta) 2.0))
1.0ms	(fma (- beta alpha) (/ 1 (+ (+ alpha beta) 2.0)) 1.0)

series87.0ms

Counts

2 → 6

Calls

2 calls:

41.0ms	(/ 1 (+ (+ alpha beta) 2.0))
45.0ms	(fma (- beta alpha) (/ 1 (+ (+ alpha beta) 2.0)) 1.0)

simplify98.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 3 (92.0ms)

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

prune75.0ms

Filtered

59 candidates to 34 candidates (57.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	58	1	59
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	58	9	67

Merged error: 2.7b

Counts

67 → 9

regimes117.0ms

Accuracy

78.8% (2.8b remaining)

Error of 5.7b against oracle of 2.9b and baseline of 16.3b

bsearch53.0ms

Steps

Iters	Range		Point
8	113.05980363979081	1896026.3864226907	1867269.1236031821

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	31
1	39	31

end0.0ms

sample729.0ms

Algorithm

intervals

Results

183.0ms	5867×	body	80	valid
129.0ms	8000×	pre	80	true
125.0ms	823×	body	1280	valid
100.0ms	754×	body	640	valid
32.0ms	364×	body	320	valid
11.0ms	192×	body	160	valid