Details

sample29.0ms

Algorithm

intervals

Results

6.0ms	190×	body	80	valid
5.0ms	33×	body	1280	valid
5.0ms	256×	pre	80	true
2.0ms	21×	body	640	valid
1.0ms	10×	body	320	valid
0.0ms	2×	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: 15.6b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
0.4b	(+ (/ (- 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)

series110.0ms

Counts

2 → 6

Calls

2 calls:

49.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
60.0ms	(+ (/ (- 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

prune196.0ms

Filtered

106 candidates to 68 candidates (64.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	97	9	106
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	98	9	107

Merged error: 15.1b

Counts

107 → 9

localize10.0ms

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

rewrite101.0ms

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))
10.0ms	(/ beta (+ (+ alpha beta) 2.0))
16.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series241.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
50.0ms	(/ alpha (+ (+ alpha beta) 2.0))
48.0ms	(/ beta (+ (+ alpha beta) 2.0))
82.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify148.0ms

Algorithm

egg-herbie

Counts

425 → 425

Iterations

Useful iterations: 2 (78.0ms)

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

prune624.0ms

Filtered

425 candidates to 198 candidates (46.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	418	7	425
Fresh	6	2	8
Picked	1	0	1
Done	0	0	0
Total	425	9	434

Merged error: 2.5b

Counts

434 → 9

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (fma (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)) (fma 1.0 1.0 (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0))) (+ (+ alpha beta) 2.0))
0.1b	(/ (fma beta (fma (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)) (fma 1.0 1.0 (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0))) (- (* (+ (+ alpha beta) 2.0) (- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))))) (* (fma (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)) (fma 1.0 1.0 (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0))) (+ (+ alpha beta) 2.0)))
0.1b	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
0.4b	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

rewrite155.0ms

Algorithm

rewrite-expression-head

Rules

853×	`*-un-lft-identity`
576×	`prod-diff`
466×	`add-sqr-sqrt`
456×	`unpow-prod-down` `cube-prod`
431×	`times-frac`
418×	`add-cube-cbrt`
255×	`distribute-lft-out`
72×	`sqr-pow`
62×	`cube-mult` `unpow3`
58×	`associate-/r/`
48×	`fma-neg`
30×	`flip3-+` `flip-+`
29×	`div-inv`
24×	`difference-of-squares`
14×	`add-exp-log` `add-cbrt-cube`
7×	`pow1`
6×	`add-log-exp`
5×	`associate-r` `distribute-lft-out--`
4×	`expm1-log1p-u` `associate-*r/` `log1p-expm1-u`
3×	`cbrt-undiv` `pow-unpow` `div-exp` `associate-l` `associate-/l*`
2×	`pow-exp` `prod-exp` `cbrt-unprod` `rem-cube-cbrt`
1×	`difference-cubes` `cube-div` `distribute-rgt-in` `pow-to-exp` `sub-neg` `flip3--` `pow-pow` `frac-2neg` `distribute-lft-in` `diff-log` `pow-prod-down` `clear-num` `associate-/r` `-commutative` `flip--` `unswap-sqr`

Counts

4 → 783

Calls

4 calls:

8.0ms	(* (fma (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)) (fma 1.0 1.0 (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0))) (+ (+ alpha beta) 2.0))
9.0ms	(/ (fma beta (fma (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)) (fma 1.0 1.0 (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0))) (- (* (+ (+ alpha beta) 2.0) (- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))))) (* (fma (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)) (fma 1.0 1.0 (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0))) (+ (+ alpha beta) 2.0)))
14.0ms	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
52.0ms	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

series787.0ms

Counts

4 → 12

Calls

4 calls:

163.0ms	(* (fma (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)) (fma 1.0 1.0 (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0))) (+ (+ alpha beta) 2.0))
433.0ms	(/ (fma beta (fma (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)) (fma 1.0 1.0 (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0))) (- (* (+ (+ alpha beta) 2.0) (- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))))) (* (fma (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)) (fma 1.0 1.0 (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0))) (+ (+ alpha beta) 2.0)))
76.0ms	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
114.0ms	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

simplify314.0ms

Algorithm

egg-herbie

Counts

795 → 795

Iterations

Useful iterations: 1 (34.0ms)

Iter	Nodes	Cost
0	1245	14117
1	4800	10117
2	5001	10117

prune707.0ms

Filtered

795 candidates to 131 candidates (16.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	790	5	795
Fresh	6	2	8
Picked	1	0	1
Done	0	0	0
Total	797	7	804

Merged error: 2.4b

Counts

804 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ (+ alpha beta) 2.0))
0.5b	(/ (- beta alpha) (sqrt (+ (+ alpha beta) 2.0)))
0.6b	(/ 1 (sqrt (+ (+ alpha beta) 2.0)))
15.8b	(fma (/ 1 (sqrt (+ (+ alpha beta) 2.0))) (/ (- beta alpha) (sqrt (+ (+ alpha beta) 2.0))) 1.0)

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

116×	`*-un-lft-identity`
64×	`add-sqr-sqrt` `times-frac`
55×	`sqrt-prod`
43×	`add-cube-cbrt`
33×	`distribute-lft-out`
16×	`associate-/r*`
10×	`add-exp-log`
9×	`distribute-lft-out--` `difference-of-squares`
8×	`add-cbrt-cube` `associate-/l*`
7×	`pow1`
6×	`sqrt-div`
4×	`expm1-log1p-u` `associate-/r/` `log1p-expm1-u` `add-log-exp`
3×	`pow-flip` `flip3-+` `div-exp` `flip-+`
2×	`cbrt-undiv` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `div-inv` `associate-/l/`
1×	`rem-sqrt-square` `rec-exp` `flip3--` `1-exp` `div-sub` `flip--` `fma-udef` `hypot-def` `inv-pow`

Counts

4 → 159

Calls

4 calls:

6.0ms	(sqrt (+ (+ alpha beta) 2.0))
13.0ms	(/ (- beta alpha) (sqrt (+ (+ alpha beta) 2.0)))
9.0ms	(/ 1 (sqrt (+ (+ alpha beta) 2.0)))
1.0ms	(fma (/ 1 (sqrt (+ (+ alpha beta) 2.0))) (/ (- beta alpha) (sqrt (+ (+ alpha beta) 2.0))) 1.0)

series350.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(sqrt (+ (+ alpha beta) 2.0))
111.0ms	(/ (- beta alpha) (sqrt (+ (+ alpha beta) 2.0)))
67.0ms	(/ 1 (sqrt (+ (+ alpha beta) 2.0)))
134.0ms	(fma (/ 1 (sqrt (+ (+ alpha beta) 2.0))) (/ (- beta alpha) (sqrt (+ (+ alpha beta) 2.0))) 1.0)

simplify58.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	536	1471
1	1845	1300
2	5002	1252

prune298.0ms

Filtered

171 candidates to 94 candidates (55.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	169	2	171
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	170	8	178

Merged error: 2.4b

Counts

178 → 8

regimes138.0ms

Accuracy

72.7% (3.7b remaining)

Error of 6.7b against oracle of 3.0b and baseline of 16.6b

bsearch65.0ms

Steps

Iters	Range		Point
7	9.743550080344205e+42	5.715496464363292e+44	9.871042388715374e+42

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	58	65
1	64	65
2	68	65
3	68	65

end0.0ms

sample737.0ms

Algorithm

intervals

Results

186.0ms	5841×	body	80	valid
129.0ms	8000×	pre	80	true
125.0ms	811×	body	1280	valid
92.0ms	760×	body	640	valid
40.0ms	385×	body	320	valid
12.0ms	203×	body	160	valid