Details

sample26.0ms

Algorithm

intervals

Results

5.0ms	182×	body	80	valid
4.0ms	31×	body	1280	valid
3.0ms	256×	pre	80	true
2.0ms	24×	body	640	valid
1.0ms	13×	body	320	valid
0.0ms	6×	body	160	valid

simplify81.0ms

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: 17.3b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
1.5b	(+ (/ (- 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:

11.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
21.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series120.0ms

Counts

2 → 6

Calls

2 calls:

53.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
67.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify40.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (31.0ms)

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

prune236.0ms

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: 16.5b

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))
1.5b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite102.0ms

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:

41.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
7.0ms	(/ alpha (+ (+ alpha beta) 2.0))
7.0ms	(/ beta (+ (+ alpha beta) 2.0))
17.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series254.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
47.0ms	(/ alpha (+ (+ alpha beta) 2.0))
54.0ms	(/ beta (+ (+ alpha beta) 2.0))
86.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify152.0ms

Algorithm

egg-herbie

Counts

425 → 425

Iterations

Useful iterations: 2 (78.0ms)

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

prune819.0ms

Filtered

425 candidates to 199 candidates (46.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	415	10	425
Fresh	10	1	11
Picked	1	0	1
Done	0	0	0
Total	426	11	437

Merged error: 3.7b

Counts

437 → 11

localize21.0ms

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	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
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)))
1.4b	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

rewrite160.0ms

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))
10.0ms	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
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)))
61.0ms	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

series798.0ms

Counts

4 → 12

Calls

4 calls:

164.0ms	(* (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))
78.0ms	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
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)))
124.0ms	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

simplify310.0ms

Algorithm

egg-herbie

Counts

795 → 795

Iterations

Useful iterations: 1 (32.0ms)

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

prune764.0ms

Filtered

795 candidates to 131 candidates (16.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	792	3	795
Fresh	8	2	10
Picked	1	0	1
Done	0	0	0
Total	801	5	806

Merged error: 3.7b

Counts

806 → 5

localize24.0ms

Local error

Found 4 expressions with local error:

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)))
0.7b	(exp (log (/ (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)))))
1.4b	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))
11.6b	(log (/ (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))))

rewrite156.0ms

Algorithm

rewrite-expression-head

Rules

802×	`*-un-lft-identity`
576×	`prod-diff`
448×	`add-sqr-sqrt`
435×	`unpow-prod-down` `cube-prod`
407×	`times-frac`
402×	`add-cube-cbrt`
234×	`distribute-lft-out`
71×	`sqr-pow`
61×	`cube-mult` `unpow3`
58×	`associate-/r/`
48×	`fma-neg`
29×	`flip3-+` `flip-+` `div-inv`
24×	`difference-of-squares`
18×	`log-prod`
15×	`add-exp-log`
9×	`exp-sum` `add-cbrt-cube`
6×	`pow1` `associate-*r/` `add-log-exp`
5×	`distribute-lft-out--`
4×	`expm1-log1p-u` `exp-prod` `div-exp` `log1p-expm1-u`
3×	`rem-log-exp` `associate-/l*`
2×	`cbrt-undiv` `log-div` `prod-exp` `log-pow`
1×	`difference-cubes` `sub-neg` `flip3--` `frac-2neg` `exp-diff` `diff-log` `clear-num` `associate-/r*` `flip--` `cbrt-unprod` `rem-exp-log`

Counts

4 → 740

Calls

4 calls:

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)))
9.0ms	(exp (log (/ (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)))))
60.0ms	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))
8.0ms	(log (/ (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))))

series2.0s

Counts

4 → 12

Calls

4 calls:

440.0ms	(/ (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)))
431.0ms	(exp (log (/ (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)))))
114.0ms	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))
1.0s	(log (/ (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))))

simplify316.0ms

Algorithm

egg-herbie

Counts

752 → 752

Iterations

Useful iterations: 2 (144.0ms)

Iter	Nodes	Cost
0	1229	15519
1	4553	11484
2	5001	11482

prune772.0ms

Filtered

752 candidates to 124 candidates (16.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	750	2	752
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	751	6	757

Merged error: 3.7b

Counts

757 → 6

regimes107.0ms

Accuracy

67.8% (4.1b remaining)

Error of 7.2b against oracle of 3.1b and baseline of 15.7b

bsearch186.0ms

Steps

Iters	Range		Point
8	5.172961417222266e+65	1.3104433616643962e+70	5.293664998180793e+65
6	1.5865537497029128e+52	2.265641445575101e+53	1.138060537537574e+53
9	4.643958454173516e+32	3.261941379769491e+39	1.6980902612943045e+38

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	66	97
1	72	97
2	76	97
3	76	97

end0.0ms

sample632.0ms

Algorithm

intervals

Results

165.0ms	5860×	body	80	valid
113.0ms	857×	body	1280	valid
97.0ms	8000×	pre	80	true
73.0ms	694×	body	640	valid
30.0ms	384×	body	320	valid
11.0ms	205×	body	160	valid