Details

sample25.0ms

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

simplify76.0ms

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

localize12.0ms

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)

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

4×	`associate-/r/`
3×	`fma-def` `flip3-+` `flip-+`
2×	`div-sub` `div-inv` `associate-/l/`
1×	`+-commutative` `associate-+l-` `flip3--` `frac-2neg` `clear-num` `flip--`

Counts

2 → 15

Calls

2 calls:

5.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
7.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series106.0ms

Counts

2 → 6

Calls

2 calls:

49.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
57.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify56.0ms

Algorithm

egg-herbie

Counts

21 → 21

Iterations

Useful iterations: 3 (53.0ms)

Iter	Nodes	Cost
0	187	121
1	556	115
2	2340	108
3	5001	102

prune69.0ms

Filtered

21 candidates to 19 candidates (90.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	13	8	21
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	14	8	22

Merged error: 16.5b

Counts

22 → 8

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)

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

8×	`associate-/r/`
6×	`fma-neg` `frac-sub`
5×	`flip3--` `flip--`
4×	`frac-2neg` `flip3-+` `clear-num` `flip-+` `div-inv`
3×	`sub-neg`
2×	`associate--r+`
1×	`associate--r-`

Counts

4 → 33

Calls

4 calls:

10.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
4.0ms	(/ alpha (+ (+ alpha beta) 2.0))
4.0ms	(/ beta (+ (+ alpha beta) 2.0))
6.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series235.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
45.0ms	(/ alpha (+ (+ alpha beta) 2.0))
50.0ms	(/ beta (+ (+ alpha beta) 2.0))
77.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify44.0ms

Algorithm

egg-herbie

Counts

45 → 45

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	388	431
1	1629	423
2	5001	419

prune143.0ms

Filtered

45 candidates to 38 candidates (84.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	40	5	45
Fresh	7	0	7
Picked	1	0	1
Done	0	0	0
Total	48	5	53

Merged error: 3.7b

Counts

53 → 5

localize22.0ms

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))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

12×	`unpow-prod-down`
11×	`sqr-pow`
10×	`prod-diff` `associate-/r/`
9×	`unpow3`
8×	`distribute-neg-in`
6×	`flip3-+` `flip-+`
5×	`fma-neg` `div-inv`
4×	`+-commutative` `distribute-rgt-in` `associate-+l+` `distribute-lft-in` `associate-*r/` `distribute-neg-frac`
3×	`associate-/r*`
2×	`neg-mul-1` `associate-r` `*-commutative`
1×	`difference-cubes` `pow-to-exp` `sub-neg` `flip3--` `frac-2neg` `clear-num` `distribute-rgt-neg-out` `flip--` `difference-of-squares`

Counts

4 → 48

Calls

4 calls:

5.0ms	(* (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)))
3.0ms	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
5.0ms	(/ (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))))
7.0ms	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

series726.0ms

Counts

4 → 12

Calls

4 calls:

159.0ms	(* (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)))
73.0ms	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
385.0ms	(/ (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))))
108.0ms	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

simplify49.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	428	920
1	1607	897
2	5001	892

prune379.0ms

Filtered

60 candidates to 45 candidates (75.0%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	59	1	60
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	60	5	65

Merged error: 3.7b

Counts

65 → 5

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (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) beta))
0.2b	(/ (- (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) beta) (- (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) beta)))
1.4b	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))
6.2b	(* (/ (+ (+ alpha beta) 2.0) beta) (- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

50×	`prod-diff`
40×	`sqr-pow`
36×	`unpow3`
33×	`unpow-prod-down`
28×	`associate-/r/`
25×	`div-sub`
24×	`distribute-rgt-in` `distribute-lft-in` `associate--r+`
16×	`flip3-+` `flip-+`
15×	`div-inv`
12×	`associate-*r/` `associate-/l/`
10×	`frac-times`
8×	`flip3--` `clear-num` `flip--`
6×	`frac-2neg`
5×	`sub-neg` `fma-neg` `associate-*l/`
4×	`associate-r`
3×	`associate-/r` `-commutative`
2×	`difference-cubes` `un-div-inv` `difference-of-squares`
1×	`associate-l`

Counts

4 → 113

Calls

4 calls:

5.0ms	(* (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) beta))
16.0ms	(/ (- (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) beta) (- (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) beta)))
7.0ms	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))
12.0ms	(* (/ (+ (+ alpha beta) 2.0) beta) (- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3)))

series758.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(* (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) beta))
420.0ms	(/ (- (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) beta) (- (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) beta)))
104.0ms	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))
86.0ms	(* (/ (+ (+ alpha beta) 2.0) beta) (- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3)))

simplify128.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 2 (96.0ms)

Iter	Nodes	Cost
0	968	3626
1	4246	3279
2	5001	3045

prune390.0ms

Filtered

125 candidates to 74 candidates (59.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	124	1	125
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	125	5	130

Merged error: 1.1b

Counts

130 → 5

regimes81.0ms

Accuracy

57.6% (6.6b remaining)

Error of 7.2b against oracle of 0.6b and baseline of 16.1b

bsearch154.0ms

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

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	65	84
1	65	84

end0.0ms

sample617.0ms

Algorithm

intervals

Results

150.0ms	5860×	body	80	valid
112.0ms	857×	body	1280	valid
104.0ms	8000×	pre	80	true
68.0ms	694×	body	640	valid
28.0ms	384×	body	320	valid
10.0ms	205×	body	160	valid