Details

sample24.0ms

Algorithm

intervals

Results

5.0ms	184×	body	80	valid
3.0ms	28×	body	1280	valid
3.0ms	256×	pre	80	true
2.0ms	16×	body	640	valid
1.0ms	19×	body	320	valid
0.0ms	9×	body	160	valid

simplify75.0ms

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: 16.9b

Counts

2 → 1

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
3.6b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite13.0ms

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)

series113.0ms

Counts

2 → 6

Calls

2 calls:

51.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
62.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify58.0ms

Algorithm

egg-herbie

Counts

21 → 21

Iterations

Useful iterations: 3 (55.0ms)

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

prune66.0ms

Filtered

21 candidates to 19 candidates (90.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	14	7	21
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	14	8	22

Merged error: 15.9b

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))
3.6b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite26.0ms

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:

11.0ms	(- (/ 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)

series247.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
48.0ms	(/ alpha (+ (+ alpha beta) 2.0))
51.0ms	(/ beta (+ (+ alpha beta) 2.0))
82.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify45.0ms

Algorithm

egg-herbie

Counts

45 → 45

Iterations

Useful iterations: 2 (39.0ms)

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

prune145.0ms

Filtered

45 candidates to 38 candidates (84.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	41	4	45
Fresh	5	1	6
Picked	1	0	1
Done	1	0	1
Total	48	5	53

Merged error: 4.2b

Counts

53 → 5

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(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)))))
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)
3.5b	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

12×	`unpow-prod-down`
11×	`sqr-pow`
10×	`prod-diff` `associate-/r/`
9×	`unpow3`
5×	`flip3-+` `fma-neg` `flip-+` `div-inv`
2×	`associate-r/` `associate-/r`
1×	`difference-cubes` `pow-to-exp` `sub-neg` `flip3--` `frac-2neg` `clear-num` `*-commutative` `flip--` `fma-udef` `difference-of-squares`

Counts

4 → 35

Calls

4 calls:

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

series812.0ms

Counts

4 → 12

Calls

4 calls:

195.0ms	(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)))))
429.0ms	(/ (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)))
77.0ms	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
111.0ms	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

simplify43.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	364	594
1	1366	570
2	5001	565

prune220.0ms

Filtered

47 candidates to 36 candidates (76.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	42	5	47
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	44	8	52

Merged error: 4.2b

Counts

52 → 8

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
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)) (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))))))
0.1b	(/ 1 (/ (* (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)) (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)))))))
3.5b	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

15×	`associate-/r/`
12×	`unpow-prod-down`
11×	`sqr-pow`
10×	`prod-diff`
9×	`unpow3`
7×	`div-inv`
6×	`flip3-+` `flip-+`
5×	`fma-neg`
4×	`associate-r/` `clear-num` `associate-/l/` `associate-/l`
3×	`frac-2neg`
2×	`*-commutative`
1×	`difference-cubes` `pow-to-exp` `sub-neg` `flip3--` `associate-/r*` `flip--` `remove-double-div` `inv-pow` `difference-of-squares`

Counts

4 → 47

Calls

4 calls:

3.0ms	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
7.0ms	(/ (* (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)) (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))))))
7.0ms	(/ 1 (/ (* (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)) (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)))))))
7.0ms	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

series1.2s

Counts

4 → 12

Calls

4 calls:

78.0ms	(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
577.0ms	(/ (* (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)) (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))))))
440.0ms	(/ 1 (/ (* (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)) (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)))))))
114.0ms	(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

simplify50.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	417	803
1	1641	779
2	5001	775

prune242.0ms

Filtered

59 candidates to 47 candidates (79.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	57	2	59
Fresh	5	2	7
Picked	1	0	1
Done	0	0	0
Total	63	4	67

Merged error: 0.4b

Counts

67 → 4

regimes58.0ms

Accuracy

80% (3.3b remaining)

Error of 3.8b against oracle of 0.5b and baseline of 17.0b

bsearch44.0ms

Steps

Iters	Range		Point
8	0.0027862087296086848	1.7188991529834365	0.0028216562709730635

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	11
1	25	11

end0.0ms

sample606.0ms

Algorithm

intervals

Results

150.0ms	5764×	body	80	valid
108.0ms	880×	body	1280	valid
97.0ms	8000×	pre	80	true
71.0ms	742×	body	640	valid
29.0ms	411×	body	320	valid
10.0ms	203×	body	160	valid