Details

sample19.0ms

Algorithm

intervals

Results

5.0ms	198×	body	80	valid
3.0ms	27×	body	640	valid
2.0ms	14×	body	1280	valid
1.0ms	9×	body	320	valid
0.0ms	8×	body	160	valid

simplify81.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (11.0ms)

Iter	Nodes	Cost
0	16	5
1	35	5
2	76	5
3	137	5
4	285	4
5	459	4
6	719	4
7	848	4
8	1064	4
9	1397	4
10	2101	4
11	5002	4

prune6.0ms

Filtered

1 candidates to 1 candidates (100.0%)

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: 13.9b

Counts

2 → 2

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ y (+ y 1.0))
2.2b	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

2×	`associate-/r/`
1×	`frac-2neg` `flip3-+` `clear-num` `flip-+` `fma-udef` `div-inv`

Counts

2 → 6

Calls

2 calls:

3.0ms	(/ y (+ y 1.0))
1.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

series95.0ms

Counts

2 → 6

Calls

2 calls:

35.0ms	(/ y (+ y 1.0))
60.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

simplify48.0ms

Algorithm

egg-herbie

Counts

12 → 12

Iterations

Useful iterations: 3 (45.0ms)

Iter	Nodes	Cost
0	105	59
1	298	52
2	1239	46
3	5002	42

prune39.0ms

Filtered

12 candidates to 10 candidates (83.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	7	5	12
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	9	5	14

Merged error: 8.2b

Counts

14 → 5

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (+ y 1.0) y)
0.1b	(/ 1 (/ (+ y 1.0) y))
2.2b	(fma (/ 1 (/ (+ y 1.0) y)) (- x 1.0) 1.0)

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

5×	`associate-/r/`
4×	`clear-num` `associate-/l/`
3×	`frac-2neg` `div-inv`
2×	`flip3-+` `flip-+`
1×	`associate-/r*` `fma-udef` `remove-double-div` `inv-pow`

Counts

3 → 17

Calls

3 calls:

3.0ms	(/ (+ y 1.0) y)
4.0ms	(/ 1 (/ (+ y 1.0) y))
1.0ms	(fma (/ 1 (/ (+ y 1.0) y)) (- x 1.0) 1.0)

series144.0ms

Counts

3 → 9

Calls

3 calls:

52.0ms	(/ (+ y 1.0) y)
34.0ms	(/ 1 (/ (+ y 1.0) y))
58.0ms	(fma (/ 1 (/ (+ y 1.0) y)) (- x 1.0) 1.0)

simplify82.0ms

Algorithm

egg-herbie

Counts

26 → 26

Iterations

Useful iterations: 3 (79.0ms)

Iter	Nodes	Cost
0	140	88
1	457	79
2	2256	72
3	5002	68

prune65.0ms

Filtered

26 candidates to 18 candidates (69.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	24	2	26
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	24	7	31

Merged error: 8.2b

Counts

31 → 7

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ 1 (* (+ y 1.0) (/ 1 y)))
0.1b	(* (+ y 1.0) (/ 1 y))
3.4b	(fma (/ 1 (* (+ y 1.0) (/ 1 y))) (- x 1.0) 1.0)

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

13×	`associate-/r/`
12×	`frac-times`
9×	`clear-num`
8×	`flip3-+` `flip-+`
7×	`frac-2neg`
6×	`associate-*r/`
4×	`associate-*l/` `un-div-inv`
3×	`associate-/r*` `div-inv`
2×	`associate-r` `*-commutative`
1×	`fma-udef` `inv-pow`

Counts

3 → 36

Calls

3 calls:

6.0ms	(/ 1 (* (+ y 1.0) (/ 1 y)))
4.0ms	(* (+ y 1.0) (/ 1 y))
1.0ms	(fma (/ 1 (* (+ y 1.0) (/ 1 y))) (- x 1.0) 1.0)

series146.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(/ 1 (* (+ y 1.0) (/ 1 y)))
48.0ms	(* (+ y 1.0) (/ 1 y))
59.0ms	(fma (/ 1 (* (+ y 1.0) (/ 1 y))) (- x 1.0) 1.0)

simplify202.0ms

Algorithm

egg-herbie

Counts

45 → 45

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	186	174
1	834	158
2	4979	149
3	5001	149

prune96.0ms

Filtered

45 candidates to 27 candidates (60.0%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	44	1	45
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	44	8	52

Merged error: 8.1b

Counts

52 → 8

localize15.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (/ y (- (* y y) (* 1.0 1.0))) (- y 1.0))
3.4b	(fma (* (/ y (- (* y y) (* 1.0 1.0))) (- y 1.0)) (- x 1.0) 1.0)
13.9b	(/ y (- (* y y) (* 1.0 1.0)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

17×	`*-commutative`
16×	`associate-/r*` `difference-of-squares`
14×	`frac-times`
10×	`flip3--` `flip--`
7×	`associate-*l/`
4×	`frac-2neg` `clear-num` `associate-/r/`
3×	`associate-l`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-*r/` `div-inv`
1×	`fma-udef`

Counts

3 → 41

Calls

3 calls:

9.0ms	(* (/ y (- (* y y) (* 1.0 1.0))) (- y 1.0))
1.0ms	(fma (* (/ y (- (* y y) (* 1.0 1.0))) (- y 1.0)) (- x 1.0) 1.0)
5.0ms	(/ y (- (* y y) (* 1.0 1.0)))

series220.0ms

Counts

3 → 9

Calls

3 calls:

59.0ms	(* (/ y (- (* y y) (* 1.0 1.0))) (- y 1.0))
86.0ms	(fma (* (/ y (- (* y y) (* 1.0 1.0))) (- y 1.0)) (- x 1.0) 1.0)
75.0ms	(/ y (- (* y y) (* 1.0 1.0)))

simplify55.0ms

Algorithm

egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	324	353
1	1645	340
2	5001	310

prune107.0ms

Filtered

50 candidates to 31 candidates (62.0%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	47	3	50
Fresh	2	3	5
Picked	1	0	1
Done	0	2	2
Total	50	8	58

Merged error: 8.1b

Counts

58 → 8

regimes79.0ms

Accuracy

97.7% (0.2b remaining)

Error of 7.6b against oracle of 7.4b and baseline of 14.3b

bsearch112.0ms

Steps

Iters	Range		Point
9	1.1581638671359371e+19	2.3534274151300485e+26	1.1800200009954589e+19
10	-1.4003922086164443e+35	-1.8120839603419894e+22	-2.5635796455149015e+22

simplify7.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	38	17
1	38	17

end0.0ms

sample481.0ms

Algorithm

intervals

Results

174.0ms	6110×	body	80	valid
66.0ms	698×	body	640	valid
45.0ms	377×	body	1280	valid
37.0ms	507×	body	320	valid
15.0ms	308×	body	160	valid