Details

sample21.0ms

Algorithm

intervals

Results

5.0ms	29×	body	640	valid
5.0ms	187×	body	80	valid
1.0ms	16×	body	320	valid
1.0ms	8×	body	1280	valid
1.0ms	16×	body	160	valid

simplify91.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (13.0ms)

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

prune5.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 15.6b

Counts

2 → 1

localize7.0ms

Local error

Found 1 expressions with local error:

3.9b	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

1 → 10

Calls

1 calls:

1.0ms

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

series57.0ms

Counts

1 → 3

Calls

1 calls:

57.0ms

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

simplify72.0ms

Algorithm

egg-herbie

Counts

13 → 13

Iterations

Useful iterations: 3 (22.0ms)

Iter	Nodes	Cost
0	59	83
1	163	71
2	523	68
3	1872	66
4	5001	66

prune45.0ms

Filtered

13 candidates to 12 candidates (92.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	9	4	13
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	9	5	14

Merged error: 8.8b

Counts

14 → 5

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cbrt (fma (/ y (+ y 1.0)) (- x 1.0) 1.0)) (cbrt (fma (/ y (+ y 1.0)) (- x 1.0) 1.0)))
3.9b	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)
3.9b	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)
3.9b	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
16×	`cbrt-prod`
12×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
8×	`add-cbrt-cube`
6×	`add-exp-log` `pow1/3` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`fma-udef`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative`

Counts

4 → 75

Calls

4 calls:

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

series308.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(* (cbrt (fma (/ y (+ y 1.0)) (- x 1.0) 1.0)) (cbrt (fma (/ y (+ y 1.0)) (- x 1.0) 1.0)))
56.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)
62.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)
60.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

simplify131.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 3 (120.0ms)

Iter	Nodes	Cost
0	212	901
1	750	786
2	3737	665
3	5002	650

prune257.0ms

Filtered

87 candidates to 66 candidates (75.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	85	2	87
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	86	6	92

Merged error: 8.8b

Counts

92 → 6

localize17.0ms

Local error

Found 4 expressions with local error:

3.9b	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)
3.9b	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)
3.9b	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)
3.9b	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

4 → 40

Calls

4 calls:

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

series241.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)
57.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)
61.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)
60.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

simplify74.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 3 (23.0ms)

Iter	Nodes	Cost
0	59	332
1	163	284
2	523	272
3	1872	264
4	5001	264

prune230.0ms

Filtered

52 candidates to 48 candidates (92.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	51	1	52
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	52	6	58

Merged error: 8.8b

Counts

58 → 6

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(exp (fma (/ y (+ y 1.0)) (- x 1.0) 1.0))
3.9b	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)
4.6b	(log (exp (fma (/ y (+ y 1.0)) (- x 1.0) 1.0)))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt` `add-cube-cbrt` `exp-prod` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `log-prod` `log-pow` `add-log-exp`
3×	`expm1-log1p-u` `add-cbrt-cube` `fma-udef` `log1p-expm1-u`
2×	`rem-log-exp` `exp-sum`
1×	`rem-exp-log`

Counts

3 → 43

Calls

3 calls:

2.0ms	(exp (fma (/ y (+ y 1.0)) (- x 1.0) 1.0))
1.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)
3.0ms	(log (exp (fma (/ y (+ y 1.0)) (- x 1.0) 1.0)))

series212.0ms

Counts

3 → 9

Calls

3 calls:

90.0ms	(exp (fma (/ y (+ y 1.0)) (- x 1.0) 1.0))
64.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)
58.0ms	(log (exp (fma (/ y (+ y 1.0)) (- x 1.0) 1.0)))

simplify121.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 3 (39.0ms)

Iter	Nodes	Cost
0	143	349
1	396	308
2	1131	298
3	3921	286
4	5001	286

prune136.0ms

Filtered

52 candidates to 41 candidates (78.8%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	51	1	52
Fresh	1	2	3
Picked	0	1	1
Done	0	2	2
Total	52	6	58

Merged error: 8.7b

Counts

58 → 6

regimes69.0ms

Accuracy

98.7% (0.1b remaining)

Error of 7.3b against oracle of 7.2b and baseline of 14.0b

bsearch97.0ms

Steps

Iters	Range		Point
9	28979454454.04592	8.183255868948431e+19	9.61602000771861e+15
9	-8.382207188783003e+18	-107831645193065.94	-8.794308534647588e+17

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	8
1	21	8

end0.0ms

sample444.0ms

Algorithm

intervals

Results

152.0ms	6137×	body	80	valid
69.0ms	700×	body	640	valid
43.0ms	349×	body	1280	valid
34.0ms	515×	body	320	valid
13.0ms	299×	body	160	valid