Details

sample19.0ms

Algorithm

intervals

Results

5.0ms	187×	body	80	valid
3.0ms	29×	body	640	valid
1.0ms	16×	body	320	valid
1.0ms	8×	body	1280	valid
1.0ms	16×	body	160	valid

simplify87.0ms

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

localize11.0ms

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)

series56.0ms

Counts

1 → 3

Calls

1 calls:

56.0ms

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

simplify61.0ms

Algorithm

egg-herbie

Counts

13 → 13

Iterations

Useful iterations: 3 (19.0ms)

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

prune44.0ms

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`
6×	`add-exp-log` `pow1/3` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `add-cbrt-cube` `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` `cbrt-unprod`

Counts

4 → 72

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)

series300.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(* (cbrt (fma (/ y (+ y 1.0)) (- x 1.0) 1.0)) (cbrt (fma (/ y (+ y 1.0)) (- x 1.0) 1.0)))
57.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)
60.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)
60.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

simplify120.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 3 (107.0ms)

Iter	Nodes	Cost
0	203	822
1	713	736
2	3312	647
3	5001	632

prune257.0ms

Filtered

84 candidates to 66 candidates (78.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	82	2	84
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	83	6	89

Merged error: 8.8b

Counts

89 → 6

localize16.0ms

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)

series229.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)
60.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)
53.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)
57.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

simplify68.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 3 (21.0ms)

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

prune225.0ms

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

localize10.0ms

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)))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 42

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

series204.0ms

Counts

3 → 9

Calls

3 calls:

86.0ms	(exp (fma (/ y (+ y 1.0)) (- x 1.0) 1.0))
59.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)
59.0ms	(log (exp (fma (/ y (+ y 1.0)) (- x 1.0) 1.0)))

simplify115.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 3 (36.0ms)

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

prune133.0ms

Filtered

51 candidates to 41 candidates (80.4%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	50	1	51
Fresh	1	2	3
Picked	0	1	1
Done	0	2	2
Total	51	6	57

Merged error: 8.7b

Counts

57 → 6

regimes67.0ms

Accuracy

98.7% (0.1b remaining)

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

bsearch85.0ms

Steps

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

simplify7.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	8
1	21	8

end0.0ms

sample469.0ms

Algorithm

intervals

Results

164.0ms	6137×	body	80	valid
67.0ms	700×	body	640	valid
44.0ms	349×	body	1280	valid
40.0ms	515×	body	320	valid
15.0ms	299×	body	160	valid