Details

sample33.0ms

Algorithm

intervals

Results

12.0ms	59×	body	1280	valid
7.0ms	49×	body	640	valid
5.0ms	198×	body	80	valid
2.0ms	21×	body	320	valid
1.0ms	16×	body	160	valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	3
1	13	3
2	15	3
3	15	3

prune4.0ms

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: 35.0b

Counts

2 → 1

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- (exp x) 1.0) x)
3.9b	(- (exp x) 1.0)

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt` `*-un-lft-identity`
19×	`add-cube-cbrt`
15×	`times-frac`
9×	`prod-diff`
5×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`fma-neg` `associate-/r*`
2×	`pow1` `expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

2 → 68

Calls

2 calls:

7.0ms	(/ (- (exp x) 1.0) x)
5.0ms	(- (exp x) 1.0)

series53.0ms

Counts

2 → 6

Calls

2 calls:

38.0ms	(/ (- (exp x) 1.0) x)
14.0ms	(- (exp x) 1.0)

simplify35.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	282	468
1	919	380
2	5001	377

prune124.0ms

Filtered

74 candidates to 52 candidates (70.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	70	4	74
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	71	4	75

Merged error: 0.1b

Counts

75 → 4

localize7.0ms

Local error

Found 1 expressions with local error:

0.3b	(fma 1/6 (pow x 2) (fma 1/2 x 1))

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 1/6 (pow x 2) (fma 1/2 x 1))

series23.0ms

Counts

1 → 3

Calls

1 calls:

23.0ms

(fma 1/6 (pow x 2) (fma 1/2 x 1))

simplify24.0ms

Algorithm

egg-herbie

Counts

13 → 13

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	36	59
1	104	52
2	535	52
3	5002	52

prune33.0ms

Filtered

13 candidates to 10 candidates (76.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	12	1	13
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	12	5	17

Merged error: 0.1b

Counts

17 → 5

localize10.0ms

Local error

Found 4 expressions with local error:

0.3b	(fma 1/6 (pow x 2) (fma 1/2 x 1))
10.9b	(cbrt (fma 1/6 (pow x 2) (fma 1/2 x 1)))
10.9b	(cbrt (fma 1/6 (pow x 2) (fma 1/2 x 1)))
10.9b	(cbrt (fma 1/6 (pow x 2) (fma 1/2 x 1)))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`fma-udef`

Counts

4 → 49

Calls

4 calls:

1.0ms	(fma 1/6 (pow x 2) (fma 1/2 x 1))
1.0ms	(cbrt (fma 1/6 (pow x 2) (fma 1/2 x 1)))
1.0ms	(cbrt (fma 1/6 (pow x 2) (fma 1/2 x 1)))
1.0ms	(cbrt (fma 1/6 (pow x 2) (fma 1/2 x 1)))

series189.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(fma 1/6 (pow x 2) (fma 1/2 x 1))
53.0ms	(cbrt (fma 1/6 (pow x 2) (fma 1/2 x 1)))
56.0ms	(cbrt (fma 1/6 (pow x 2) (fma 1/2 x 1)))
55.0ms	(cbrt (fma 1/6 (pow x 2) (fma 1/2 x 1)))

simplify38.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 2 (9.0ms)

Iter	Nodes	Cost
0	109	494
1	258	460
2	988	454
3	5002	454

prune201.0ms

Filtered

61 candidates to 55 candidates (90.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	60	1	61
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	61	5	66

Merged error: 0.0b

Counts

66 → 5

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(fma 1/6 (pow x 3) x)
4.2b	(/ (fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x)) x)
11.6b	(fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
5×	`add-exp-log` `add-cbrt-cube`
3×	`pow1` `expm1-log1p-u` `associate-/r` `log1p-expm1-u` `associate-/l` `add-log-exp`
2×	`fma-udef`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

3 → 49

Calls

3 calls:

1.0ms	(fma 1/6 (pow x 3) x)
3.0ms	(/ (fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x)) x)
4.0ms	(fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x))

series142.0ms

Counts

3 → 9

Calls

3 calls:

73.0ms	(fma 1/6 (pow x 3) x)
43.0ms	(/ (fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x)) x)
26.0ms	(fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x))

simplify85.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	140	391
1	510	356
2	2915	356
3	5002	356

prune136.0ms

Filtered

58 candidates to 44 candidates (75.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	58	0	58
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	58	5	63

Merged error: 0.0b

Counts

63 → 5

regimes28.0ms

Accuracy

98.5% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 21.3b

bsearch30.0ms

Steps

Iters	Range		Point
9	-17.831791951177678	-3.7534567552478157e-06	-0.00014405859289179878

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	11
1	23	11

end0.0ms

sample1.0s

Algorithm

intervals

Results

447.0ms	2264×	body	1280	valid
219.0ms	1631×	body	640	valid
129.0ms	5450×	body	80	valid
70.0ms	828×	body	320	valid
25.0ms	447×	body	160	valid

Details

sample33.0ms

simplify7.0ms

prune4.0ms

localize4.0ms

rewrite14.0ms

series53.0ms

simplify35.0ms

prune124.0ms

localize7.0ms

rewrite1.0ms

series23.0ms

simplify24.0ms

prune33.0ms

localize10.0ms

rewrite5.0ms

series189.0ms

simplify38.0ms

prune201.0ms

localize10.0ms

rewrite9.0ms

series142.0ms

simplify85.0ms

prune136.0ms

regimes28.0ms

bsearch30.0ms

simplify1.0ms

end0.0ms

sample1.0s

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