Details

sample36.0ms

Algorithm

intervals

Results

13.0ms	68×	body	1280	valid
6.0ms	46×	body	640	valid
4.0ms	158×	body	80	valid
3.0ms	13×	body	160	valid
3.0ms	30×	body	320	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

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: 37.8b

Counts

2 → 1

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- (exp x) 1.0) x)
4.3b	(- (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)

series60.0ms

Counts

2 → 6

Calls

2 calls:

45.0ms	(/ (- (exp x) 1.0) x)
15.0ms	(- (exp x) 1.0)

simplify37.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 2 (30.0ms)

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

prune122.0ms

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: 0.0b

Counts

75 → 4

localize7.0ms

Local error

Found 1 expressions with local error:

0.1b	(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))

series21.0ms

Counts

1 → 3

Calls

1 calls:

21.0ms

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

simplify27.0ms

Algorithm

egg-herbie

Counts

13 → 13

Iterations

Useful iterations: 1 (4.0ms)

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

prune32.0ms

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: 0.0b

Counts

17 → 5

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cbrt (fma 1/6 (pow x 2) (fma 1/2 x 1))) (cbrt (fma 1/6 (pow x 2) (fma 1/2 x 1))))
9.9b	(cbrt (fma 1/6 (pow x 2) (fma 1/2 x 1)))
9.9b	(cbrt (fma 1/6 (pow x 2) (fma 1/2 x 1)))
9.9b	(cbrt (fma 1/6 (pow x 2) (fma 1/2 x 1)))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 81

Calls

4 calls:

6.0ms	(* (cbrt (fma 1/6 (pow x 2) (fma 1/2 x 1))) (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)))
1.0ms	(cbrt (fma 1/6 (pow x 2) (fma 1/2 x 1)))

series227.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(* (cbrt (fma 1/6 (pow x 2) (fma 1/2 x 1))) (cbrt (fma 1/6 (pow x 2) (fma 1/2 x 1))))
57.0ms	(cbrt (fma 1/6 (pow x 2) (fma 1/2 x 1)))
57.0ms	(cbrt (fma 1/6 (pow x 2) (fma 1/2 x 1)))
54.0ms	(cbrt (fma 1/6 (pow x 2) (fma 1/2 x 1)))

simplify103.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 3 (89.0ms)

Iter	Nodes	Cost
0	216	936
1	676	870
2	3111	805
3	5002	790

prune236.0ms

Filtered

93 candidates to 72 candidates (77.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	93	5	98

Merged error: 0.0b

Counts

98 → 5

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(fma 1/6 (pow x 3) x)
3.1b	(/ (fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x)) x)
10.3b	(fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x))

rewrite6.0ms

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

series150.0ms

Counts

3 → 9

Calls

3 calls:

75.0ms	(fma 1/6 (pow x 3) x)
44.0ms	(/ (fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x)) x)
31.0ms	(fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x))

simplify86.0ms

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

prune127.0ms

Filtered

58 candidates to 44 candidates (75.9%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	58	0	58
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	58	5	63

Merged error: 0.0b

Counts

63 → 5

regimes26.0ms

Accuracy

98.3% (0.4b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 21.2b

bsearch20.0ms

Steps

Iters	Range		Point
6	-7.74497267090904e-05	-1.272348569829707e-05	-7.372861788394869e-05

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	8
1	19	8

end0.0ms

sample1.0s

Algorithm

intervals

Results

448.0ms	2194×	body	1280	valid
217.0ms	1672×	body	640	valid
130.0ms	5413×	body	80	valid
77.0ms	863×	body	320	valid
28.0ms	436×	body	160	valid