Details

sample32.0ms

Algorithm

intervals

Results

12.0ms	76×	body	1280	valid
6.0ms	56×	body	640	valid
3.0ms	174×	body	80	valid
3.0ms	17×	body	160	valid
1.0ms	16×	body	320	valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 39.2b

Counts

2 → 1

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- (exp x) 1.0) x)
4.6b	(- (exp x) 1.0)

rewrite13.0ms

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)
4.0ms	(- (exp x) 1.0)

series64.0ms

Counts

2 → 6

Calls

2 calls:

47.0ms	(/ (- (exp x) 1.0) x)
16.0ms	(- (exp x) 1.0)

simplify37.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	280	469
1	901	380
2	5001	377

prune111.0ms

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

localize6.0ms

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))

series25.0ms

Counts

1 → 3

Calls

1 calls:

25.0ms

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

simplify26.0ms

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	5001	52

prune30.0ms

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

localize9.0ms

Local error

Found 4 expressions with local error:

0.3b	(fma 1/6 (pow x 2) (fma 1/2 x 1))
0.3b	(fma 1/6 (pow x 2) (fma 1/2 x 1))
10.4b	(sqrt (fma 1/6 (pow x 2) (fma 1/2 x 1)))
10.4b	(sqrt (fma 1/6 (pow x 2) (fma 1/2 x 1)))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-udef`

Counts

4 → 50

Calls

4 calls:

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

series176.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(fma 1/6 (pow x 2) (fma 1/2 x 1))
22.0ms	(fma 1/6 (pow x 2) (fma 1/2 x 1))
66.0ms	(sqrt (fma 1/6 (pow x 2) (fma 1/2 x 1)))
64.0ms	(sqrt (fma 1/6 (pow x 2) (fma 1/2 x 1)))

simplify78.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 3 (72.0ms)

Iter	Nodes	Cost
0	116	342
1	403	314
2	2097	312
3	5002	310

prune153.0ms

Filtered

62 candidates to 50 candidates (80.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	61	1	62
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	62	5	67

Merged error: 0.1b

Counts

67 → 5

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sqrt (fma 1/6 (pow x 2) (fma 1/2 x 1))) (fma 5/96 (pow x 2) (fma 1/4 x 1)))
0.3b	(fma 1/6 (pow x 2) (fma 1/2 x 1))
0.5b	(fma 5/96 (pow x 2) (fma 1/4 x 1))
10.4b	(sqrt (fma 1/6 (pow x 2) (fma 1/2 x 1)))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`pow1` `sqrt-prod`
6×	`add-exp-log` `associate-l` `add-cbrt-cube`
4×	`expm1-log1p-u` `fma-udef` `log1p-expm1-u` `add-log-exp`
3×	`associate-r`
2×	`unswap-sqr`
1×	`distribute-rgt-in` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `pow1/2` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 61

Calls

4 calls:

4.0ms	(* (sqrt (fma 1/6 (pow x 2) (fma 1/2 x 1))) (fma 5/96 (pow x 2) (fma 1/4 x 1)))
1.0ms	(fma 1/6 (pow x 2) (fma 1/2 x 1))
1.0ms	(fma 5/96 (pow x 2) (fma 1/4 x 1))
2.0ms	(sqrt (fma 1/6 (pow x 2) (fma 1/2 x 1)))

series240.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(* (sqrt (fma 1/6 (pow x 2) (fma 1/2 x 1))) (fma 5/96 (pow x 2) (fma 1/4 x 1)))
26.0ms	(fma 1/6 (pow x 2) (fma 1/2 x 1))
21.0ms	(fma 5/96 (pow x 2) (fma 1/4 x 1))
67.0ms	(sqrt (fma 1/6 (pow x 2) (fma 1/2 x 1)))

simplify42.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	243	562
1	1061	518
2	5001	515

prune185.0ms

Filtered

73 candidates to 55 candidates (75.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	72	1	73
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	73	5	78

Merged error: 0.1b

Counts

78 → 5

regimes26.0ms

Accuracy

98.4% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 20.8b

bsearch26.0ms

Steps

Iters	Range		Point
8	-0.00024695944164034034	-6.132196241634436e-08	-0.00014555830829536084

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	11
1	23	11

end0.0ms

sample853.0ms

Algorithm

intervals

Results

362.0ms	2195×	body	1280	valid
173.0ms	1709×	body	640	valid
100.0ms	5364×	body	80	valid
61.0ms	875×	body	320	valid
24.0ms	460×	body	160	valid