Details

sample33.0ms

Algorithm

intervals

Results

13.0ms	74×	body	1280	valid
7.0ms	58×	body	640	valid
2.0ms	89×	body	80	valid
2.0ms	24×	body	320	valid
1.0ms	75×	body	80	overflowed
1.0ms	11×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	7	4
1	8	4
2	8	4

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: 43.1b

Counts

2 → 1

localize4.0ms

Local error

Found 2 expressions with local error:

1.2b	(/ (exp x) (- (exp x) 1.0))
3.6b	(- (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-/r*` `distribute-lft-out--` `difference-of-squares`
4×	`add-cbrt-cube` `add-log-exp`
3×	`add-exp-log` `fma-neg` `associate-/l*`
2×	`pow1` `expm1-log1p-u` `flip3--` `associate-/r/` `flip--` `log1p-expm1-u`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `clear-num` `div-inv`

Counts

2 → 67

Calls

2 calls:

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

series44.0ms

Counts

2 → 6

Calls

2 calls:

26.0ms	(/ (exp x) (- (exp x) 1.0))
18.0ms	(- (exp x) 1.0)

simplify186.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 3 (179.0ms)

Iter	Nodes	Cost
0	237	520
1	786	429
2	4651	416
3	5001	404

prune116.0ms

Filtered

73 candidates to 50 candidates (68.5%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	71	2	73
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	72	2	74

Merged error: 0.0b

Counts

74 → 2

localize5.0ms

Local error

Found 1 expressions with local error:

0.1b	(fma 1/12 x (/ 1 x))

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 1/12 x (/ 1 x))

series43.0ms

Counts

1 → 3

Calls

1 calls:

43.0ms

(fma 1/12 x (/ 1 x))

simplify62.0ms

Algorithm

egg-herbie

Counts

13 → 13

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	21	43
1	49	38
2	150	38
3	482	38
4	2338	38
5	5002	38

prune21.0ms

Filtered

13 candidates to 10 candidates (76.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	12	1	13
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	12	3	15

Merged error: 0.0b

Counts

15 → 3

localize9.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (fma 1/12 x (/ 1 x)))
0.5b	(cbrt (fma 1/12 x (/ 1 x)))
0.5b	(cbrt (fma 1/12 x (/ 1 x)))
0.5b	(* (cbrt (fma 1/12 x (/ 1 x))) (cbrt (fma 1/12 x (/ 1 x))))

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:

1.0ms	(cbrt (fma 1/12 x (/ 1 x)))
1.0ms	(cbrt (fma 1/12 x (/ 1 x)))
1.0ms	(cbrt (fma 1/12 x (/ 1 x)))
6.0ms	(* (cbrt (fma 1/12 x (/ 1 x))) (cbrt (fma 1/12 x (/ 1 x))))

series407.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(cbrt (fma 1/12 x (/ 1 x)))
100.0ms	(cbrt (fma 1/12 x (/ 1 x)))
100.0ms	(cbrt (fma 1/12 x (/ 1 x)))
107.0ms	(* (cbrt (fma 1/12 x (/ 1 x))) (cbrt (fma 1/12 x (/ 1 x))))

simplify124.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 3 (115.0ms)

Iter	Nodes	Cost
0	277	823
1	917	765
2	4127	688
3	5002	652

prune220.0ms

Filtered

93 candidates to 72 candidates (77.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	92	1	93
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	93	3	96

Merged error: 0.0b

Counts

96 → 3

localize5.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (- 1 (/ 1.0 (exp x))))
0.0b	(/ 1.0 (exp x))
3.5b	(- 1 (/ 1.0 (exp x)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

99×	`add-sqr-sqrt`
79×	`*-un-lft-identity`
70×	`times-frac`
59×	`add-cube-cbrt`
39×	`prod-diff`
20×	`difference-of-squares`
11×	`associate-/r*`
8×	`add-exp-log`
7×	`add-cbrt-cube`
6×	`associate-/l*`
5×	`div-inv` `distribute-lft-out--` `add-log-exp`
4×	`pow1`
3×	`expm1-log1p-u` `fma-neg` `div-exp` `log1p-expm1-u`
2×	`cbrt-undiv` `flip3--` `frac-2neg` `clear-num` `associate-/r/` `flip--`
1×	`sub-neg` `rec-exp` `pow-flip` `diff-log` `1-exp` `inv-pow`

Counts

3 → 145

Calls

3 calls:

10.0ms	(/ 1 (- 1 (/ 1.0 (exp x))))
4.0ms	(/ 1.0 (exp x))
9.0ms	(- 1 (/ 1.0 (exp x)))

series100.0ms

Counts

3 → 9

Calls

3 calls:

48.0ms	(/ 1 (- 1 (/ 1.0 (exp x))))
17.0ms	(/ 1.0 (exp x))
35.0ms	(- 1 (/ 1.0 (exp x)))

simplify64.0ms

Algorithm

egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	552	1839
1	2298	1281
2	5001	1188

prune142.0ms

Filtered

154 candidates to 73 candidates (47.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	154	0	154
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	154	3	157

Merged error: 0.0b

Counts

157 → 3

regimes43.0ms

Accuracy

99% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 21.6b

bsearch3.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	9
1	24	9

end0.0ms

sample952.0ms

Algorithm

intervals

Results

411.0ms	2224×	body	1280	valid
202.0ms	1664×	body	640	valid
66.0ms	816×	body	320	valid
65.0ms	2891×	body	80	valid
54.0ms	2556×	body	80	overflowed
21.0ms	408×	body	160	valid