Details

sample31.0ms

Algorithm

intervals

Results

11.0ms	63×	body	1280	valid
6.0ms	57×	body	640	valid
4.0ms	181×	body	80	valid
2.0ms	29×	body	320	valid
1.0ms	12×	body	160	valid

simplify8.0ms

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

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.8b

localize5.0ms

Local error

Found 2 expressions with local error:

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

rewrite20.0ms

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:

12.0ms	(/ (- (exp x) 1.0) x)
6.0ms	(- (exp x) 1.0)

series60.0ms

Counts

2 → 6

Calls

2 calls:

44.0ms	(/ (- (exp x) 1.0) x)
16.0ms	(- (exp x) 1.0)

simplify35.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 2 (29.0ms)

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

prune145.0ms

Filtered

74 candidates to 52 candidates (70.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

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:

0.0ms

(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

prune40.0ms

Filtered

13 candidates to 10 candidates (76.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cbrt (fma 1/6 (pow x 2) (fma 1/2 x 1))) (cbrt (fma 1/6 (pow x 2) (fma 1/2 x 1))))
11.3b	(cbrt (fma 1/6 (pow x 2) (fma 1/2 x 1)))
11.3b	(cbrt (fma 1/6 (pow x 2) (fma 1/2 x 1)))
11.3b	(cbrt (fma 1/6 (pow x 2) (fma 1/2 x 1)))

rewrite9.0ms

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))))
0.0ms	(cbrt (fma 1/6 (pow x 2) (fma 1/2 x 1)))
0.0ms	(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:

61.0ms	(* (cbrt (fma 1/6 (pow x 2) (fma 1/2 x 1))) (cbrt (fma 1/6 (pow x 2) (fma 1/2 x 1))))
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)))
57.0ms	(cbrt (fma 1/6 (pow x 2) (fma 1/2 x 1)))

simplify99.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 3 (88.0ms)

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

prune279.0ms

Filtered

93 candidates to 72 candidates (77.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma 1/12 (pow x 2) (fma 1/3 x 1))
0.1b	(fma 1/6 (pow x 2) (fma 1/2 x 1))
0.1b	(fma 1/3 x 1)
11.3b	(cbrt (fma 1/6 (pow x 2) (fma 1/2 x 1)))

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

5×	`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×	`cbrt-prod` `fma-udef`
1×	`pow1/3`

Counts

4 → 43

Calls

4 calls:

0.0ms	(fma 1/12 (pow x 2) (fma 1/3 x 1))
0.0ms	(fma 1/6 (pow x 2) (fma 1/2 x 1))
0.0ms	(fma 1/3 x 1)
1.0ms	(cbrt (fma 1/6 (pow x 2) (fma 1/2 x 1)))

series131.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(fma 1/12 (pow x 2) (fma 1/3 x 1))
20.0ms	(fma 1/6 (pow x 2) (fma 1/2 x 1))
30.0ms	(fma 1/3 x 1)
56.0ms	(cbrt (fma 1/6 (pow x 2) (fma 1/2 x 1)))

simplify49.0ms

Algorithm

egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 2 (12.0ms)

Iter	Nodes	Cost
0	144	291
1	378	265
2	1596	263
3	5001	263

prune189.0ms

Filtered

55 candidates to 45 candidates (81.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

regimes28.0ms

Accuracy

98.9% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 20.9b

bsearch22.0ms

Steps

Iters	Range		Point
5	-0.00018190622123830468	-8.316448984380752e-05	-0.00017545399214217864

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	18
1	32	18

end0.0ms

sample890.0ms

Algorithm

intervals

Results

391.0ms	2279×	body	1280	valid
182.0ms	1694×	body	640	valid
102.0ms	5340×	body	80	valid
55.0ms	797×	body	320	valid
21.0ms	458×	body	160	valid