Details

sample29.0ms

Algorithm

intervals

Results

11.0ms	59×	body	1280	valid
5.0ms	57×	body	640	valid
3.0ms	184×	body	80	valid
2.0ms	28×	body	320	valid
1.0ms	19×	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

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.1b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- (exp x) 1.0) x)
5.1b	(- (exp x) 1.0)

rewrite19.0ms

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:

11.0ms	(/ (- (exp x) 1.0) x)
5.0ms	(- (exp x) 1.0)

series53.0ms

Counts

2 → 6

Calls

2 calls:

39.0ms	(/ (- (exp x) 1.0) x)
14.0ms	(- (exp x) 1.0)

simplify223.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 2 (28.0ms)

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

prune138.0ms

Filtered

74 candidates to 52 candidates (70.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize9.0ms

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))

series20.0ms

Counts

1 → 3

Calls

1 calls:

20.0ms

(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	5002	52

prune35.0ms

Filtered

13 candidates to 10 candidates (76.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 3 expressions with local error:

0.1b	(fma 1/6 (pow x 2) (fma 1/2 x 1))
0.8b	(expm1 (log1p (fma 1/6 (pow x 2) (fma 1/2 x 1))))
12.4b	(log1p (fma 1/6 (pow x 2) (fma 1/2 x 1)))

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 32

Calls

3 calls:

0.0ms	(fma 1/6 (pow x 2) (fma 1/2 x 1))
0.0ms	(expm1 (log1p (fma 1/6 (pow x 2) (fma 1/2 x 1))))
0.0ms	(log1p (fma 1/6 (pow x 2) (fma 1/2 x 1)))

series121.0ms

Counts

3 → 9

Calls

3 calls:

20.0ms	(fma 1/6 (pow x 2) (fma 1/2 x 1))
64.0ms	(expm1 (log1p (fma 1/6 (pow x 2) (fma 1/2 x 1))))
37.0ms	(log1p (fma 1/6 (pow x 2) (fma 1/2 x 1)))

simplify68.0ms

Algorithm

egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 3 (63.0ms)

Iter	Nodes	Cost
0	174	255
1	529	226
2	2138	203
3	5001	197

prune116.0ms

Filtered

41 candidates to 33 candidates (80.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma 1/4 x (log 2))
0.0b	(fma 5/96 (pow x 2) (fma 1/4 x (log 2)))
0.0b	(expm1 (fma 5/96 (pow x 2) (fma 1/4 x (log 2))))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 31

Calls

3 calls:

0.0ms	(fma 1/4 x (log 2))
0.0ms	(fma 5/96 (pow x 2) (fma 1/4 x (log 2)))
0.0ms	(expm1 (fma 5/96 (pow x 2) (fma 1/4 x (log 2))))

series229.0ms

Counts

3 → 9

Calls

3 calls:

161.0ms	(fma 1/4 x (log 2))
29.0ms	(fma 5/96 (pow x 2) (fma 1/4 x (log 2)))
39.0ms	(expm1 (fma 5/96 (pow x 2) (fma 1/4 x (log 2))))

simplify35.0ms

Algorithm

egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 3 (31.0ms)

Iter	Nodes	Cost
0	74	205
1	213	180
2	876	180
3	5001	178

prune104.0ms

Filtered

40 candidates to 29 candidates (72.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

regimes31.0ms

Accuracy

98.5% (0.3b remaining)

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

bsearch24.0ms

Steps

Iters	Range		Point
7	-0.00123344211380614	-3.4186969038389056e-05	-0.0001697150105858214

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	13
1	22	13

end0.0ms

sample866.0ms

Algorithm

intervals

Results

388.0ms	2270×	body	1280	valid
178.0ms	1652×	body	640	valid
98.0ms	5412×	body	80	valid
54.0ms	826×	body	320	valid
18.0ms	420×	body	160	valid