Details

sample33.0ms

Algorithm

intervals

Results

12.0ms	75×	body	1280	valid
6.0ms	183×	body	80	valid
3.0ms	36×	body	640	valid
2.0ms	28×	body	320	valid
1.0ms	18×	body	160	valid

simplify60.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	3
1	18	3
2	27	3
3	50	3
4	115	3
5	329	3
6	1642	3
7	5001	3

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.3b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(exp (* a x))
5.0b	(- (exp (* a x)) 1.0)

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`add-cube-cbrt` `prod-diff`
6×	`add-log-exp`
3×	`fma-neg`
2×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
1×	`sub-neg` `exp-prod` `flip3--` `exp-to-pow` `diff-log` `flip--` `rem-exp-log` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 40

Calls

2 calls:

1.0ms	(exp (* a x))
5.0ms	(- (exp (* a x)) 1.0)

series47.0ms

Counts

2 → 6

Calls

2 calls:

12.0ms	(exp (* a x))
34.0ms	(- (exp (* a x)) 1.0)

simplify81.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 3 (77.0ms)

Iter	Nodes	Cost
0	173	292
1	562	211
2	2710	200
3	5002	164

prune100.0ms

Filtered

46 candidates to 28 candidates (60.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 8.7b

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (* a x))
0.1b	(pow (- (exp (* a x)) 1.0) 3)
0.1b	(cbrt (pow (- (exp (* a x)) 1.0) 3))
5.0b	(- (exp (* a x)) 1.0)

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt` `*-un-lft-identity`
17×	`add-cube-cbrt`
16×	`cbrt-prod`
10×	`unpow-prod-down` `cube-prod`
9×	`prod-diff`
8×	`add-log-exp`
5×	`pow1` `add-exp-log` `add-cbrt-cube` `distribute-lft-out--` `difference-of-squares`
4×	`cube-div` `expm1-log1p-u` `log1p-expm1-u`
3×	`pow-unpow` `flip3--` `fma-neg` `flip--`
2×	`cube-mult` `cbrt-div` `unpow3` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `exp-prod` `exp-to-pow` `pow-pow` `pow1/3` `diff-log` `pow-exp` `rem-cbrt-cube` `rem-exp-log` `rem-cube-cbrt`

Counts

4 → 100

Calls

4 calls:

1.0ms	(exp (* a x))
6.0ms	(pow (- (exp (* a x)) 1.0) 3)
9.0ms	(cbrt (pow (- (exp (* a x)) 1.0) 3))
5.0ms	(- (exp (* a x)) 1.0)

series135.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(exp (* a x))
53.0ms	(pow (- (exp (* a x)) 1.0) 3)
35.0ms	(cbrt (pow (- (exp (* a x)) 1.0) 3))
35.0ms	(- (exp (* a x)) 1.0)

simplify44.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	333	721
1	1342	623
2	5001	613

prune222.0ms

Filtered

112 candidates to 59 candidates (52.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 8.7b

localize9.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (exp (* a x)))
0.3b	(cbrt (exp (* a x)))
0.3b	(cbrt (exp (* a x)))
5.1b	(fma (* (cbrt (exp (* a x))) (cbrt (exp (* a x)))) (cbrt (exp (* a x))) (- 1.0))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`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×	`pow1/3`
1×	`fma-udef`

Counts

4 → 49

Calls

4 calls:

1.0ms	(cbrt (exp (* a x)))
1.0ms	(cbrt (exp (* a x)))
1.0ms	(cbrt (exp (* a x)))
0.0ms	(fma (* (cbrt (exp (* a x))) (cbrt (exp (* a x)))) (cbrt (exp (* a x))) (- 1.0))

series336.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(cbrt (exp (* a x)))
43.0ms	(cbrt (exp (* a x)))
48.0ms	(cbrt (exp (* a x)))
195.0ms	(fma (* (cbrt (exp (* a x))) (cbrt (exp (* a x)))) (cbrt (exp (* a x))) (- 1.0))

simplify48.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 3 (43.0ms)

Iter	Nodes	Cost
0	118	446
1	355	393
2	1425	378
3	5002	363

prune202.0ms

Filtered

61 candidates to 50 candidates (82.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 8.7b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(sqrt (exp (* a x)))
0.3b	(cbrt (exp (* a x)))
0.3b	(cbrt (exp (* a x)))
5.1b	(fma (* (cbrt (exp (* a x))) (* (cbrt (sqrt (exp (* a x)))) (cbrt (sqrt (exp (* a x)))))) (cbrt (exp (* a x))) (- 1.0))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-prod`
5×	`pow1` `add-log-exp`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`sqrt-pow1` `sqrt-prod`
2×	`pow1/3`
1×	`rem-sqrt-square` `exp-prod` `exp-to-pow` `pow1/2` `fma-udef`

Counts

4 → 53

Calls

4 calls:

1.0ms	(sqrt (exp (* a x)))
1.0ms	(cbrt (exp (* a x)))
1.0ms	(cbrt (exp (* a x)))
0.0ms	(fma (* (cbrt (exp (* a x))) (* (cbrt (sqrt (exp (* a x)))) (cbrt (sqrt (exp (* a x)))))) (cbrt (exp (* a x))) (- 1.0))

series309.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(sqrt (exp (* a x)))
48.0ms	(cbrt (exp (* a x)))
44.0ms	(cbrt (exp (* a x)))
196.0ms	(fma (* (cbrt (exp (* a x))) (* (cbrt (sqrt (exp (* a x)))) (cbrt (sqrt (exp (* a x)))))) (cbrt (exp (* a x))) (- 1.0))

simplify60.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 3 (54.0ms)

Iter	Nodes	Cost
0	157	517
1	454	464
2	1772	460
3	5001	454

prune204.0ms

Filtered

65 candidates to 51 candidates (78.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 8.7b

regimes321.0ms

Accuracy

94% (1.3b remaining)

Error of 9.3b against oracle of 8.1b and baseline of 29.2b

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	17
1	28	17

end0.0ms

sample884.0ms

Algorithm

intervals

Results

407.0ms	2707×	body	1280	valid
124.0ms	1275×	body	640	valid
105.0ms	5449×	body	80	valid
53.0ms	812×	body	320	valid
15.0ms	359×	body	160	valid