Details

sample37.0ms

Algorithm

intervals

Results

15.0ms	84×	body	1280	valid
6.0ms	188×	body	80	valid
5.0ms	40×	body	640	valid
2.0ms	23×	body	320	valid
1.0ms	16×	body	160	valid

simplify63.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.4b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(exp (* a x))
4.1b	(- (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)

series51.0ms

Counts

2 → 6

Calls

2 calls:

16.0ms	(exp (* a x))
36.0ms	(- (exp (* a x)) 1.0)

simplify84.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 3 (80.0ms)

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

prune88.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 9.2b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (- (exp (* a x)) 1.0))
4.1b	(- (exp (* a x)) 1.0)
4.1b	(- (exp (* a x)) 1.0)
4.1b	(- (exp (* a x)) 1.0)

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt` `*-un-lft-identity`
27×	`prod-diff`
26×	`add-cube-cbrt`
10×	`add-log-exp`
9×	`fma-neg`
5×	`cbrt-prod`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `flip3--` `add-cbrt-cube` `flip--` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`sub-neg` `diff-log`
2×	`cbrt-div`
1×	`pow1/3`

Counts

4 → 101

Calls

4 calls:

3.0ms	(cbrt (- (exp (* a x)) 1.0))
5.0ms	(- (exp (* a x)) 1.0)
5.0ms	(- (exp (* a x)) 1.0)
5.0ms	(- (exp (* a x)) 1.0)

series202.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(cbrt (- (exp (* a x)) 1.0))
38.0ms	(- (exp (* a x)) 1.0)
34.0ms	(- (exp (* a x)) 1.0)
35.0ms	(- (exp (* a x)) 1.0)

simplify110.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 3 (101.0ms)

Iter	Nodes	Cost
0	227	927
1	730	660
2	3541	616
3	5001	569

prune267.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 9.2b

localize12.0ms

Local error

Found 4 expressions with local error:

4.1b	(- (exp (* a x)) 1.0)
4.1b	(- (exp (* a x)) 1.0)
4.1b	(- (exp (* a x)) 1.0)
4.1b	(- (exp (* a x)) 1.0)

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt` `*-un-lft-identity`
36×	`prod-diff`
32×	`add-cube-cbrt`
12×	`fma-neg` `add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 112

Calls

4 calls:

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

series142.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(- (exp (* a x)) 1.0)
34.0ms	(- (exp (* a x)) 1.0)
34.0ms	(- (exp (* a x)) 1.0)
37.0ms	(- (exp (* a x)) 1.0)

simplify86.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 3 (77.0ms)

Iter	Nodes	Cost
0	162	1012
1	526	688
2	2608	644
3	5002	500

prune313.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 9.2b

localize8.0ms

Local error

Found 4 expressions with local error:

0.2b	(cbrt (exp (* a x)))
0.2b	(cbrt (exp (* a x)))
0.2b	(cbrt (exp (* a x)))
4.0b	(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))

series323.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(cbrt (exp (* a x)))
46.0ms	(cbrt (exp (* a x)))
43.0ms	(cbrt (exp (* a x)))
190.0ms	(fma (* (cbrt (exp (* a x))) (cbrt (exp (* a x)))) (cbrt (exp (* a x))) (- 1.0))

simplify51.0ms

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

prune157.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 9.2b

regimes182.0ms

Accuracy

94.3% (1.2b remaining)

Error of 9.2b against oracle of 8.0b and baseline of 28.9b

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	22
1	27	22

end0.0ms

sample1.1s

Algorithm

intervals

Results

469.0ms	2696×	body	1280	valid
175.0ms	5580×	body	80	valid
148.0ms	1303×	body	640	valid
59.0ms	728×	body	320	valid
22.0ms	375×	body	160	valid