Details

sample29.0ms

Algorithm

intervals

Results

10.0ms	67×	body	1280	valid
4.0ms	44×	body	640	valid
4.0ms	191×	body	80	valid
2.0ms	25×	body	320	valid
1.0ms	14×	body	160	valid

simplify63.0ms

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: 29.3b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(exp (* a x))
3.3b	(- (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)

series49.0ms

Counts

2 → 6

Calls

2 calls:

16.0ms	(exp (* a x))
33.0ms	(- (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

prune86.0ms

Filtered

46 candidates to 28 candidates (60.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 8.0b

localize10.0ms

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))
3.3b	(- (exp (* a x)) 1.0)

rewrite22.0ms

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

series126.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(exp (* a x))
46.0ms	(pow (- (exp (* a x)) 1.0) 3)
36.0ms	(cbrt (pow (- (exp (* a x)) 1.0) 3))
33.0ms	(- (exp (* a x)) 1.0)

simplify46.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (37.0ms)

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

prune202.0ms

Filtered

112 candidates to 60 candidates (53.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 8.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (pow (* (cbrt (* (- (exp (* a x)) 1.0) (- (exp (* a x)) 1.0))) (cbrt (- (exp (* a x)) 1.0))) 3))
3.3b	(- (exp (* a x)) 1.0)
3.3b	(- (exp (* a x)) 1.0)
3.3b	(- (exp (* a x)) 1.0)

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

68×	`cbrt-div`
32×	`add-sqr-sqrt` `*-un-lft-identity`
30×	`flip3--` `flip--`
28×	`frac-times`
27×	`prod-diff`
26×	`cube-div` `add-cube-cbrt`
14×	`associate-*l/`
10×	`add-log-exp`
9×	`fma-neg`
8×	`cbrt-prod` `associate-*r/`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`sub-neg` `diff-log` `distribute-lft-out--` `difference-of-squares`
1×	`cube-mult` `unpow-prod-down` `pow1/3` `unpow3` `cube-prod` `rem-cbrt-cube` `sqr-pow`

Counts

4 → 129

Calls

4 calls:

14.0ms	(cbrt (pow (* (cbrt (* (- (exp (* a x)) 1.0) (- (exp (* a x)) 1.0))) (cbrt (- (exp (* a x)) 1.0))) 3))
7.0ms	(- (exp (* a x)) 1.0)
5.0ms	(- (exp (* a x)) 1.0)
5.0ms	(- (exp (* a x)) 1.0)

series135.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(cbrt (pow (* (cbrt (* (- (exp (* a x)) 1.0) (- (exp (* a x)) 1.0))) (cbrt (- (exp (* a x)) 1.0))) 3))
32.0ms	(- (exp (* a x)) 1.0)
36.0ms	(- (exp (* a x)) 1.0)
33.0ms	(- (exp (* a x)) 1.0)

simplify80.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	690	2056
1	2712	1802
2	5001	1591

prune382.0ms

Filtered

141 candidates to 88 candidates (62.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 8.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (pow (* (cbrt (* (- (exp (* a x)) 1.0) (- (exp (* a x)) 1.0))) (cbrt (fma (sqrt (exp (* a x))) (sqrt (exp (* a x))) (- 1.0)))) 3))
3.3b	(- (exp (* a x)) 1.0)
3.3b	(- (exp (* a x)) 1.0)
3.4b	(fma (sqrt (exp (* a x))) (sqrt (exp (* a x))) (- 1.0))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt` `*-un-lft-identity`
19×	`add-cube-cbrt`
18×	`prod-diff`
16×	`cbrt-div`
10×	`associate-*l/`
8×	`cube-div` `cbrt-prod` `flip3--` `flip--` `add-log-exp`
6×	`fma-neg`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `frac-times` `add-cbrt-cube` `log1p-expm1-u`
2×	`sub-neg` `diff-log` `associate-*r/` `distribute-lft-out--` `difference-of-squares`
1×	`cube-mult` `unpow-prod-down` `pow1/3` `unpow3` `cube-prod` `rem-cbrt-cube` `fma-udef` `sqr-pow`

Counts

4 → 93

Calls

4 calls:

10.0ms	(cbrt (pow (* (cbrt (* (- (exp (* a x)) 1.0) (- (exp (* a x)) 1.0))) (cbrt (fma (sqrt (exp (* a x))) (sqrt (exp (* a x))) (- 1.0)))) 3))
5.0ms	(- (exp (* a x)) 1.0)
5.0ms	(- (exp (* a x)) 1.0)
0.0ms	(fma (sqrt (exp (* a x))) (sqrt (exp (* a x))) (- 1.0))

series345.0ms

Counts

4 → 12

Calls

4 calls:

195.0ms	(cbrt (pow (* (cbrt (* (- (exp (* a x)) 1.0) (- (exp (* a x)) 1.0))) (cbrt (fma (sqrt (exp (* a x))) (sqrt (exp (* a x))) (- 1.0)))) 3))
37.0ms	(- (exp (* a x)) 1.0)
32.0ms	(- (exp (* a x)) 1.0)
81.0ms	(fma (sqrt (exp (* a x))) (sqrt (exp (* a x))) (- 1.0))

simplify62.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	458	1315
1	1927	857
2	5002	852

prune316.0ms

Filtered

105 candidates to 73 candidates (69.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 7.8b

regimes396.0ms

Accuracy

91.3% (1.9b remaining)

Error of 9.0b against oracle of 7.1b and baseline of 29.3b

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	32
1	37	32

end0.0ms

sample923.0ms

Algorithm

intervals

Results

415.0ms	2659×	body	1280	valid
136.0ms	1331×	body	640	valid
109.0ms	5510×	body	80	valid
56.0ms	759×	body	320	valid
18.0ms	405×	body	160	valid