Details

sample44.0ms

Algorithm

intervals

Results

15.0ms	67×	body	1280	valid
9.0ms	44×	body	640	valid
5.0ms	191×	body	80	valid
2.0ms	25×	body	320	valid
1.0ms	14×	body	160	valid

simplify61.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	3
1	18	3
2	26	3
3	48	3
4	110	3
5	318	3
6	1623	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

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b	(exp (* a x))
3.3b	(- (exp (* a x)) 1.0)

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 24

Calls

2 calls:

1.0ms	(exp (* a x))
4.0ms	(- (exp (* a x)) 1.0)

series46.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify40.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 2 (10.0ms)

Iter	Nodes	Cost
0	115	135
1	333	127
2	1116	125
3	5001	125

prune73.0ms

Filtered

30 candidates to 20 candidates (66.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 8.0b

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

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt` `*-un-lft-identity`
16×	`cbrt-prod`
10×	`add-cube-cbrt` `unpow-prod-down` `cube-prod`
8×	`add-log-exp`
5×	`pow1` `add-exp-log` `add-cbrt-cube` `distribute-lft-out--` `difference-of-squares`
4×	`cube-div`
3×	`pow-unpow` `flip3--` `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 → 80

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))
4.0ms	(- (exp (* a x)) 1.0)

series131.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(exp (* a x))
48.0ms	(pow (- (exp (* a x)) 1.0) 3)
37.0ms	(cbrt (pow (- (exp (* a x)) 1.0) 3))
34.0ms	(- (exp (* a x)) 1.0)

simplify43.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	269	550
1	1076	527
2	5001	516

prune157.0ms

Filtered

92 candidates to 46 candidates (50.0%)

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 8.0b

localize15.0ms

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)

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

68×	`cbrt-div`
30×	`flip3--` `flip--`
28×	`frac-times`
26×	`cube-div`
14×	`associate-*l/`
11×	`add-sqr-sqrt` `*-un-lft-identity`
10×	`add-log-exp`
8×	`cbrt-prod` `associate-*r/`
5×	`add-cube-cbrt`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
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 → 85

Calls

4 calls:

13.0ms	(cbrt (pow (* (cbrt (* (- (exp (* a x)) 1.0) (- (exp (* a x)) 1.0))) (cbrt (- (exp (* a x)) 1.0))) 3))
4.0ms	(- (exp (* a x)) 1.0)
4.0ms	(- (exp (* a x)) 1.0)
4.0ms	(- (exp (* a x)) 1.0)

series146.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(cbrt (pow (* (cbrt (* (- (exp (* a x)) 1.0) (- (exp (* a x)) 1.0))) (cbrt (- (exp (* a x)) 1.0))) 3))
33.0ms	(- (exp (* a x)) 1.0)
39.0ms	(- (exp (* a x)) 1.0)
34.0ms	(- (exp (* a x)) 1.0)

simplify65.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	632	1567
1	2451	1529
2	5001	1350

prune294.0ms

Filtered

97 candidates to 66 candidates (68.0%)

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 8.0b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

212×	`cbrt-div`
136×	`frac-times`
84×	`flip3--` `flip--`
80×	`cube-div`
50×	`associate-*l/`
44×	`associate-*r/`
27×	`flip3-+` `flip-+`
17×	`add-sqr-sqrt`
13×	`*-un-lft-identity`
10×	`add-log-exp`
8×	`cbrt-prod`
6×	`sqrt-prod` `difference-of-squares`
5×	`add-cube-cbrt`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `distribute-lft-out--`
3×	`sub-neg` `diff-log`
1×	`cube-mult` `unpow-prod-down` `pow1/3` `unpow3` `cube-prod` `rem-cbrt-cube` `sqr-pow`

Counts

4 → 143

Calls

4 calls:

38.0ms	(cbrt (pow (* (cbrt (* (- (exp (* a x)) 1.0) (* (+ (sqrt (exp (* a x))) (sqrt 1.0)) (- (sqrt (exp (* a x))) (sqrt 1.0))))) (cbrt (- (exp (* a x)) 1.0))) 3))
4.0ms	(- (exp (* a x)) 1.0)
4.0ms	(- (exp (* a x)) 1.0)
8.0ms	(- (sqrt (exp (* a x))) (sqrt 1.0))

series2.0s

Counts

4 → 12

Calls

4 calls:

1.8s	(cbrt (pow (* (cbrt (* (- (exp (* a x)) 1.0) (* (+ (sqrt (exp (* a x))) (sqrt 1.0)) (- (sqrt (exp (* a x))) (sqrt 1.0))))) (cbrt (- (exp (* a x)) 1.0))) 3))
33.0ms	(- (exp (* a x)) 1.0)
33.0ms	(- (exp (* a x)) 1.0)
60.0ms	(- (sqrt (exp (* a x))) (sqrt 1.0))

simplify89.0ms

Algorithm

egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 1 (45.0ms)

Iter	Nodes	Cost
0	2235	5744
1	5001	5657

prune804.0ms

Filtered

155 candidates to 131 candidates (84.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 8.0b

regimes405.0ms

Accuracy

94.5% (1.2b remaining)

Error of 9.0b against oracle of 7.8b and baseline of 29.3b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	72	77
1	72	77

end0.0ms

sample910.0ms

Algorithm

intervals

Results

416.0ms	2659×	body	1280	valid
131.0ms	1331×	body	640	valid
108.0ms	5510×	body	80	valid
51.0ms	759×	body	320	valid
18.0ms	405×	body	160	valid