Details

sample41.0ms

Algorithm

intervals

Results

17.0ms	96×	body	1280	valid
5.0ms	42×	body	640	valid
4.0ms	167×	body	80	valid
1.0ms	17×	body	320	valid
1.0ms	10×	body	160	valid

simplify57.0ms

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

prune3.0ms

Filtered

1 candidates to 0 candidates (100.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 25.8b

Counts

2 → 1

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b	(exp (* a x))
2.6b	(- (exp (* a x)) 1.0)

rewrite6.0ms

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)

series16.0ms

Counts

2 → 6

Calls

2 calls:

4.0ms	(exp (* a x))
12.0ms	(- (exp (* a x)) 1.0)

simplify39.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 2 (9.0ms)

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

prune60.0ms

Filtered

30 candidates to 20 candidates (33.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	23	7	30
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	24	7	31

Merged error: 6.8b

Counts

31 → 7

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (* a x))
0.0b	(exp (* a x))
0.0b	(* (+ (sqrt (exp (* a x))) (sqrt 1.0)) (- (sqrt (exp (* a x))) (sqrt 1.0)))
2.6b	(- (sqrt (exp (* a x))) (sqrt 1.0))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
18×	`*-un-lft-identity`
14×	`sqrt-prod`
10×	`add-log-exp`
9×	`associate-r`
8×	`difference-of-squares`
6×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
5×	`associate-l`
4×	`frac-times` `flip3--` `flip--` `distribute-lft-out--`
3×	`sub-neg` `flip3-+` `flip-+`
2×	`distribute-rgt-in` `exp-prod` `exp-to-pow` `distribute-lft-in` `associate-r/` `associate-l/` `rem-exp-log` `distribute-lft-out`
1×	`diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 76

Calls

4 calls:

2.0ms	(exp (* a x))
2.0ms	(exp (* a x))
14.0ms	(* (+ (sqrt (exp (* a x))) (sqrt 1.0)) (- (sqrt (exp (* a x))) (sqrt 1.0)))
6.0ms	(- (sqrt (exp (* a x))) (sqrt 1.0))

series39.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(exp (* a x))
4.0ms	(exp (* a x))
20.0ms	(* (+ (sqrt (exp (* a x))) (sqrt 1.0)) (- (sqrt (exp (* a x))) (sqrt 1.0)))
9.0ms	(- (sqrt (exp (* a x))) (sqrt 1.0))

simplify38.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	262	833
1	1208	723
2	5003	698

prune126.0ms

Filtered

88 candidates to 56 candidates (36.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	86	2	88
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	89	6	95

Merged error: 6.8b

Counts

95 → 6

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (- (sqrt (exp (* a x))) (sqrt 1.0)))
0.0b	(* (+ (sqrt (exp (* a x))) (sqrt 1.0)) (log (exp (- (sqrt (exp (* a x))) (sqrt 1.0)))))
2.6b	(log (exp (- (sqrt (exp (* a x))) (sqrt 1.0))))
2.6b	(- (sqrt (exp (* a x))) (sqrt 1.0))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-sqr-sqrt`
32×	`*-un-lft-identity`
27×	`exp-prod`
26×	`sqrt-prod`
20×	`log-pow`
16×	`difference-of-squares`
15×	`log-prod`
13×	`associate-r`
12×	`add-cube-cbrt`
9×	`add-log-exp`
8×	`pow1` `exp-sum` `distribute-lft-out--`
6×	`add-exp-log` `add-cbrt-cube`
5×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-l`
2×	`exp-diff` `diff-log` `associate-*l/` `rem-exp-log` `distribute-lft-out`
1×	`log-div` `flip3--` `flip3-+` `rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 105

Calls

4 calls:

7.0ms	(exp (- (sqrt (exp (* a x))) (sqrt 1.0)))
16.0ms	(* (+ (sqrt (exp (* a x))) (sqrt 1.0)) (log (exp (- (sqrt (exp (* a x))) (sqrt 1.0)))))
7.0ms	(log (exp (- (sqrt (exp (* a x))) (sqrt 1.0))))
6.0ms	(- (sqrt (exp (* a x))) (sqrt 1.0))

series55.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(exp (- (sqrt (exp (* a x))) (sqrt 1.0)))
20.0ms	(* (+ (sqrt (exp (* a x))) (sqrt 1.0)) (log (exp (- (sqrt (exp (* a x))) (sqrt 1.0)))))
9.0ms	(log (exp (- (sqrt (exp (* a x))) (sqrt 1.0))))
11.0ms	(- (sqrt (exp (* a x))) (sqrt 1.0))

simplify40.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	322	1204
1	1239	1037
2	5001	989

prune182.0ms

Filtered

117 candidates to 71 candidates (39.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	114	3	117
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	115	8	123

Merged error: 2.0b

Counts

123 → 8

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (* a x))
0.0b	(* (+ (sqrt (exp (* a x))) (sqrt 1.0)) (+ (- 1 (sqrt 1.0)) (* x (+ (* 1/2 a) (* (* 1/8 (pow a 2)) x)))))
1.2b	(* x (+ (* 1/2 a) (* (* 1/8 (pow a 2)) x)))
7.5b	(* (* 1/8 (pow a 2)) x)

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

20×	`associate-*r/`
18×	`add-exp-log`
17×	`flip3-+` `flip-+`
13×	`add-sqr-sqrt` `*-un-lft-identity` `add-cbrt-cube`
12×	`frac-times` `frac-add`
10×	`pow1`
9×	`add-cube-cbrt` `associate-r` `associate-l` `prod-exp`
6×	`flip3--` `flip--` `add-log-exp`
5×	`cbrt-unprod`
3×	`pow-prod-down` `*-commutative`
2×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/` `sqrt-prod` `distribute-lft-out` `unswap-sqr`
1×	`pow-to-exp` `exp-prod` `exp-to-pow` `pow-exp` `rem-exp-log`

Counts

4 → 93

Calls

4 calls:

2.0ms	(exp (* a x))
16.0ms	(* (+ (sqrt (exp (* a x))) (sqrt 1.0)) (+ (- 1 (sqrt 1.0)) (* x (+ (* 1/2 a) (* (* 1/8 (pow a 2)) x)))))
5.0ms	(* x (+ (* 1/2 a) (* (* 1/8 (pow a 2)) x)))
6.0ms	(* (* 1/8 (pow a 2)) x)

series57.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(exp (* a x))
36.0ms	(* (+ (sqrt (exp (* a x))) (sqrt 1.0)) (+ (- 1 (sqrt 1.0)) (* x (+ (* 1/2 a) (* (* 1/8 (pow a 2)) x)))))
13.0ms	(* x (+ (* 1/2 a) (* (* 1/8 (pow a 2)) x)))
4.0ms	(* (* 1/8 (pow a 2)) x)

simplify40.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	827	1697
1	5001	1605

prune258.0ms

Filtered

105 candidates to 74 candidates (29.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	104	1	105
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	107	6	113

Merged error: 0.2b

Counts

113 → 6

regimes353.0ms

Accuracy

97.3% (0.6b remaining)

Error of 0.8b against oracle of 0.2b and baseline of 21.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	35
1	31	35

end0.0ms

sample1.2s

Algorithm

intervals

Results

492.0ms	2647×	body	1280	valid
165.0ms	1358×	body	640	valid
136.0ms	5425×	body	80	valid
65.0ms	763×	body	320	valid
24.0ms	425×	body	160	valid

Details

sample41.0ms

simplify57.0ms

prune3.0ms

localize4.0ms

rewrite6.0ms

series16.0ms

simplify39.0ms

prune60.0ms

localize9.0ms

rewrite26.0ms

series39.0ms

simplify38.0ms

prune126.0ms

localize12.0ms

rewrite40.0ms

series55.0ms

simplify40.0ms

prune182.0ms

localize19.0ms

rewrite32.0ms

series57.0ms

simplify40.0ms

prune258.0ms

regimes353.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.2s

Profiling