Details

sample36.0ms

Algorithm

intervals

Results

16.0ms	89×	body	1280	valid
4.0ms	40×	body	640	valid
3.0ms	162×	body	80	valid
2.0ms	26×	body	320	valid
1.0ms	11×	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

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: 29.2b

Counts

2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(exp (* a x))
3.5b	(- (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:

2.0ms	(exp (* a x))
4.0ms	(- (exp (* a x)) 1.0)

series50.0ms

Counts

2 → 6

Calls

2 calls:

12.0ms	(exp (* a x))
38.0ms	(- (exp (* a x)) 1.0)

simplify43.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 2 (11.0ms)

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

prune64.0ms

Filtered

30 candidates to 20 candidates (66.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	25	5	30
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	26	5	31

Merged error: 6.1b

Counts

31 → 5

localize15.0ms

Local error

Found 4 expressions with local error:

1.4b	(* x (+ a (* (* 1/2 (pow a 2)) x)))
6.2b	(* (* 1/2 (pow a 2)) x)
10.5b	(+ (* x (+ a (* (* 1/2 (pow a 2)) x))) (* 1/6 (* (pow a 3) (pow x 3))))
16.4b	(* (pow a 3) (pow x 3))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-sqr-sqrt`
28×	`add-exp-log`
18×	`associate-r`
17×	`prod-exp` `unswap-sqr`
16×	`associate-l`
14×	`unpow-prod-down` `cube-prod`
13×	`add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
10×	`sqr-pow`
8×	`pow1`
7×	`pow-to-exp` `pow-exp`
6×	`add-log-exp`
5×	`cbrt-unprod`
3×	`pow-prod-down` `*-commutative`
2×	`distribute-rgt-in` `cube-mult` `associate-+l+` `distribute-lft-in` `flip3-+` `unpow3` `associate-*r/` `flip-+`
1×	`+-commutative` `sum-log`

Counts

4 → 113

Calls

4 calls:

5.0ms	(* x (+ a (* (* 1/2 (pow a 2)) x)))
6.0ms	(* (* 1/2 (pow a 2)) x)
7.0ms	(+ (* x (+ a (* (* 1/2 (pow a 2)) x))) (* 1/6 (* (pow a 3) (pow x 3))))
9.0ms	(* (pow a 3) (pow x 3))

series245.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* x (+ a (* (* 1/2 (pow a 2)) x)))
21.0ms	(* (* 1/2 (pow a 2)) x)
98.0ms	(+ (* x (+ a (* (* 1/2 (pow a 2)) x))) (* 1/6 (* (pow a 3) (pow x 3))))
65.0ms	(* (pow a 3) (pow x 3))

simplify102.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	471	797
1	2758	738
2	5001	738

prune273.0ms

Filtered

125 candidates to 75 candidates (60.0%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	122	3	125
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	124	6	130

Merged error: 2.0b

Counts

130 → 6

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (* a x) 3)
1.4b	(* x (+ a (* (* 1/2 (pow a 2)) x)))
6.2b	(* (* 1/2 (pow a 2)) x)
10.5b	(+ (* x (+ a (* (* 1/2 (pow a 2)) x))) (* 1/6 (pow (* a x) 3)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-exp-log`
14×	`add-cbrt-cube`
11×	`pow1`
10×	`add-sqr-sqrt`
9×	`prod-exp`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`associate-r` `add-log-exp`
5×	`cbrt-unprod`
4×	`associate-l`
3×	`pow-unpow` `pow-prod-down` `pow-exp`
2×	`distribute-rgt-in` `pow-to-exp` `associate-+l+` `pow-pow` `distribute-lft-in` `flip3-+` `associate-r/` `-commutative` `flip-+` `rem-cube-cbrt`
1×	`+-commutative` `cube-mult` `unpow-prod-down` `unpow3` `cube-prod` `sum-log` `unswap-sqr` `sqr-pow`

Counts

4 → 76

Calls

4 calls:

4.0ms	(pow (* a x) 3)
9.0ms	(* x (+ a (* (* 1/2 (pow a 2)) x)))
6.0ms	(* (* 1/2 (pow a 2)) x)
7.0ms	(+ (* x (+ a (* (* 1/2 (pow a 2)) x))) (* 1/6 (pow (* a x) 3)))

series227.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(pow (* a x) 3)
60.0ms	(* x (+ a (* (* 1/2 (pow a 2)) x)))
21.0ms	(* (* 1/2 (pow a 2)) x)
99.0ms	(+ (* x (+ a (* (* 1/2 (pow a 2)) x))) (* 1/6 (pow (* a x) 3)))

simplify78.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	376	525
1	2297	478
2	5003	478

prune186.0ms

Filtered

88 candidates to 56 candidates (63.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	86	2	88
Fresh	3	2	5
Picked	1	0	1
Done	0	0	0
Total	90	4	94

Merged error: 0.1b

Counts

94 → 4

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (* a x) 2)
0.3b	(pow (* a x) 3)
4.0b	(+ (* a x) (* 1/2 (pow (* a x) 2)))
10.5b	(+ (+ (* a x) (* 1/2 (pow (* a x) 2))) (* 1/6 (pow (* a x) 3)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-log-exp`
10×	`pow1` `add-exp-log`
7×	`add-cbrt-cube`
6×	`add-sqr-sqrt` `add-cube-cbrt` `pow-unpow` `*-un-lft-identity`
4×	`pow-pow` `pow-exp` `sum-log`
2×	`+-commutative` `pow-to-exp` `unpow-prod-down` `flip3-+` `pow-prod-down` `prod-exp` `flip-+` `rem-cube-cbrt` `sqr-pow`
1×	`cube-mult` `associate-+l+` `unpow3` `cube-prod` `cbrt-unprod` `unpow2`

Counts

4 → 64

Calls

4 calls:

4.0ms	(pow (* a x) 2)
4.0ms	(pow (* a x) 3)
4.0ms	(+ (* a x) (* 1/2 (pow (* a x) 2)))
7.0ms	(+ (+ (* a x) (* 1/2 (pow (* a x) 2))) (* 1/6 (pow (* a x) 3)))

series240.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(pow (* a x) 2)
51.0ms	(pow (* a x) 3)
62.0ms	(+ (* a x) (* 1/2 (pow (* a x) 2)))
100.0ms	(+ (+ (* a x) (* 1/2 (pow (* a x) 2))) (* 1/6 (pow (* a x) 3)))

simplify63.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	285	425
1	1624	392
2	5001	392

prune128.0ms

Filtered

76 candidates to 48 candidates (63.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	76	0	76
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	76	4	80

Merged error: 0.1b

Counts

80 → 4

regimes165.0ms

Accuracy

98.9% (0.2b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 21.4b

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	15
1	26	15

end0.0ms

sample952.0ms

Algorithm

intervals

Results

438.0ms	2708×	body	1280	valid
135.0ms	1324×	body	640	valid
113.0ms	5511×	body	80	valid
54.0ms	759×	body	320	valid
18.0ms	388×	body	160	valid