Details

sample60.0ms

Algorithm

intervals

Results

24.0ms	85×	body	1280	valid
7.0ms	38×	body	640	valid
7.0ms	178×	body	80	valid
3.0ms	22×	body	320	valid
1.0ms	12×	body	160	valid

simplify3.2s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	6
1	11	6
2	18	6
3	26	6
4	49	6
5	111	6
6	273	6
7	810	6
8	2970	6
done	5001	6

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.3b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(exp (* a x))
4.2b	(- (exp (* a x)) 1.0)

rewrite32.0ms

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:

6.0ms	(exp (* a x))
24.0ms	(- (exp (* a x)) 1.0)

series59.0ms

Counts

2 → 6

Calls

2 calls:

14.0ms	(exp (* a x))
46.0ms	(- (exp (* a x)) 1.0)

simplify2.1s

Counts

30 → 30

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	53	263
1	116	248
2	282	232
3	751	228
4	2588	228
done	5000	224

prune95.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 2.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* a x) 1/6)
0.7b	(* (pow a 2) (+ (* (* a x) 1/6) 1/2))
0.7b	(* x (+ a (* x (* (pow a 2) (+ (* (* a x) 1/6) 1/2)))))
8.0b	(* x (* (pow a 2) (+ (* (* a x) 1/6) 1/2)))

rewrite268.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-exp-log`
19×	`add-sqr-sqrt`
18×	`add-cbrt-cube`
15×	`associate-l`
14×	`prod-exp`
13×	`pow1`
11×	`add-cube-cbrt` `*-un-lft-identity`
10×	`associate-r`
8×	`associate-*r/` `cbrt-unprod`
6×	`distribute-rgt-in` `distribute-lft-in`
5×	`pow-prod-down` `unswap-sqr`
4×	`unpow-prod-down` `*-commutative` `add-log-exp`
3×	`flip3-+` `flip-+`
2×	`pow-to-exp` `pow-exp` `unpow2` `sqr-pow`

Counts

4 → 96

Calls

4 calls:

34.0ms	(* (* a x) 1/6)
99.0ms	(* (pow a 2) (+ (* (* a x) 1/6) 1/2))
22.0ms	(* x (+ a (* x (* (pow a 2) (+ (* (* a x) 1/6) 1/2)))))
108.0ms	(* x (* (pow a 2) (+ (* (* a x) 1/6) 1/2)))

series361.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* (* a x) 1/6)
55.0ms	(* (pow a 2) (+ (* (* a x) 1/6) 1/2))
156.0ms	(* x (+ a (* x (* (pow a 2) (+ (* (* a x) 1/6) 1/2)))))
128.0ms	(* x (* (pow a 2) (+ (* (* a x) 1/6) 1/2)))

simplify1.8s

Counts

108 → 108

Iterations

Useful iterations: 2 (596.0ms)

Iter	Nodes	Cost
0	174	1752
1	501	1640
2	2024	1427
done	5001	1427

prune306.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* (* a x) a) (+ (* (* a x) 1/6) 1/2))
0.1b	(* (* a x) a)
0.3b	(* (* a x) 1/6)
0.7b	(* x (+ a (* (* (* a x) a) (+ (* (* a x) 1/6) 1/2))))

rewrite225.0ms

Algorithm

rewrite-expression-head

Rules

25×	`pow1` `add-exp-log` `add-cbrt-cube`
13×	`pow-prod-down` `prod-exp` `cbrt-unprod`
12×	`associate-r`
11×	`add-sqr-sqrt`
9×	`add-cube-cbrt` `*-un-lft-identity`
6×	`associate-l`
4×	`associate-r/` `-commutative` `add-log-exp`
2×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `flip-+`
1×	`unswap-sqr`

Counts

4 → 83

Calls

4 calls:

119.0ms	(* (* (* a x) a) (+ (* (* a x) 1/6) 1/2))
38.0ms	(* (* a x) a)
33.0ms	(* (* a x) 1/6)
32.0ms	(* x (+ a (* (* (* a x) a) (+ (* (* a x) 1/6) 1/2))))

series286.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(* (* (* a x) a) (+ (* (* a x) 1/6) 1/2))
24.0ms	(* (* a x) a)
27.0ms	(* (* a x) 1/6)
132.0ms	(* x (+ a (* (* (* a x) a) (+ (* (* a x) 1/6) 1/2))))

simplify1.4s

Counts

95 → 95

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	144	1407
1	429	1318
2	1899	1118
done	5000	1116

prune211.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (- (exp (* a x)) 1.0))
0.0b	(exp (* a x))
4.2b	(log (exp (- (exp (* a x)) 1.0)))
4.2b	(- (exp (* a x)) 1.0)

rewrite120.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 61

Calls

4 calls:

30.0ms	(exp (- (exp (* a x)) 1.0))
8.0ms	(exp (* a x))
52.0ms	(log (exp (- (exp (* a x)) 1.0)))
28.0ms	(- (exp (* a x)) 1.0)

series145.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(exp (- (exp (* a x)) 1.0))
14.0ms	(exp (* a x))
38.0ms	(log (exp (- (exp (* a x)) 1.0)))
36.0ms	(- (exp (* a x)) 1.0)

simplify2.7s

Counts

73 → 73

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	84	689
1	161	622
2	366	574
3	964	566
4	3265	566
done	5000	562

prune199.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

regimes268.0ms

Accuracy

98.9% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 21.6b

bsearch1.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	34
1	29	34
done	29	34

end0.0ms

sample1.5s

Algorithm

intervals

Results

623.0ms	2640×	body	1280	valid
203.0ms	1317×	body	640	valid
158.0ms	5440×	body	80	valid
77.0ms	795×	body	320	valid
28.0ms	423×	body	160	valid