Details

sample74.0ms

Algorithm

intervals

Results

29.0ms	81×	body	1280	valid
10.0ms	46×	body	640	valid
7.0ms	165×	body	80	valid
4.0ms	23×	body	320	valid
1.0ms	13×	body	160	valid

simplify2.4s

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	113	6
6	440	6
7	3255	6
done	5002	6

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.1b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(exp (* a x))
4.3b	(- (exp (* a x)) 1.0)

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 24

Calls

2 calls:

6.0ms	(exp (* a x))
14.0ms	(- (exp (* a x)) 1.0)

series66.0ms

Counts

2 → 6

Calls

2 calls:

24.0ms	(exp (* a x))
41.0ms	(- (exp (* a x)) 1.0)

simplify1.1s

Counts

30 → 30

Iterations

Useful iterations: 3 (387.0ms)

Iter	Nodes	Cost
0	53	263
1	116	248
2	389	232
3	2000	228
done	5000	228

prune155.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 6.6b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 1/6 (pow a 3))
6.2b	(* (* 1/6 (pow a 3)) x)
10.8b	(+ (* (* 1/6 (pow a 3)) x) (* 1/2 (pow a 2)))
13.8b	(* (pow x 2) (+ (* (* 1/6 (pow a 3)) x) (* 1/2 (pow a 2))))

rewrite181.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
24×	`add-exp-log`
18×	`associate-r`
13×	`add-cbrt-cube` `prod-exp`
12×	`-un-lft-identity` `associate-l*` `add-cube-cbrt`
8×	`unpow-prod-down` `unswap-sqr`
6×	`pow1` `add-log-exp`
5×	`cbrt-unprod`
4×	`cube-prod` `sqr-pow`
3×	`pow-to-exp` `pow-exp` `*-commutative`
2×	`flip3-+` `associate-*r/` `flip-+` `unpow2`
1×	`distribute-rgt-in` `cube-mult` `+-commutative` `sum-log` `distribute-lft-in` `unpow3` `pow-prod-down`

Counts

4 → 92

Calls

4 calls:

15.0ms	(* 1/6 (pow a 3))
20.0ms	(* (* 1/6 (pow a 3)) x)
23.0ms	(+ (* (* 1/6 (pow a 3)) x) (* 1/2 (pow a 2)))
121.0ms	(* (pow x 2) (+ (* (* 1/6 (pow a 3)) x) (* 1/2 (pow a 2))))

series383.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(* 1/6 (pow a 3))
35.0ms	(* (* 1/6 (pow a 3)) x)
100.0ms	(+ (* (* 1/6 (pow a 3)) x) (* 1/2 (pow a 2)))
189.0ms	(* (pow x 2) (+ (* (* 1/6 (pow a 3)) x) (* 1/2 (pow a 2))))

simplify1.9s

Counts

104 → 104

Iterations

Useful iterations: 2 (738.0ms)

Iter	Nodes	Cost
0	149	1562
1	442	1451
2	2652	1284
done	5001	1284

prune537.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 4.9b

localize32.0ms

Local error

Found 4 expressions with local error:

3.2b	(* x (* x (+ (* (* 1/6 (pow a 3)) x) (* 1/2 (pow a 2)))))
5.4b	(* x (+ (* (* 1/6 (pow a 3)) x) (* 1/2 (pow a 2))))
6.2b	(* (* 1/6 (pow a 3)) x)
10.8b	(+ (* (* 1/6 (pow a 3)) x) (* 1/2 (pow a 2)))

rewrite230.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-exp-log`
16×	`add-cbrt-cube`
13×	`pow1`
11×	`prod-exp`
10×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
7×	`associate-r` `associate-l` `cbrt-unprod`
6×	`associate-*r/` `add-log-exp`
5×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down`
3×	`flip3-+` `*-commutative` `flip-+`
1×	`pow-to-exp` `+-commutative` `sum-log` `pow-exp` `unswap-sqr`

Counts

4 → 76

Calls

4 calls:

84.0ms	(* x (* x (+ (* (* 1/6 (pow a 3)) x) (* 1/2 (pow a 2)))))
82.0ms	(* x (+ (* (* 1/6 (pow a 3)) x) (* 1/2 (pow a 2))))
35.0ms	(* (* 1/6 (pow a 3)) x)
25.0ms	(+ (* (* 1/6 (pow a 3)) x) (* 1/2 (pow a 2)))

series546.0ms

Counts

4 → 12

Calls

4 calls:

202.0ms	(* x (* x (+ (* (* 1/6 (pow a 3)) x) (* 1/2 (pow a 2)))))
207.0ms	(* x (+ (* (* 1/6 (pow a 3)) x) (* 1/2 (pow a 2))))
49.0ms	(* (* 1/6 (pow a 3)) x)
88.0ms	(+ (* (* 1/6 (pow a 3)) x) (* 1/2 (pow a 2)))

simplify1.7s

Counts

88 → 88

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	128	1621
1	420	1553
2	2789	1325
done	5000	1323

prune472.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 4.9b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (- (exp (* a x)) 1.0))
4.3b	(- (exp (* a x)) 1.0)
4.3b	(- (exp (* a x)) 1.0)
4.3b	(- (exp (* a x)) 1.0)

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `*-un-lft-identity`
10×	`add-log-exp`
5×	`cbrt-prod` `add-cube-cbrt`
4×	`pow1` `flip3--` `add-cbrt-cube` `add-exp-log` `flip--` `distribute-lft-out--` `difference-of-squares`
3×	`sub-neg` `diff-log`
2×	`cbrt-div`
1×	`pow1/3`

Counts

4 → 57

Calls

4 calls:

6.0ms	(cbrt (- (exp (* a x)) 1.0))
9.0ms	(- (exp (* a x)) 1.0)
11.0ms	(- (exp (* a x)) 1.0)
10.0ms	(- (exp (* a x)) 1.0)

series273.0ms

Counts

4 → 12

Calls

4 calls:

151.0ms	(cbrt (- (exp (* a x)) 1.0))
39.0ms	(- (exp (* a x)) 1.0)
40.0ms	(- (exp (* a x)) 1.0)
42.0ms	(- (exp (* a x)) 1.0)

simplify1.7s

Counts

69 → 69

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	77	831
1	171	808
2	563	714
3	2864	694
done	5001	688

prune394.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 4.9b

regimes542.0ms

Accuracy

94.6% (1.2b remaining)

Error of 5.3b against oracle of 4.2b and baseline of 25.6b

bsearch2.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	35
1	32	35
done	32	35

end0.0ms

sample2.4s

Algorithm

intervals

Results

843.0ms	2713×	body	1280	valid
698.0ms	5337×	body	80	valid
294.0ms	1382×	body	640	valid
140.0ms	775×	body	320	valid
33.0ms	400×	body	160	valid