Details

sample78.0ms

Algorithm

intervals

Results

31.0ms	88×	body	1280	valid
10.0ms	40×	body	640	valid
9.0ms	195×	body	80	valid
5.0ms	30×	body	320	valid
1.0ms	12×	body	160	valid

simplify3.6s

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	3314	6
done	5002	6

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.1b

localize5.0ms

Local error

Found 1 expressions with local error:

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

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

3×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
1×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

1 → 14

Calls

1 calls:

17.0ms

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

series70.0ms

Counts

1 → 3

Calls

1 calls:

70.0ms

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

simplify1.3s

Counts

17 → 17

Iterations

Useful iterations: 3 (462.0ms)

Iter	Nodes	Cost
0	45	188
1	105	183
2	366	167
3	1792	165
done	5001	165

prune72.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 6.0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 1/6 (pow a 3))
5.0b	(* (* 1/6 (pow a 3)) x)
9.3b	(+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x))
13.1b	(* (pow x 2) (+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x)))

rewrite125.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
24×	`add-exp-log`
18×	`associate-r`
13×	`prod-exp` `add-cbrt-cube`
12×	`add-cube-cbrt` `-un-lft-identity` `associate-l*`
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×	`+-commutative` `distribute-rgt-in` `cube-mult` `distribute-lft-in` `unpow3` `pow-prod-down` `sum-log`

Counts

4 → 92

Calls

4 calls:

18.0ms	(* 1/6 (pow a 3))
32.0ms	(* (* 1/6 (pow a 3)) x)
29.0ms	(+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x))
41.0ms	(* (pow x 2) (+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x)))

series395.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* 1/6 (pow a 3))
53.0ms	(* (* 1/6 (pow a 3)) x)
93.0ms	(+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x))
188.0ms	(* (pow x 2) (+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x)))

simplify2.2s

Counts

104 → 104

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	148	1562
1	443	1447
2	2572	1288
done	5001	1282

prune462.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 4.0b

localize43.0ms

Local error

Found 4 expressions with local error:

3.3b	(* (pow x (/ 2 2)) (* x (+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x))))
5.0b	(* (* 1/6 (pow a 3)) x)
6.4b	(* x (+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x)))
9.3b	(+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x))

rewrite173.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 82

Calls

4 calls:

82.0ms	(* (pow x (/ 2 2)) (* x (+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x))))
31.0ms	(* (* 1/6 (pow a 3)) x)
32.0ms	(* x (+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x)))
25.0ms	(+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x))

series525.0ms

Counts

4 → 12

Calls

4 calls:

196.0ms	(* (pow x (/ 2 2)) (* x (+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x))))
39.0ms	(* (* 1/6 (pow a 3)) x)
203.0ms	(* x (+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x)))
86.0ms	(+ (* 1/2 (pow a 2)) (* (* 1/6 (pow a 3)) x))

simplify2.8s

Counts

94 → 94

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	145	1897
1	473	1731
2	3210	1427
done	5001	1418

prune437.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 4.0b

localize18.0ms

Local error

Found 2 expressions with local error:

3.2b	(log (exp (- (exp (* a x)) 1.0)))
3.3b	(- (exp (* a x)) 1.0)

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 34

Calls

2 calls:

29.0ms	(log (exp (- (exp (* a x)) 1.0)))
24.0ms	(- (exp (* a x)) 1.0)

series103.0ms

Counts

2 → 6

Calls

2 calls:

49.0ms	(log (exp (- (exp (* a x)) 1.0)))
54.0ms	(- (exp (* a x)) 1.0)

simplify1.3s

Counts

40 → 40

Iterations

Useful iterations: 3 (488.0ms)

Iter	Nodes	Cost
0	73	447
1	153	395
2	464	360
3	2157	356
done	5001	356

prune106.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 4.0b

regimes341.0ms

Accuracy

96.5% (0.8b remaining)

Error of 5.1b against oracle of 4.3b and baseline of 26.7b

bsearch2.0ms

simplify17.0ms

Iterations

Useful iterations: 2 (9.0ms)

Iter	Nodes	Cost
0	24	37
1	33	35
2	41	33
3	49	33
4	51	33
done	51	33

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.2s	2727×	body	1280	valid
321.0ms	5484×	body	80	valid
271.0ms	1260×	body	640	valid
120.0ms	773×	body	320	valid
32.0ms	397×	body	160	valid