Details

sample37.0ms

Algorithm

intervals

Results

15.0ms	84×	body	1280	valid
5.0ms	39×	body	640	valid
4.0ms	166×	body	80	valid
2.0ms	23×	body	320	valid
1.0ms	18×	body	160	valid

simplify3.9s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	153
1	11	153
2	16	153
3	23	153
4	44	153
5	93	153
6	221	153
7	883	153
8	3392	153
done	5028	153

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.1b

localize16.0ms

Local error

Found 2 expressions with local error:

0.1b	(exp (* a x))
5.2b	(- (exp (* a x)) 1.0)

rewrite16.0ms

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:

3.0ms	(exp (* a x))
13.0ms	(- (exp (* a x)) 1.0)

series68.0ms

Counts

2 → 6

Calls

2 calls:

21.0ms	(exp (* a x))
47.0ms	(- (exp (* a x)) 1.0)

simplify4.0s

Counts

30 → 30

Iterations

Useful iterations: 4 (1.9s)

Iter	Nodes	Cost
0	53	7474
1	116	5940
2	310	5860
3	1117	5740
4	4038	5622
done	5002	5622

prune156.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize44.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* a x) (* a x))
0.3b	(* (* a x) (* a x))
5.2b	(+ (* a x) (* (* (* a x) (* a x)) 1/2))
12.3b	(+ (* (* (* a x) (* (* a x) (* a x))) 1/6) (+ (* a x) (* (* (* a x) (* a x)) 1/2)))

rewrite448.0ms

Algorithm

rewrite-expression-head

Rules

82×	`pow1`
34×	`pow-prod-down`
28×	`add-cbrt-cube` `add-exp-log`
16×	`prod-exp` `cbrt-unprod`
11×	`add-log-exp`
8×	`pow-sqr` `pow-prod-up`
4×	`add-sqr-sqrt` `sum-log` `*-un-lft-identity` `pow-plus` `add-cube-cbrt`
2×	`pow2` `+-commutative` `flip3-+` `swap-sqr` `associate-r` `associate-l` `*-commutative` `flip-+`
1×	`associate-+r+`

Counts

4 → 92

Calls

4 calls:

21.0ms	(* (* a x) (* a x))
35.0ms	(* (* a x) (* a x))
14.0ms	(+ (* a x) (* (* (* a x) (* a x)) 1/2))
374.0ms	(+ (* (* (* a x) (* (* a x) (* a x))) 1/6) (+ (* a x) (* (* (* a x) (* a x)) 1/2)))

series348.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* (* a x) (* a x))
41.0ms	(* (* a x) (* a x))
88.0ms	(+ (* a x) (* (* (* a x) (* a x)) 1/2))
179.0ms	(+ (* (* (* a x) (* (* a x) (* a x))) 1/6) (+ (* a x) (* (* (* a x) (* a x)) 1/2)))

simplify2.0s

Counts

104 → 104

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	93	23863
1	273	14920
2	1157	14920
done	5009	14440

prune322.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* a x) (* (* (* a x) (* a x)) (+ 1/2 (* (* a x) 1/6))))
0.1b	(* (* (* a x) (* a x)) (+ 1/2 (* (* a x) 1/6)))
0.3b	(* (* a x) (* a x))
0.3b	(* (* a x) 1/6)

rewrite203.0ms

Algorithm

rewrite-expression-head

Rules

66×	`pow1`
39×	`add-cbrt-cube` `add-exp-log`
33×	`pow-prod-down`
24×	`prod-exp` `cbrt-unprod`
7×	`add-sqr-sqrt` `associate-r`
6×	`*-un-lft-identity` `add-cube-cbrt` `add-log-exp`
4×	`pow-sqr` `pow-prod-up`
3×	`associate-l` `*-commutative`
2×	`distribute-rgt-in` `associate-+r+` `distribute-lft-in` `flip3-+` `pow-plus` `associate-*r/` `flip-+`
1×	`pow2` `+-commutative` `sum-log` `swap-sqr` `unswap-sqr`

Counts

4 → 97

Calls

4 calls:

14.0ms	(+ (* a x) (* (* (* a x) (* a x)) (+ 1/2 (* (* a x) 1/6))))
113.0ms	(* (* (* a x) (* a x)) (+ 1/2 (* (* a x) 1/6)))
40.0ms	(* (* a x) (* a x))
30.0ms	(* (* a x) 1/6)

series391.0ms

Counts

4 → 12

Calls

4 calls:

151.0ms	(+ (* a x) (* (* (* a x) (* a x)) (+ 1/2 (* (* a x) 1/6))))
144.0ms	(* (* (* a x) (* a x)) (+ 1/2 (* (* a x) 1/6)))
62.0ms	(* (* a x) (* a x))
34.0ms	(* (* a x) 1/6)

simplify3.1s

Counts

109 → 109

Iterations

Useful iterations: 2 (949.0ms)

Iter	Nodes	Cost
0	135	29317
1	457	19565
2	2009	19085
done	5002	19085

prune472.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize46.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (* (* (- (exp (* a x)) 1.0) (- (exp (* a x)) 1.0)) (- (exp (* a x)) 1.0)))
5.2b	(- (exp (* a x)) 1.0)
5.2b	(- (exp (* a x)) 1.0)
5.2b	(- (exp (* a x)) 1.0)

rewrite206.0ms

Algorithm

rewrite-expression-head

Rules

30×	`flip3--` `flip--`
28×	`frac-times`
26×	`cbrt-div`
14×	`associate-*l/`
10×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
8×	`associate-*r/`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
3×	`sub-neg` `diff-log` `distribute-lft-out--` `difference-of-squares`
1×	`cbrt-prod` `pow1/3` `pow3` `rem-cbrt-cube`

Counts

4 → 78

Calls

4 calls:

141.0ms	(cbrt (* (* (- (exp (* a x)) 1.0) (- (exp (* a x)) 1.0)) (- (exp (* a x)) 1.0)))
23.0ms	(- (exp (* a x)) 1.0)
17.0ms	(- (exp (* a x)) 1.0)
18.0ms	(- (exp (* a x)) 1.0)

series222.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(cbrt (* (* (- (exp (* a x)) 1.0) (- (exp (* a x)) 1.0)) (- (exp (* a x)) 1.0)))
37.0ms	(- (exp (* a x)) 1.0)
60.0ms	(- (exp (* a x)) 1.0)
63.0ms	(- (exp (* a x)) 1.0)

simplify2.4s

Counts

90 → 90

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	140	49994
1	308	38994
2	1125	38874
done	5003	36954

prune443.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes341.0ms

Accuracy

98.3% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 20.8b

bsearch25.0ms

Steps

Iters	Range		Point
8	-0.019789888393231057	-2.2549730062480893e-06	-0.00015746637018926318

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	607
1	25	607
done	25	607

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.1s	2704×	body	1280	valid
335.0ms	5420×	body	80	valid
281.0ms	1353×	body	640	valid
99.0ms	794×	body	320	valid
31.0ms	391×	body	160	valid