Details

sample635.0ms

Algorithm

intervals

Results

366.0ms	35×	body	640	valid
128.0ms	73×	body	1280	valid
21.0ms	216×	body	80	valid
16.0ms	22×	body	320	valid
2.0ms	19×	body	160	valid

simplify17.3s

Counts

1 → 1

Iterations

Iter	Nodes
done	5020
8	3533
7	890
6	221
5	93
4	44
3	23
2	16
1	11
0	6

prune59.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.2b

localize26.0ms

Local error

Found 2 expressions with local error:

0.0b	(exp (* a x))
5.0b	(- (exp (* a x)) 1.0)

rewrite213.0ms

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:

8.0ms	(exp (* a x))
200.0ms	(- (exp (* a x)) 1.0)

series129.0ms

Counts

2 → 6

Calls

2 calls:

37.0ms	(exp (* a x))
92.0ms	(- (exp (* a x)) 1.0)

simplify14.4s

Counts

30 → 30

Iterations

Iter	Nodes
done	5000
4	3552
3	1024
2	308
1	116
0	53

prune515.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize94.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* a x) (* a x))
0.2b	(* (* a x) (* (* a x) 1/2))
3.8b	(+ (* (* a x) (* (* a x) 1/2)) (* a x))
15.6b	(+ (* 1/6 (* (* a x) (* (* a x) (* a x)))) (+ (* (* a x) (* (* a x) 1/2)) (* a x)))

rewrite2.2s

Algorithm

rewrite-expression-head

Rules

64×	`pow1`
37×	`add-exp-log` `add-cbrt-cube`
32×	`pow-prod-down`
23×	`prod-exp` `cbrt-unprod`
11×	`add-log-exp`
4×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `sum-log` `pow-sqr` `pow-prod-up`
2×	`+-commutative` `flip3-+` `pow-plus` `associate-r` `associate-l` `*-commutative` `flip-+`
1×	`pow2` `associate-+r+` `swap-sqr`

Counts

4 → 86

Calls

4 calls:

174.0ms	(* (* a x) (* a x))
239.0ms	(* (* a x) (* (* a x) 1/2))
210.0ms	(+ (* (* a x) (* (* a x) 1/2)) (* a x))
1.5s	(+ (* 1/6 (* (* a x) (* (* a x) (* a x)))) (+ (* (* a x) (* (* a x) 1/2)) (* a x)))

series1.0s

Counts

4 → 12

Calls

4 calls:

88.0ms	(* (* a x) (* a x))
108.0ms	(* (* a x) (* (* a x) 1/2))
335.0ms	(+ (* (* a x) (* (* a x) 1/2)) (* a x))
505.0ms	(+ (* 1/6 (* (* a x) (* (* a x) (* a x)))) (+ (* (* a x) (* (* a x) 1/2)) (* a x)))

simplify10.1s

Counts

98 → 98

Iterations

Iter	Nodes
done	5000
2	1562
1	368
0	122

prune1.5s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize192.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x a) (* (* (* x a) (* x a)) (+ (* (* x a) 1/6) 1/2)))
0.0b	(* (* (* x a) (* x a)) (+ (* (* x a) 1/6) 1/2))
0.2b	(* (* x a) (* x a))
0.3b	(* (* x a) 1/6)

rewrite647.0ms

Algorithm

rewrite-expression-head

Rules

66×	`pow1`
39×	`add-exp-log` `add-cbrt-cube`
33×	`pow-prod-down`
24×	`prod-exp` `cbrt-unprod`
7×	`add-sqr-sqrt` `associate-r`
6×	`add-cube-cbrt` `*-un-lft-identity` `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×	`+-commutative` `pow2` `swap-sqr` `sum-log` `unswap-sqr`

Counts

4 → 97

Calls

4 calls:

24.0ms	(+ (* x a) (* (* (* x a) (* x a)) (+ (* (* x a) 1/6) 1/2)))
404.0ms	(* (* (* x a) (* x a)) (+ (* (* x a) 1/6) 1/2))
58.0ms	(* (* x a) (* x a))
49.0ms	(* (* x a) 1/6)

series1.2s

Counts

4 → 12

Calls

4 calls:

510.0ms	(+ (* x a) (* (* (* x a) (* x a)) (+ (* (* x a) 1/6) 1/2)))
314.0ms	(* (* (* x a) (* x a)) (+ (* (* x a) 1/6) 1/2))
163.0ms	(* (* x a) (* x a))
182.0ms	(* (* x a) 1/6)

simplify9.0s

Counts

109 → 109

Iterations

Iter	Nodes
done	5002
2	1965
1	453
0	135

prune1.2s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize105.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt (+ (* x a) (* (* (* x a) (* x a)) (+ (* (* x a) 1/6) 1/2)))) (cbrt (+ (* x a) (* (* (* x a) (* x a)) (+ (* (* x a) 1/6) 1/2)))))
21.5b	(cbrt (+ (* x a) (* (* (* x a) (* x a)) (+ (* (* x a) 1/6) 1/2))))
21.5b	(cbrt (+ (* x a) (* (* (* x a) (* x a)) (+ (* (* x a) 1/6) 1/2))))
21.5b	(cbrt (+ (* x a) (* (* (* x a) (* x a)) (+ (* (* x a) 1/6) 1/2))))

rewrite213.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
18×	`cbrt-div`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`flip3-+` `pow1/3` `flip-+`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`frac-times` `add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 87

Calls

4 calls:

169.0ms	(* (cbrt (+ (* x a) (* (* (* x a) (* x a)) (+ (* (* x a) 1/6) 1/2)))) (cbrt (+ (* x a) (* (* (* x a) (* x a)) (+ (* (* x a) 1/6) 1/2)))))
16.0ms	(cbrt (+ (* x a) (* (* (* x a) (* x a)) (+ (* (* x a) 1/6) 1/2))))
9.0ms	(cbrt (+ (* x a) (* (* (* x a) (* x a)) (+ (* (* x a) 1/6) 1/2))))
10.0ms	(cbrt (+ (* x a) (* (* (* x a) (* x a)) (+ (* (* x a) 1/6) 1/2))))

series4.3s

Counts

4 → 12

Calls

4 calls:

1.4s	(* (cbrt (+ (* x a) (* (* (* x a) (* x a)) (+ (* (* x a) 1/6) 1/2)))) (cbrt (+ (* x a) (* (* (* x a) (* x a)) (+ (* (* x a) 1/6) 1/2)))))
1.0s	(cbrt (+ (* x a) (* (* (* x a) (* x a)) (+ (* (* x a) 1/6) 1/2))))
770.0ms	(cbrt (+ (* x a) (* (* (* x a) (* x a)) (+ (* (* x a) 1/6) 1/2))))
1.1s	(cbrt (+ (* x a) (* (* (* x a) (* x a)) (+ (* (* x a) 1/6) 1/2))))

simplify10.7s

Counts

99 → 99

Iterations

Iter	Nodes
done	5001
2	1506
1	439
0	167

prune2.6s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

regimes1.8s

Accuracy

97% (0.6b remaining)

Error of 0.7b against oracle of 0.1b and baseline of 21.2b

bsearch45.0ms

simplify18.0ms

Iterations

Iter	Nodes
done	25
1	25
0	20

end11.0ms

sample10.4s

Algorithm

intervals

Results

4.2s	748×	body	320	valid
2.9s	2733×	body	1280	valid
2.1s	5387×	body	80	valid
424.0ms	1291×	body	640	valid
114.0ms	427×	body	160	valid