Details

sample93.0ms

Algorithm

intervals

Results

37.0ms	78×	body	1280	valid
14.0ms	46×	body	640	valid
12.0ms	187×	body	80	valid
12.0ms	24×	body	320	valid
2.0ms	16×	body	160	valid

simplify6.1s

Counts

1 → 1

Iterations

Iter	Nodes
8	6498
7	1279
6	374
5	133
4	54
3	27
2	17
1	12
0	6

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.2b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(exp (* a x))
4.3b	(- (exp (* a x)) 1)

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt` `add-log-exp`
5×	`*-un-lft-identity`
2×	`pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `difference-of-squares`
1×	`exp-prod` `sub-neg` `flip3--` `exp-to-pow` `diff-log` `difference-of-sqr-1` `flip--` `distribute-lft-out--` `rem-exp-log`

Counts

2 → 28

Calls

2 calls:

8.0ms	(exp (* a x))
14.0ms	(- (exp (* a x)) 1)

series54.0ms

Counts

2 → 6

Calls

2 calls:

14.0ms	(exp (* a x))
39.0ms	(- (exp (* a x)) 1)

simplify1.7s

Counts

34 → 34

Iterations

Iter	Nodes
4	3072
3	882
2	295
1	115
0	56

prune345.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* a x) (* (* a x) 1/2))
0.2b	(* (* a x) (* a x))
5.0b	(+ (* (* a x) (* (* a x) 1/2)) (* a x))
13.6b	(+ (+ (* (* a x) (* (* a x) 1/2)) (* a x)) (* (* (* (* a x) (* a x)) (* a x)) 1/6))

rewrite566.0ms

Algorithm

rewrite-expression-head

Rules

64×	`pow1`
37×	`add-cbrt-cube` `add-exp-log`
32×	`pow-prod-down`
23×	`prod-exp` `cbrt-unprod`
11×	`add-log-exp`
4×	`add-sqr-sqrt` `sum-log` `*-un-lft-identity` `pow-sqr` `pow-prod-up` `add-cube-cbrt` `insert-posit16`
2×	`+-commutative` `flip3-+` `pow-plus` `associate-r` `associate-l` `*-commutative` `flip-+`
1×	`pow2` `associate-+l+` `swap-sqr`

Counts

4 → 90

Calls

4 calls:

90.0ms	(* (* a x) (* (* a x) 1/2))
24.0ms	(* (* a x) (* a x))
61.0ms	(+ (* (* a x) (* (* a x) 1/2)) (* a x))
389.0ms	(+ (+ (* (* a x) (* (* a x) 1/2)) (* a x)) (* (* (* (* a x) (* a x)) (* a x)) 1/6))

series355.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(* (* a x) (* (* a x) 1/2))
46.0ms	(* (* a x) (* a x))
100.0ms	(+ (* (* a x) (* (* a x) 1/2)) (* a x))
157.0ms	(+ (+ (* (* a x) (* (* a x) 1/2)) (* a x)) (* (* (* (* a x) (* a x)) (* a x)) 1/6))

simplify8.5s

Counts

102 → 102

Iterations

Iter	Nodes
3	12932
2	1526
1	366
0	125

prune984.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.1b

localize64.0ms

Local error

Found 4 expressions with local error:

13.6b	(+ (* (* (cbrt (+ (* (* a x) (* (* a x) 1/2)) (* a x))) (cbrt (+ (* (* a x) (* (* a x) 1/2)) (* a x)))) (cbrt (+ (* (* a x) (* (* a x) 1/2)) (* a x)))) (* (* (* (* a x) (* a x)) (* a x)) 1/6))
21.2b	(cbrt (+ (* (* a x) (* (* a x) 1/2)) (* a x)))
21.2b	(cbrt (+ (* (* a x) (* (* a x) 1/2)) (* a x)))
21.2b	(cbrt (+ (* (* a x) (* (* a x) 1/2)) (* a x)))

rewrite1.0s

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`cbrt-div` `add-log-exp`
4×	`pow1` `flip3-+` `add-cbrt-cube` `add-exp-log` `flip-+` `insert-posit16`
3×	`pow1/3`
1×	`+-commutative` `sum-log`

Counts

4 → 54

Calls

4 calls:

878.0ms	(+ (* (* (cbrt (+ (* (* a x) (* (* a x) 1/2)) (* a x))) (cbrt (+ (* (* a x) (* (* a x) 1/2)) (* a x)))) (cbrt (+ (* (* a x) (* (* a x) 1/2)) (* a x)))) (* (* (* (* a x) (* a x)) (* a x)) 1/6))
51.0ms	(cbrt (+ (* (* a x) (* (* a x) 1/2)) (* a x)))
50.0ms	(cbrt (+ (* (* a x) (* (* a x) 1/2)) (* a x)))
62.0ms	(cbrt (+ (* (* a x) (* (* a x) 1/2)) (* a x)))

series1.0s

Counts

4 → 12

Calls

4 calls:

144.0ms	(+ (* (* (cbrt (+ (* (* a x) (* (* a x) 1/2)) (* a x))) (cbrt (+ (* (* a x) (* (* a x) 1/2)) (* a x)))) (cbrt (+ (* (* a x) (* (* a x) 1/2)) (* a x)))) (* (* (* (* a x) (* a x)) (* a x)) 1/6))
299.0ms	(cbrt (+ (* (* a x) (* (* a x) 1/2)) (* a x)))
286.0ms	(cbrt (+ (* (* a x) (* (* a x) 1/2)) (* a x)))
294.0ms	(cbrt (+ (* (* a x) (* (* a x) 1/2)) (* a x)))

simplify6.8s

Counts

66 → 66

Iterations

Iter	Nodes
3	10068
2	1307
1	355
0	126

prune739.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.1b

localize63.0ms

Local error

Found 4 expressions with local error:

21.2b	(cbrt (+ (* (* a x) (* (* a x) 1/2)) (* a x)))
21.2b	(cbrt (+ (* (* a x) (* (* a x) 1/2)) (* a x)))
21.2b	(cbrt (+ (* (* a x) (* (* a x) 1/2)) (* a x)))
21.2b	(cbrt (* (* (cbrt (+ (* (* a x) (* (* a x) 1/2)) (* a x))) (cbrt (+ (* (* a x) (* (* a x) 1/2)) (* a x)))) (cbrt (+ (* (* a x) (* (* a x) 1/2)) (* a x)))))

rewrite678.0ms

Algorithm

rewrite-expression-head

Rules

86×	`cbrt-div`
30×	`flip3-+` `flip-+`
28×	`frac-times`
14×	`associate-*l/`
10×	`cbrt-prod`
8×	`associate-*r/`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`pow1` `add-cbrt-cube` `pow1/3` `add-exp-log` `insert-posit16` `add-log-exp`
1×	`pow3` `rem-cbrt-cube`

Counts

4 → 79

Calls

4 calls:

52.0ms	(cbrt (+ (* (* a x) (* (* a x) 1/2)) (* a x)))
51.0ms	(cbrt (+ (* (* a x) (* (* a x) 1/2)) (* a x)))
41.0ms	(cbrt (+ (* (* a x) (* (* a x) 1/2)) (* a x)))
529.0ms	(cbrt (* (* (cbrt (+ (* (* a x) (* (* a x) 1/2)) (* a x))) (cbrt (+ (* (* a x) (* (* a x) 1/2)) (* a x)))) (cbrt (+ (* (* a x) (* (* a x) 1/2)) (* a x)))))

series1.2s

Counts

4 → 12

Calls

4 calls:

366.0ms	(cbrt (+ (* (* a x) (* (* a x) 1/2)) (* a x)))
283.0ms	(cbrt (+ (* (* a x) (* (* a x) 1/2)) (* a x)))
292.0ms	(cbrt (+ (* (* a x) (* (* a x) 1/2)) (* a x)))
264.0ms	(cbrt (* (* (cbrt (+ (* (* a x) (* (* a x) 1/2)) (* a x))) (cbrt (+ (* (* a x) (* (* a x) 1/2)) (* a x)))) (cbrt (+ (* (* a x) (* (* a x) 1/2)) (* a x)))))

simplify2.1s

Counts

91 → 91

Iterations

Iter	Nodes
3	4178
2	919
1	370
0	189

prune1.6s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0.1b

regimes588.0ms

Accuracy

98.7% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 21.3b

bsearch2.0ms

simplify7.0ms

Iterations

Iter	Nodes
2	39
1	39
0	27

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.2s	2649×	body	1280	valid
743.0ms	5418×	body	80	valid
386.0ms	1341×	body	640	valid
133.0ms	759×	body	320	valid
48.0ms	400×	body	160	valid