Details

sample85.0ms

Algorithm

intervals

Results

35.0ms	76×	body	1280	valid
16.0ms	49×	body	640	valid
11.0ms	162×	body	80	valid
6.0ms	27×	body	320	valid
2.0ms	12×	body	160	valid

simplify1.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	2061
8	2061
7	1575
6	382
5	135
4	56
3	29
2	19
1	14
0	6

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.2b

localize10.0ms

Local error

Found 1 expressions with local error:

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

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 17

Calls

1 calls:

11.0ms

(- (exp (* a x)) 1)

series46.0ms

Counts

1 → 3

Calls

1 calls:

46.0ms

(- (exp (* a x)) 1)

simplify1.0s

Counts

20 → 20

Iterations

Iter	Nodes
done	2032
4	2032
3	977
2	307
1	113
0	48

prune206.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* a x) (* a x))
0.7b	(* a (* (* a x) (* a x)))
1.7b	(* x (+ (* (* a (* (* a x) (* a x))) 1/6) a))
10.6b	(+ (* x (+ (* (* a (* (* a x) (* a x))) 1/6) a)) (* 1/2 (* (* a x) (* a x))))

rewrite1.4s

Algorithm

rewrite-expression-head

Rules

63×	`pow1`
36×	`add-cbrt-cube` `add-exp-log`
31×	`pow-prod-down`
22×	`prod-exp` `cbrt-unprod`
10×	`add-sqr-sqrt`
7×	`-un-lft-identity` `associate-l*` `add-cube-cbrt`
6×	`add-log-exp`
5×	`associate-r`
4×	`pow-sqr` `pow-prod-up` `insert-posit16`
3×	`*-commutative`
2×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in` `flip3-+` `pow-plus` `associate-*r/` `flip-+` `unswap-sqr`
1×	`pow2` `+-commutative` `sum-log` `swap-sqr`

Counts

4 → 101

Calls

4 calls:

45.0ms	(* (* a x) (* a x))
87.0ms	(* a (* (* a x) (* a x)))
896.0ms	(* x (+ (* (* a (* (* a x) (* a x))) 1/6) a))
320.0ms	(+ (* x (+ (* (* a (* (* a x) (* a x))) 1/6) a)) (* 1/2 (* (* a x) (* a x))))

series382.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* (* a x) (* a x))
68.0ms	(* a (* (* a x) (* a x)))
119.0ms	(* x (+ (* (* a (* (* a x) (* a x))) 1/6) a))
144.0ms	(+ (* x (+ (* (* a (* (* a x) (* a x))) 1/6) a)) (* 1/2 (* (* a x) (* a x))))

simplify1.4s

Counts

113 → 113

Iterations

Iter	Nodes
done	2002
3	2002
2	1792
1	418
0	135

prune1.1s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 1/6 (* (* a x) (* (* a x) (* a x))))
0.2b	(* (* a x) (* a x))
0.2b	(* (* a x) (* a x))
10.6b	(+ (+ (* 1/6 (* (* a x) (* (* a x) (* a x)))) (* a x)) (* 1/2 (* (* a x) (* a x))))

rewrite1.5s

Algorithm

rewrite-expression-head

Rules

135×	`pow1`
81×	`add-cbrt-cube` `add-exp-log`
76×	`pow-prod-down`
58×	`prod-exp` `cbrt-unprod`
9×	`add-log-exp`
8×	`pow-sqr` `pow-prod-up`
5×	`add-sqr-sqrt` `-un-lft-identity` `associate-l*` `add-cube-cbrt`
4×	`pow-plus` `insert-posit16`
3×	`sum-log` `associate-r` `*-commutative`
2×	`pow2` `swap-sqr`
1×	`+-commutative` `associate-+l+` `flip3-+` `flip-+`

Counts

4 → 130

Calls

4 calls:

259.0ms	(* 1/6 (* (* a x) (* (* a x) (* a x))))
28.0ms	(* (* a x) (* a x))
29.0ms	(* (* a x) (* a x))
1.2s	(+ (+ (* 1/6 (* (* a x) (* (* a x) (* a x)))) (* a x)) (* 1/2 (* (* a x) (* a x))))

series280.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(* 1/6 (* (* a x) (* (* a x) (* a x))))
32.0ms	(* (* a x) (* a x))
38.0ms	(* (* a x) (* a x))
130.0ms	(+ (+ (* 1/6 (* (* a x) (* (* a x) (* a x)))) (* a x)) (* 1/2 (* (* a x) (* a x))))

simplify1.6s

Counts

142 → 142

Iterations

Iter	Nodes
done	2000
3	2000
2	1867
1	439
0	141

prune1.4s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize72.0ms

Local error

Found 4 expressions with local error:

10.6b	(+ (+ (* 1/6 (* (* a x) (* (* a x) (* a x)))) (* a x)) (* 1/2 (* (* a x) (* a x))))
17.6b	(cbrt (+ (+ (* 1/6 (* (* a x) (* (* a x) (* a x)))) (* a x)) (* 1/2 (* (* a x) (* a x)))))
17.6b	(cbrt (+ (+ (* 1/6 (* (* a x) (* (* a x) (* a x)))) (* a x)) (* 1/2 (* (* a x) (* a x)))))
17.6b	(cbrt (+ (+ (* 1/6 (* (* a x) (* (* a x) (* a x)))) (* a x)) (* 1/2 (* (* a x) (* a x)))))

rewrite3.1s

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 56

Calls

4 calls:

1.3s	(+ (+ (* 1/6 (* (* a x) (* (* a x) (* a x)))) (* a x)) (* 1/2 (* (* a x) (* a x))))
616.0ms	(cbrt (+ (+ (* 1/6 (* (* a x) (* (* a x) (* a x)))) (* a x)) (* 1/2 (* (* a x) (* a x)))))
545.0ms	(cbrt (+ (+ (* 1/6 (* (* a x) (* (* a x) (* a x)))) (* a x)) (* 1/2 (* (* a x) (* a x)))))
630.0ms	(cbrt (+ (+ (* 1/6 (* (* a x) (* (* a x) (* a x)))) (* a x)) (* 1/2 (* (* a x) (* a x)))))

series1.2s

Counts

4 → 12

Calls

4 calls:

140.0ms	(+ (+ (* 1/6 (* (* a x) (* (* a x) (* a x)))) (* a x)) (* 1/2 (* (* a x) (* a x))))
366.0ms	(cbrt (+ (+ (* 1/6 (* (* a x) (* (* a x) (* a x)))) (* a x)) (* 1/2 (* (* a x) (* a x)))))
337.0ms	(cbrt (+ (+ (* 1/6 (* (* a x) (* (* a x) (* a x)))) (* a x)) (* 1/2 (* (* a x) (* a x)))))
346.0ms	(cbrt (+ (+ (* 1/6 (* (* a x) (* (* a x) (* a x)))) (* a x)) (* 1/2 (* (* a x) (* a x)))))

simplify1.7s

Counts

68 → 68

Iterations

Iter	Nodes
done	2003
3	2003
2	1063
1	299
0	112

prune743.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

regimes275.0ms

Accuracy

98.6% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 21.4b

bsearch1.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	27
1	27
0	19

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.2s	2768×	body	1280	valid
765.0ms	1344×	body	640	valid
370.0ms	5504×	body	80	valid
116.0ms	672×	body	320	valid
41.0ms	369×	body	160	valid