Details

sample59.0ms

Algorithm

intervals

Results

29.0ms	99×	body	1280	valid
8.0ms	36×	body	640	valid
6.0ms	166×	body	80	valid
3.0ms	21×	body	320	valid
1.0ms	13×	body	160	valid

simplify2.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
7	1575
6	382
5	135
4	56
3	29
2	19
1	14
0	6

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.4b

localize13.0ms

Local error

Found 1 expressions with local error:

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

rewrite23.0ms

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:

22.0ms

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

series55.0ms

Counts

1 → 3

Calls

1 calls:

55.0ms

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

simplify2.0s

Counts

20 → 20

Iterations

Iter	Nodes
done	5000
4	2910
3	977
2	307
1	113
0	48

prune71.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (* (* x a) (* x a)) (+ 1/2 (* (* 1/6 x) a)))
0.1b	(* (* 1/6 x) a)
0.2b	(* (* x a) (* x a))
0.4b	(* 1/6 x)

rewrite177.0ms

Algorithm

rewrite-expression-head

Rules

68×	`pow1`
41×	`add-cbrt-cube` `add-exp-log`
34×	`pow-prod-down`
25×	`prod-exp` `cbrt-unprod`
11×	`add-sqr-sqrt`
10×	`associate-r`
8×	`*-un-lft-identity` `add-cube-cbrt`
6×	`associate-l`
4×	`pow-sqr` `*-commutative` `pow-prod-up` `insert-posit16` `add-log-exp`
2×	`pow-plus` `associate-*r/` `unswap-sqr`
1×	`pow2` `distribute-rgt-in` `distribute-lft-in` `flip3-+` `swap-sqr` `flip-+`

Counts

4 → 106

Calls

4 calls:

122.0ms	(* (* (* x a) (* x a)) (+ 1/2 (* (* 1/6 x) a)))
14.0ms	(* (* 1/6 x) a)
27.0ms	(* (* x a) (* x a))
10.0ms	(* 1/6 x)

series205.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(* (* (* x a) (* x a)) (+ 1/2 (* (* 1/6 x) a)))
32.0ms	(* (* 1/6 x) a)
36.0ms	(* (* x a) (* x a))
16.0ms	(* 1/6 x)

simplify2.1s

Counts

118 → 118

Iterations

Iter	Nodes
done	5000
2	1991
1	413
0	137

prune356.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (* (* x x) (* a a)) (+ 1/2 (* (* 1/6 x) a)))
0.1b	(* (* 1/6 x) a)
0.4b	(* 1/6 x)
14.2b	(* (* x x) (* a a))

rewrite120.0ms

Algorithm

rewrite-expression-head

Rules

57×	`pow1`
41×	`add-cbrt-cube` `add-exp-log`
31×	`pow-prod-down`
25×	`prod-exp` `cbrt-unprod`
10×	`add-sqr-sqrt` `associate-r`
8×	`*-un-lft-identity` `add-cube-cbrt`
6×	`associate-l`
4×	`pow-plus` `*-commutative` `pow-prod-up` `insert-posit16` `add-log-exp`
2×	`pow2` `associate-*r/` `pow-sqr` `unswap-sqr`
1×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `flip-+`

Counts

4 → 100

Calls

4 calls:

74.0ms	(* (* (* x x) (* a a)) (+ 1/2 (* (* 1/6 x) a)))
14.0ms	(* (* 1/6 x) a)
5.0ms	(* 1/6 x)
25.0ms	(* (* x x) (* a a))

series197.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(* (* (* x x) (* a a)) (+ 1/2 (* (* 1/6 x) a)))
18.0ms	(* (* 1/6 x) a)
22.0ms	(* 1/6 x)
35.0ms	(* (* x x) (* a a))

simplify1.8s

Counts

112 → 112

Iterations

Iter	Nodes
done	5020
2	1961
1	425
0	140

prune311.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (exp (* x a)) 1)
0.0b	(/ (- (exp (* (* 3 x) a)) 1) (+ 1 (* (exp (* x a)) (+ (exp (* x a)) 1))))
0.2b	(* (* 3 x) a)
4.3b	(- (exp (* (* 3 x) a)) 1)

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
34×	`*-un-lft-identity`
21×	`times-frac`
17×	`add-cube-cbrt`
11×	`add-cbrt-cube` `add-exp-log`
10×	`difference-of-squares`
9×	`pow1`
8×	`add-log-exp`
7×	`associate-/l*`
5×	`difference-of-sqr-1` `distribute-lft-out--`
4×	`insert-posit16`
3×	`associate-/r` `associate-r*` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`flip3-+` `flip3--` `associate-/r/` `flip-+` `flip--` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `associate-l` `*-commutative` `div-inv` `distribute-lft-out`

Counts

4 → 98

Calls

4 calls:

16.0ms	(+ (exp (* x a)) 1)
39.0ms	(/ (- (exp (* (* 3 x) a)) 1) (+ 1 (* (exp (* x a)) (+ (exp (* x a)) 1))))
19.0ms	(* (* 3 x) a)
20.0ms	(- (exp (* (* 3 x) a)) 1)

series260.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(+ (exp (* x a)) 1)
140.0ms	(/ (- (exp (* (* 3 x) a)) 1) (+ 1 (* (exp (* x a)) (+ (exp (* x a)) 1))))
26.0ms	(* (* 3 x) a)
69.0ms	(- (exp (* (* 3 x) a)) 1)

simplify1.8s

Counts

110 → 110

Iterations

Iter	Nodes
done	5009
2	1732
1	487
0	183

prune558.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes130.0ms

Accuracy

36.4% (13.5b remaining)

Error of 13.5b against oracle of 0.1b and baseline of 21.2b

bsearch127.0ms

Steps

Iters	Range		Point
4	3.73373204307318e+54	5.3335735992532233e+54	4.1836874807488166e+54
8	-3.5498477693853334e+107	-1.65227804131582e+103	-5.0289586708105234e+104

simplify9.0ms

Iterations

Iter	Nodes
done	59
1	59
0	38

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.0s	2702×	body	1280	valid
663.0ms	5541×	body	80	valid
409.0ms	1244×	body	640	valid
149.0ms	788×	body	320	valid
39.0ms	387×	body	160	valid