Details

sample81.0ms

Algorithm

intervals

Results

38.0ms	84×	body	1280	valid
14.0ms	48×	body	640	valid
9.0ms	155×	body	80	valid
7.0ms	32×	body	320	valid
3.0ms	20×	body	160	valid

simplify16.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	18
3	18
2	16
1	13
0	5

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.1b

localize28.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- (exp x) 1) x)
5.2b	(- (exp x) 1)

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
29×	`*-un-lft-identity`
21×	`times-frac`
14×	`add-cube-cbrt`
10×	`difference-of-squares`
7×	`associate-/l*`
5×	`difference-of-sqr-1` `distribute-lft-out--`
4×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`associate-/r*`
2×	`pow1` `flip3--` `insert-posit16` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `div-inv`

Counts

2 → 64

Calls

2 calls:

19.0ms	(/ (- (exp x) 1) x)
10.0ms	(- (exp x) 1)

series76.0ms

Counts

2 → 6

Calls

2 calls:

59.0ms	(/ (- (exp x) 1) x)
16.0ms	(- (exp x) 1)

simplify1.5s

Counts

70 → 70

Iterations

Iter	Nodes
done	2009
4	2009
3	1887
2	592
1	239
0	108

prune267.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 2 expressions with local error:

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

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 42

Calls

2 calls:

26.0ms	(* x (+ (* 1/6 x) 1/2))
12.0ms	(* 1/6 x)

series107.0ms

Counts

2 → 6

Calls

2 calls:

91.0ms	(* x (+ (* 1/6 x) 1/2))
16.0ms	(* 1/6 x)

simplify1.1s

Counts

48 → 48

Iterations

Iter	Nodes
done	2059
3	2059
2	650
1	205
0	72

prune152.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (pow (exp x) 3) (pow 1 3)) (+ (* (exp x) (+ (* x (exp x)) x)) x))
0.0b	(* (exp x) (+ (* x (exp x)) x))
0.0b	(pow (exp x) 3)
5.1b	(- (pow (exp x) 3) (pow 1 3))

rewrite159.0ms

Algorithm

rewrite-expression-head

Rules

201×	`add-sqr-sqrt`
144×	`*-un-lft-identity`
120×	`difference-of-squares`
102×	`times-frac`
93×	`unpow-prod-down` `cube-prod`
51×	`sqr-pow`
49×	`add-cube-cbrt`
34×	`associate-/l*`
30×	`distribute-lft-out--`
9×	`add-cbrt-cube`
7×	`pow1` `add-exp-log`
6×	`cube-mult` `add-log-exp`
5×	`difference-cubes`
4×	`pow-pow` `insert-posit16`
3×	`pow-unpow` `exp-prod` `associate-/r` `associate-r` `associate-l*`
2×	`flip3-+` `flip3--` `associate-*r/` `associate-/r/` `flip-+` `flip--` `associate-/l/`
1×	`distribute-rgt-in` `pow-to-exp` `cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `distribute-lft-in` `diff-log` `unpow3` `div-sub` `div-exp` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `cbrt-unprod` `div-inv` `rem-cube-cbrt` `unswap-sqr`

Counts

4 → 251

Calls

4 calls:

81.0ms	(/ (- (pow (exp x) 3) (pow 1 3)) (+ (* (exp x) (+ (* x (exp x)) x)) x))
49.0ms	(* (exp x) (+ (* x (exp x)) x))
4.0ms	(pow (exp x) 3)
19.0ms	(- (pow (exp x) 3) (pow 1 3))

series346.0ms

Counts

4 → 12

Calls

4 calls:

171.0ms	(/ (- (pow (exp x) 3) (pow 1 3)) (+ (* (exp x) (+ (* x (exp x)) x)) x))
89.0ms	(* (exp x) (+ (* x (exp x)) x))
42.0ms	(pow (exp x) 3)
44.0ms	(- (pow (exp x) 3) (pow 1 3))

simplify1.4s

Counts

263 → 263

Iterations

Iter	Nodes
done	2000
2	2000
1	812
0	307

prune971.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.0b

regimes22.0ms

Accuracy

99.1% (0.2b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 20.5b

bsearch51.0ms

Steps

Iters	Range		Point
10	-0.005838610583870787	-4.910260011938944e-13	-0.00018534463155854764

simplify4.0ms

Iterations

Iter	Nodes
done	31
1	31
0	21

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.5s	2321×	body	1280	valid
608.0ms	1684×	body	640	valid
304.0ms	5330×	body	80	valid
181.0ms	805×	body	320	valid
57.0ms	444×	body	160	valid