Details

sample91.0ms

Algorithm

intervals

Results

43.0ms	87×	body	1280	valid
16.0ms	51×	body	640	valid
11.0ms	168×	body	80	valid
7.0ms	30×	body	320	valid
1.0ms	9×	body	160	valid

simplify14.0ms

Counts

1 → 1

Iterations

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.7b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- (exp x) 1) x)
3.3b	(- (exp x) 1)

rewrite60.0ms

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:

49.0ms	(/ (- (exp x) 1) x)
9.0ms	(- (exp x) 1)

series75.0ms

Counts

2 → 6

Calls

2 calls:

50.0ms	(/ (- (exp x) 1) x)
24.0ms	(- (exp x) 1)

simplify1.0s

Counts

70 → 70

Iterations

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

prune235.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 2 expressions with local error:

0.1b	(* 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))
11.0ms	(* 1/6 x)

series138.0ms

Counts

2 → 6

Calls

2 calls:

119.0ms	(* x (+ (* 1/6 x) 1/2))
19.0ms	(* 1/6 x)

simplify562.0ms

Counts

48 → 48

Iterations

Iter	Nodes
done	2007
2	650
1	205
0	72

prune142.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (exp x) x)
3.2b	(- (/ (exp x) x) (/ 1 x))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 57

Calls

2 calls:

6.0ms	(/ (exp x) x)
32.0ms	(- (/ (exp x) x) (/ 1 x))

series72.0ms

Counts

2 → 6

Calls

2 calls:

30.0ms	(/ (exp x) x)
42.0ms	(- (/ (exp x) x) (/ 1 x))

simplify1.0s

Counts

63 → 63

Iterations

Iter	Nodes
done	2001
3	1916
2	621
1	236
0	109

prune181.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (exp x))
0.0b	(sqrt (exp x))
0.0b	(* (sqrt (exp x)) (/ (sqrt (exp x)) x))
2.9b	(- (* (sqrt (exp x)) (/ (sqrt (exp x)) x)) (/ 1 x))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
23×	`*-un-lft-identity` `add-cube-cbrt` `sqrt-prod`
22×	`times-frac` `associate-r`
9×	`add-cbrt-cube` `add-exp-log`
8×	`pow1` `sqrt-pow1`
6×	`exp-prod` `associate-l` `add-log-exp` `unswap-sqr`
4×	`insert-posit16`
3×	`associate-*r/`
2×	`rem-sqrt-square` `pow1/2` `prod-exp` `cbrt-unprod`
1×	`cbrt-undiv` `sub-neg` `flip3--` `diff-log` `div-exp` `pow-prod-down` `*-commutative` `frac-sub` `div-inv` `flip--` `sub-div`

Counts

4 → 98

Calls

4 calls:

4.0ms	(sqrt (exp x))
4.0ms	(sqrt (exp x))
40.0ms	(* (sqrt (exp x)) (/ (sqrt (exp x)) x))
34.0ms	(- (* (sqrt (exp x)) (/ (sqrt (exp x)) x)) (/ 1 x))

series115.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(sqrt (exp x))
21.0ms	(sqrt (exp x))
43.0ms	(* (sqrt (exp x)) (/ (sqrt (exp x)) x))
38.0ms	(- (* (sqrt (exp x)) (/ (sqrt (exp x)) x)) (/ 1 x))

simplify624.0ms

Counts

110 → 110

Iterations

Iter	Nodes
done	2000
2	1043
1	344
0	135

prune416.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes39.0ms

Accuracy

98.8% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 20.7b

bsearch39.0ms

Steps

Iters	Range		Point
8	-0.0015977726548224043	-3.438608481379167e-06	-0.00023107496311143165

simplify3.0ms

Iterations

Iter	Nodes
done	21
1	21
0	15

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.5s	2323×	body	1280	valid
517.0ms	1653×	body	640	valid
394.0ms	5420×	body	80	valid
191.0ms	828×	body	320	valid
56.0ms	439×	body	160	valid