Details

sample117.0ms

Algorithm

intervals

Results

43.0ms	84×	body	1280	valid
33.0ms	80×	body	10240	exit
15.0ms	48×	body	640	valid
7.0ms	30×	body	320	valid
5.0ms	74×	body	80	valid
3.0ms	20×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	11
2	11
1	10
0	5

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.5b

localize9.0ms

Local error

Found 2 expressions with local error:

0.5b	(/ (exp x) (- (exp x) 1))
5.2b	(- (exp x) 1)

rewrite38.0ms

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-/r*`
5×	`difference-of-sqr-1` `distribute-lft-out--`
4×	`add-cbrt-cube` `add-log-exp`
3×	`add-exp-log` `associate-/l*`
2×	`pow1` `flip3--` `associate-/r/` `insert-posit16` `flip--`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-exp` `div-inv`

Counts

2 → 63

Calls

2 calls:

28.0ms	(/ (exp x) (- (exp x) 1))
8.0ms	(- (exp x) 1)

series51.0ms

Counts

2 → 6

Calls

2 calls:

27.0ms	(/ (exp x) (- (exp x) 1))
25.0ms	(- (exp x) 1)

simplify1.1s

Counts

69 → 69

Iterations

Iter	Nodes
done	2018
4	2018
3	1632
2	502
1	203
0	101

prune231.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize14.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
0.3b	(* 1/12 x)

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-log-exp`
6×	`add-sqr-sqrt`
4×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
3×	`sum-log` `associate-r` `associate-l`
2×	`insert-posit16`
1×	`+-commutative` `associate-+r+` `flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

2 → 33

Calls

2 calls:

23.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
5.0ms	(* 1/12 x)

series37.0ms

Counts

2 → 6

Calls

2 calls:

19.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
18.0ms	(* 1/12 x)

simplify1.2s

Counts

39 → 39

Iterations

Iter	Nodes
done	2005
4	2005
3	1777
2	480
1	156
0	60

prune147.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (+ (/ 1 x) 1/2) (* 1/12 x))
0.3b	(* 1/12 x)

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-log-exp`
6×	`add-sqr-sqrt`
4×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
3×	`sum-log` `associate-r` `associate-l`
2×	`insert-posit16`
1×	`+-commutative` `associate-+l+` `flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

2 → 33

Calls

2 calls:

44.0ms	(+ (+ (/ 1 x) 1/2) (* 1/12 x))
7.0ms	(* 1/12 x)

series41.0ms

Counts

2 → 6

Calls

2 calls:

19.0ms	(+ (+ (/ 1 x) 1/2) (* 1/12 x))
22.0ms	(* 1/12 x)

simplify1.6s

Counts

39 → 39

Iterations

Iter	Nodes
done	2003
4	2003
3	1903
2	478
1	152
0	61

prune134.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.4b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (exp x) (exp x))
0.5b	(/ (exp x) (- (exp (+ (+ x x) x)) 1))
0.5b	(* (/ (exp x) (- (exp (+ (+ x x) x)) 1)) (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1))))
5.3b	(- (exp (+ (+ x x) x)) 1)

rewrite1.0s

Algorithm

rewrite-expression-head

Rules

77×	`add-sqr-sqrt`
62×	`*-un-lft-identity`
43×	`times-frac`
38×	`add-cube-cbrt`
30×	`associate-l`
18×	`exp-prod`
16×	`difference-of-squares`
13×	`pow1` `add-cbrt-cube`
9×	`add-exp-log`
8×	`difference-of-sqr-1` `distribute-lft-out--`
7×	`associate-/r*`
6×	`associate-r` `add-log-exp`
5×	`pow-prod-down`
4×	`associate-/r/` `pow-sqr` `pow-prod-up` `insert-posit16`
3×	`flip3--` `swap-sqr` `prod-exp` `cbrt-unprod` `flip--` `associate-/l*` `unswap-sqr`
2×	`frac-times` `cbrt-undiv` `flip3-+` `div-exp` `associate-r/` `-commutative` `flip-+` `div-inv`
1×	`pow2` `distribute-rgt-in` `clear-num` `sub-neg` `frac-2neg` `distribute-lft-in` `pow-plus` `diff-log` `associate-*l/`

Counts

4 → 151

Calls

4 calls:

22.0ms	(* (exp x) (exp x))
186.0ms	(/ (exp x) (- (exp (+ (+ x x) x)) 1))
642.0ms	(* (/ (exp x) (- (exp (+ (+ x x) x)) 1)) (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1))))
177.0ms	(- (exp (+ (+ x x) x)) 1)

series212.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* (exp x) (exp x))
48.0ms	(/ (exp x) (- (exp (+ (+ x x) x)) 1))
122.0ms	(* (/ (exp x) (- (exp (+ (+ x x) x)) 1)) (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1))))
20.0ms	(- (exp (+ (+ x x) x)) 1)

simplify1.3s

Counts

163 → 163

Iterations

Iter	Nodes
done	2005
2	2005
1	738
0	219

prune624.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.4b

regimes36.0ms

Accuracy

99.4% (0.1b remaining)

Error of 0.5b against oracle of 0.3b and baseline of 20.8b

bsearch52.0ms

Steps

Iters	Range		Point
10	-0.005838610583870787	-4.910260011938944e-13	-0.0013573601244548715

simplify5.0ms

Iterations

Iter	Nodes
done	34
1	34
0	24

end0.0ms

sample3.9s

Algorithm

intervals

Results

1.5s	2312×	body	1280	valid
1.2s	2532×	body	10240	exit
613.0ms	1680×	body	640	valid
177.0ms	2773×	body	80	valid
168.0ms	794×	body	320	valid
61.0ms	442×	body	160	valid