Details

sample311.0ms

Algorithm

intervals

Results

99.0ms	55×	body	10240	exit
70.0ms	322×	body	80	valid
61.0ms	45×	body	1280	valid
37.0ms	46×	body	640	valid
11.0ms	18×	body	320	valid
3.0ms	9×	body	160	valid

simplify1.9s

Counts

1 → 1

Iterations

Iter	Nodes
5	3061
4	844
3	296
2	120
1	46
0	19

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.3b

localize78.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ 1 eps) x)
0.1b	(exp (- (* (- 1 eps) x)))
0.1b	(exp (- (* (+ 1 eps) x)))
2.7b	(- (* (+ 1 (/ 1 eps)) (exp (- (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (- (* (+ 1 eps) x)))))

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

81×	`frac-sub`
74×	`exp-neg`
72×	`frac-times`
56×	`neg-sub0` `exp-diff`
38×	`associate-*l/`
36×	`associate-*r/`
28×	`flip3-+` `flip3--` `flip-+` `flip--`
18×	`un-div-inv`
12×	`exp-prod`
10×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
8×	`add-cube-cbrt`
6×	`pow1` `add-cbrt-cube` `add-exp-log`
4×	`associate-l` `rem-exp-log`
3×	`associate-r`
2×	`distribute-lft-neg-in` `neg-mul-1` `distribute-rgt-neg-in` `neg-log`
1×	`sub-neg` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out` `unswap-sqr`

Counts

4 → 148

Calls

4 calls:

24.0ms	(* (+ 1 eps) x)
13.0ms	(exp (- (* (- 1 eps) x)))
11.0ms	(exp (- (* (+ 1 eps) x)))
57.0ms	(- (* (+ 1 (/ 1 eps)) (exp (- (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (- (* (+ 1 eps) x)))))

series269.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (+ 1 eps) x)
29.0ms	(exp (- (* (- 1 eps) x)))
31.0ms	(exp (- (* (+ 1 eps) x)))
167.0ms	(- (* (+ 1 (/ 1 eps)) (exp (- (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (- (* (+ 1 eps) x)))))

simplify2.1s

Counts

160 → 160

Iterations

Iter	Nodes
2	3018
1	1145
0	360

prune2.4s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize21.0ms

Local error

Found 3 expressions with local error:

0.1b	(* x (* x x))
0.1b	(* (* x (* x x)) 2/3)
7.2b	(+ (- 2 (* x x)) (* (* x (* x x)) 2/3))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

26×	`pow1`
17×	`add-cbrt-cube` `add-exp-log`
9×	`pow-prod-down` `prod-exp` `cbrt-unprod`
8×	`add-log-exp`
6×	`add-sqr-sqrt`
5×	`*-un-lft-identity` `pow-prod-up` `add-cube-cbrt`
4×	`associate-r` `associate-l`
2×	`associate-+l+` `sum-log` `*-commutative`
1×	`pow2` `+-commutative` `sub-neg` `flip3-+` `pow-plus` `diff-log` `cube-unmult` `pow-sqr` `associate-+l-` `flip-+` `unswap-sqr`

Counts

3 → 60

Calls

3 calls:

24.0ms	(* x (* x x))
50.0ms	(* (* x (* x x)) 2/3)
21.0ms	(+ (- 2 (* x x)) (* (* x (* x x)) 2/3))

series182.0ms

Counts

3 → 9

Calls

3 calls:

48.0ms	(* x (* x x))
74.0ms	(* (* x (* x x)) 2/3)
60.0ms	(+ (- 2 (* x x)) (* (* x (* x x)) 2/3))

simplify2.2s

Counts

69 → 69

Iterations

Iter	Nodes
3	4522
2	848
1	228
0	91

prune578.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.4b

localize36.0ms

Local error

Found 4 expressions with local error:

7.2b	(+ (- 2 (* x x)) (* (* x (* x x)) 2/3))
11.6b	(cbrt (+ (- 2 (* x x)) (* (* x (* x x)) 2/3)))
11.6b	(cbrt (+ (- 2 (* x x)) (* (* x (* x x)) 2/3)))
11.6b	(cbrt (+ (- 2 (* x x)) (* (* x (* x x)) 2/3)))

rewrite105.0ms

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-+`
3×	`pow1/3`
2×	`associate-+l+` `sum-log`
1×	`+-commutative` `sub-neg` `diff-log` `associate-+l-`

Counts

4 → 54

Calls

4 calls:

36.0ms	(+ (- 2 (* x x)) (* (* x (* x x)) 2/3))
14.0ms	(cbrt (+ (- 2 (* x x)) (* (* x (* x x)) 2/3)))
20.0ms	(cbrt (+ (- 2 (* x x)) (* (* x (* x x)) 2/3)))
34.0ms	(cbrt (+ (- 2 (* x x)) (* (* x (* x x)) 2/3)))

series354.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(+ (- 2 (* x x)) (* (* x (* x x)) 2/3))
115.0ms	(cbrt (+ (- 2 (* x x)) (* (* x (* x x)) 2/3)))
82.0ms	(cbrt (+ (- 2 (* x x)) (* (* x (* x x)) 2/3)))
111.0ms	(cbrt (+ (- 2 (* x x)) (* (* x (* x x)) 2/3)))

simplify1.5s

Counts

66 → 66

Iterations

Iter	Nodes
3	3163
2	719
1	238
0	95

prune769.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.4b

localize89.0ms

Local error

Found 4 expressions with local error:

7.2b	(+ (- 2 (* x x)) (* (* x (* x x)) 2/3))
7.2b	(+ (- 2 (* x x)) (* (* x (* x x)) 2/3))
11.6b	(cbrt (+ (- 2 (* x x)) (* (* x (* x x)) 2/3)))
11.6b	(cbrt (+ (- 2 (* x x)) (* (* x (* x x)) 2/3)))

rewrite144.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-log-exp`
6×	`cbrt-prod` `add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`pow1` `associate-+l+` `cbrt-div` `sum-log` `flip3-+` `add-cbrt-cube` `add-exp-log` `flip-+`
2×	`+-commutative` `sub-neg` `pow1/3` `diff-log` `associate-+l-`

Counts

4 → 56

Calls

4 calls:

40.0ms	(+ (- 2 (* x x)) (* (* x (* x x)) 2/3))
47.0ms	(+ (- 2 (* x x)) (* (* x (* x x)) 2/3))
29.0ms	(cbrt (+ (- 2 (* x x)) (* (* x (* x x)) 2/3)))
28.0ms	(cbrt (+ (- 2 (* x x)) (* (* x (* x x)) 2/3)))

series725.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(+ (- 2 (* x x)) (* (* x (* x x)) 2/3))
58.0ms	(+ (- 2 (* x x)) (* (* x (* x x)) 2/3))
95.0ms	(cbrt (+ (- 2 (* x x)) (* (* x (* x x)) 2/3)))
511.0ms	(cbrt (+ (- 2 (* x x)) (* (* x (* x x)) 2/3)))

simplify1.5s

Counts

68 → 68

Iterations

Iter	Nodes
3	3163
2	719
1	238
0	95

prune609.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.4b

regimes170.0ms

Accuracy

96% (0.6b remaining)

Error of 1.0b against oracle of 0.4b and baseline of 16.4b

bsearch321.0ms

Steps

Iters	Range		Point
9	0.4148577645705283	50016.8179159125	226.33586080847886

simplify24.0ms

Iterations

Iter	Nodes
4	58
3	58
2	56
1	47
0	31

end0.0ms

sample11.5s

Algorithm

intervals

Results

3.5s	1975×	body	10240	exit
3.5s	1743×	body	1280	valid
2.2s	10116×	body	80	valid
1.3s	1265×	body	640	valid
503.0ms	624×	body	320	valid
116.0ms	309×	body	160	valid