Details

sample166.0ms

Algorithm

intervals

Results

88.0ms	93×	body	1280	valid
24.0ms	44×	body	640	valid
23.0ms	32×	body	2560	valid
9.0ms	24×	body	320	valid
6.0ms	51×	body	80	valid
3.0ms	12×	body	160	valid

simplify6.0ms

Counts

1 → 1

Iterations

Iter	Nodes
2	9
1	9
0	7

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 53.8b

localize26.0ms

Local error

Found 3 expressions with local error:

1.0b	(+ x (sqrt (+ (* x x) 1)))
2.6b	(log (+ x (sqrt (+ (* x x) 1))))
14.5b	(sqrt (+ (* x x) 1))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity`
6×	`add-sqr-sqrt`
5×	`pow1` `add-cube-cbrt` `add-log-exp`
4×	`log-prod` `add-exp-log`
3×	`flip3-+` `add-cbrt-cube` `sqrt-prod` `flip-+` `insert-posit16`
2×	`log-div` `sqrt-div` `distribute-lft-out`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `sqrt-pow1` `pow1/2` `rem-log-exp` `log-pow`

Counts

3 → 45

Calls

3 calls:

24.0ms	(+ x (sqrt (+ (* x x) 1)))
44.0ms	(log (+ x (sqrt (+ (* x x) 1))))
15.0ms	(sqrt (+ (* x x) 1))

series247.0ms

Counts

3 → 9

Calls

3 calls:

77.0ms	(+ x (sqrt (+ (* x x) 1)))
125.0ms	(log (+ x (sqrt (+ (* x x) 1))))
45.0ms	(sqrt (+ (* x x) 1))

simplify2.1s

Counts

54 → 54

Iterations

Iter	Nodes
4	3922
3	1654
2	660
1	271
0	121

prune365.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* x x) x)
0.1b	(* (* x x) x)
0.1b	(* -1/6 (* (* x x) x))
19.0b	(+ (* -1/6 (* (* x x) x)) (* 3/40 (* (* x x) (* (* x x) x))))

rewrite147.0ms

Algorithm

rewrite-expression-head

Rules

51×	`pow1`
23×	`add-cbrt-cube` `add-exp-log`
12×	`pow-plus` `pow-prod-down` `prod-exp` `pow-prod-up` `cbrt-unprod`
9×	`add-sqr-sqrt`
7×	`-un-lft-identity` `associate-r*` `add-cube-cbrt`
6×	`add-log-exp`
5×	`associate-l`
4×	`pow2` `pow-sqr` `insert-posit16`
3×	`*-commutative`
2×	`pow3` `unswap-sqr`
1×	`+-commutative` `sum-log` `flip3-+` `flip-+`

Counts

4 → 92

Calls

4 calls:

16.0ms	(* (* x x) x)
14.0ms	(* (* x x) x)
63.0ms	(* -1/6 (* (* x x) x))
52.0ms	(+ (* -1/6 (* (* x x) x)) (* 3/40 (* (* x x) (* (* x x) x))))

series427.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(* (* x x) x)
40.0ms	(* (* x x) x)
71.0ms	(* -1/6 (* (* x x) x))
252.0ms	(+ (* -1/6 (* (* x x) x)) (* 3/40 (* (* x x) (* (* x x) x))))

simplify2.7s

Counts

104 → 104

Iterations

Iter	Nodes
3	5081
2	907
1	256
0	88

prune535.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ 1/8 x) (* x x))
0.1b	(/ -1/16 (* (* x x) (* (* x x) x)))
16.3b	(log (+ (- (/ (/ 1/8 x) (* x x)) (/ 1/2 x)) (/ -1/16 (* (* x x) (* (* x x) x)))))
21.8b	(+ (- (/ (/ 1/8 x) (* x x)) (/ 1/2 x)) (/ -1/16 (* (* x x) (* (* x x) x))))

rewrite448.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-exp-log`
45×	`add-cbrt-cube`
34×	`times-frac`
31×	`*-un-lft-identity`
21×	`add-sqr-sqrt` `add-cube-cbrt`
17×	`prod-exp` `cbrt-unprod`
16×	`associate-/l*`
13×	`cbrt-undiv` `div-exp`
9×	`add-log-exp`
6×	`frac-add`
5×	`pow1` `log-div` `log-prod`
4×	`insert-posit16` `div-inv` `distribute-lft-out`
2×	`associate-+l+` `clear-num` `associate-/r*` `sum-log` `frac-2neg` `flip3-+` `flip3--` `frac-sub` `flip-+` `flip--` `distribute-lft-out--`
1×	`+-commutative` `sub-neg` `diff-log` `rem-log-exp` `log-pow` `associate-+l-` `associate-/l/`

Counts

4 → 120

Calls

4 calls:

20.0ms	(/ (/ 1/8 x) (* x x))
65.0ms	(/ -1/16 (* (* x x) (* (* x x) x)))
144.0ms	(log (+ (- (/ (/ 1/8 x) (* x x)) (/ 1/2 x)) (/ -1/16 (* (* x x) (* (* x x) x)))))
215.0ms	(+ (- (/ (/ 1/8 x) (* x x)) (/ 1/2 x)) (/ -1/16 (* (* x x) (* (* x x) x))))

series383.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(/ (/ 1/8 x) (* x x))
101.0ms	(/ -1/16 (* (* x x) (* (* x x) x)))
154.0ms	(log (+ (- (/ (/ 1/8 x) (* x x)) (/ 1/2 x)) (/ -1/16 (* (* x x) (* (* x x) x)))))
73.0ms	(+ (- (/ (/ 1/8 x) (* x x)) (/ 1/2 x)) (/ -1/16 (* (* x x) (* (* x x) x))))

simplify1.3s

Counts

132 → 132

Iterations

Iter	Nodes
2	2651
1	733
0	277

prune883.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ 1/2 x) x)
0.1b	(* (* x x) x)
0.3b	(/ -1/8 (* (* x x) x))
14.3b	(log (+ x (+ (+ (/ 1/2 x) x) (/ -1/8 (* (* x x) x)))))

rewrite249.0ms

Algorithm

rewrite-expression-head

Rules

24×	`pow1`
19×	`*-un-lft-identity` `add-exp-log`
18×	`add-cbrt-cube`
9×	`add-sqr-sqrt`
8×	`add-cube-cbrt`
7×	`distribute-lft-out`
6×	`log-prod` `pow-plus` `prod-exp` `pow-prod-up` `cbrt-unprod` `add-log-exp`
4×	`insert-posit16`
3×	`cbrt-undiv` `times-frac` `div-exp` `associate-r` `pow-prod-down` `associate-/l*`
2×	`pow2` `log-div` `flip3-+` `pow-sqr` `flip-+`
1×	`+-commutative` `clear-num` `associate-/r` `sum-log` `frac-2neg` `rem-log-exp` `associate-l` `pow3` `log-pow` `-commutative` `div-inv` `unswap-sqr`

Counts

4 → 84

Calls

4 calls:

16.0ms	(+ (/ 1/2 x) x)
27.0ms	(* (* x x) x)
26.0ms	(/ -1/8 (* (* x x) x))
177.0ms	(log (+ x (+ (+ (/ 1/2 x) x) (/ -1/8 (* (* x x) x)))))

series297.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(+ (/ 1/2 x) x)
65.0ms	(* (* x x) x)
55.0ms	(/ -1/8 (* (* x x) x))
134.0ms	(log (+ x (+ (+ (/ 1/2 x) x) (/ -1/8 (* (* x x) x)))))

simplify3.7s

Counts

96 → 96

Iterations

Iter	Nodes
3	6311
2	1365
1	370
0	154

prune444.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes102.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.1b

bsearch115.0ms

Steps

Iters	Range		Point
10	0.002603609100038161	6235082944194588.0	0.9442966733188264
8	-145.89507053458865	-0.006947246361207331	-1.0432984552881022

simplify12.0ms

Iterations

Iter	Nodes
2	42
1	42
0	32

end0.0ms

sample4.6s

Algorithm

intervals

Results

2.0s	2366×	body	1280	valid
1.0s	860×	body	2560	valid
820.0ms	1506×	body	640	valid
309.0ms	799×	body	320	valid
162.0ms	2063×	body	80	valid
78.0ms	406×	body	160	valid