Details

sample160.0ms

Algorithm

intervals

Results

85.0ms	81×	body	1280	valid
27.0ms	46×	body	640	valid
18.0ms	26×	body	2560	valid
7.0ms	20×	body	320	valid
6.0ms	66×	body	80	valid
4.0ms	17×	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: 53.1b

localize24.0ms

Local error

Found 3 expressions with local error:

1.1b	(+ x (sqrt (+ (* x x) 1)))
3.2b	(log (+ x (sqrt (+ (* x x) 1))))
16.2b	(sqrt (+ (* x x) 1))

rewrite49.0ms

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:

21.0ms	(+ x (sqrt (+ (* x x) 1)))
12.0ms	(log (+ x (sqrt (+ (* x x) 1))))
15.0ms	(sqrt (+ (* x x) 1))

series250.0ms

Counts

3 → 9

Calls

3 calls:

70.0ms	(+ x (sqrt (+ (* x x) 1)))
141.0ms	(log (+ x (sqrt (+ (* x x) 1))))
38.0ms	(sqrt (+ (* x x) 1))

simplify1.9s

Counts

54 → 54

Iterations

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

prune267.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* x x) x)
0.1b	(* (* x x) x)
0.3b	(* -1/6 (* (* x x) x))
20.8b	(+ (* -1/6 (* (* x x) x)) (* 3/40 (* (* x x) (* (* x x) x))))

rewrite158.0ms

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:

28.0ms	(* (* x x) x)
23.0ms	(* (* x x) x)
38.0ms	(* -1/6 (* (* x x) x))
67.0ms	(+ (* -1/6 (* (* x x) x)) (* 3/40 (* (* x x) (* (* x x) x))))

series345.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (* x x) x)
44.0ms	(* (* x x) x)
48.0ms	(* -1/6 (* (* x x) x))
205.0ms	(+ (* -1/6 (* (* x x) x)) (* 3/40 (* (* x x) (* (* x x) x))))

simplify2.8s

Counts

104 → 104

Iterations

Iter	Nodes
3	5081
2	907
1	256
0	88

prune280.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize56.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ -1/16 (* (* x x) (* (* x x) x)))
0.1b	(* (* x x) x)
11.7b	(log (+ (- (/ (/ 1/8 x) (* x x)) (/ 1/2 x)) (/ -1/16 (* (* x x) (* (* x x) x)))))
19.4b	(+ (- (/ (/ 1/8 x) (* x x)) (/ 1/2 x)) (/ -1/16 (* (* x x) (* (* x x) x))))

rewrite415.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 102

Calls

4 calls:

58.0ms	(/ -1/16 (* (* x x) (* (* x x) x)))
14.0ms	(* (* x x) x)
139.0ms	(log (+ (- (/ (/ 1/8 x) (* x x)) (/ 1/2 x)) (/ -1/16 (* (* x x) (* (* x x) x)))))
202.0ms	(+ (- (/ (/ 1/8 x) (* x x)) (/ 1/2 x)) (/ -1/16 (* (* x x) (* (* x x) x))))

series369.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(/ -1/16 (* (* x x) (* (* x x) x)))
58.0ms	(* (* x x) x)
162.0ms	(log (+ (- (/ (/ 1/8 x) (* x x)) (/ 1/2 x)) (/ -1/16 (* (* x x) (* (* x x) x)))))
74.0ms	(+ (- (/ (/ 1/8 x) (* x x)) (/ 1/2 x)) (/ -1/16 (* (* x x) (* (* x x) x))))

simplify790.0ms

Counts

114 → 114

Iterations

Iter	Nodes
2	2107
1	580
0	211

prune355.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (/ 1/2 x) (- (/ (/ 1/8 x) (* x x)) (+ x x)))
0.1b	(/ (/ 1/8 x) (* x x))
10.2b	(log (- (/ 1/2 x) (- (/ (/ 1/8 x) (* x x)) (+ x x))))

rewrite227.0ms

Algorithm

rewrite-expression-head

Rules

36×	`*-un-lft-identity`
33×	`times-frac`
28×	`add-sqr-sqrt`
18×	`add-cube-cbrt`
16×	`add-exp-log`
15×	`add-cbrt-cube`
13×	`associate-/l*`
12×	`frac-sub` `add-log-exp`
10×	`distribute-lft-out--`
8×	`log-prod`
6×	`cbrt-undiv` `log-div` `div-exp`
5×	`diff-log`
4×	`pow1` `flip3--` `flip--` `difference-of-squares`
3×	`insert-posit16` `div-inv`
2×	`sub-neg` `flip3-+` `prod-exp` `cbrt-unprod` `flip-+` `distribute-lft-out` `associate--r+`
1×	`clear-num` `associate-/r*` `sum-log` `frac-2neg` `rem-log-exp` `log-pow` `associate--r-` `associate-/l/`

Counts

3 → 98

Calls

3 calls:

100.0ms	(- (/ 1/2 x) (- (/ (/ 1/8 x) (* x x)) (+ x x)))
13.0ms	(/ (/ 1/8 x) (* x x))
112.0ms	(log (- (/ 1/2 x) (- (/ (/ 1/8 x) (* x x)) (+ x x))))

series282.0ms

Counts

3 → 9

Calls

3 calls:

66.0ms	(- (/ 1/2 x) (- (/ (/ 1/8 x) (* x x)) (+ x x)))
62.0ms	(/ (/ 1/8 x) (* x x))
153.0ms	(log (- (/ 1/2 x) (- (/ (/ 1/8 x) (* x x)) (+ x x))))

simplify11.9s

Counts

107 → 107

Iterations

Iter	Nodes
3	9204
2	1872
1	637
0	248

prune331.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes113.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 31.6b

bsearch105.0ms

Steps

Iters	Range		Point
10	1.8230705747381016e-09	4364471.442644652	0.9581083600858236
9	-32298.533864343164	-0.030639508246526274	-1.0612400279589977

simplify5.0ms

Iterations

Iter	Nodes
2	37
1	37
0	30

end0.0ms

sample4.0s

Algorithm

intervals

Results

1.7s	2289×	body	1280	valid
1.1s	1615×	body	640	valid
526.0ms	793×	body	2560	valid
248.0ms	764×	body	320	valid
176.0ms	2105×	body	80	valid
128.0ms	434×	body	160	valid