Details

sample166.0ms

Algorithm

intervals

Results

88.0ms	87×	body	1280	valid
28.0ms	46×	body	640	valid
17.0ms	23×	body	2560	valid
10.0ms	28×	body	320	valid
6.0ms	65×	body	80	valid
2.0ms	7×	body	160	valid

simplify5.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	11
1	11
0	7

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 54.2b

localize16.0ms

Local error

Found 3 expressions with local error:

0.9b	(+ x (sqrt (+ (* x x) 1)))
1.7b	(log (+ x (sqrt (+ (* x x) 1))))
14.2b	(sqrt (+ (* x x) 1))

rewrite52.0ms

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:

30.0ms	(+ x (sqrt (+ (* x x) 1)))
13.0ms	(log (+ x (sqrt (+ (* x x) 1))))
8.0ms	(sqrt (+ (* x x) 1))

series302.0ms

Counts

3 → 9

Calls

3 calls:

94.0ms	(+ x (sqrt (+ (* x x) 1)))
149.0ms	(log (+ x (sqrt (+ (* x x) 1))))
59.0ms	(sqrt (+ (* x x) 1))

simplify1.5s

Counts

54 → 54

Iterations

Iter	Nodes
done	5000
3	2036
2	733
1	273
0	121

prune292.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 3/40 (pow x 5))
0.1b	(* (* x x) x)
0.1b	(* -1/6 (* (* x x) x))
18.0b	(+ (* -1/6 (* (* x x) x)) (* 3/40 (pow x 5)))

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 89

Calls

4 calls:

9.0ms	(* 3/40 (pow x 5))
17.0ms	(* (* x x) x)
39.0ms	(* -1/6 (* (* x x) x))
46.0ms	(+ (* -1/6 (* (* x x) x)) (* 3/40 (pow x 5)))

series515.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(* 3/40 (pow x 5))
71.0ms	(* (* x x) x)
47.0ms	(* -1/6 (* (* x x) x))
293.0ms	(+ (* -1/6 (* (* x x) x)) (* 3/40 (pow x 5)))

simplify1.4s

Counts

101 → 101

Iterations

Iter	Nodes
done	5000
2	1129
1	332
0	124

prune355.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ -1/16 (pow x 5))
0.5b	(/ 1/8 (* (* x x) x))
11.4b	(log (- (/ -1/16 (pow x 5)) (- (/ 1/2 x) (/ 1/8 (* (* x x) x)))))
22.3b	(- (/ -1/16 (pow x 5)) (- (/ 1/2 x) (/ 1/8 (* (* x x) x))))

rewrite171.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt`
33×	`*-un-lft-identity`
30×	`times-frac`
23×	`add-cube-cbrt`
19×	`add-exp-log`
15×	`add-cbrt-cube`
14×	`unpow-prod-down`
9×	`log-prod` `add-log-exp`
8×	`associate-/r*` `frac-sub` `difference-of-squares`
6×	`div-exp` `associate-/l*` `distribute-lft-out--` `sqr-pow`
5×	`pow1` `log-div`
4×	`cbrt-undiv` `flip3--` `insert-posit16` `flip--`
3×	`diff-log` `prod-exp` `cbrt-unprod`
2×	`clear-num` `sub-neg` `frac-2neg` `div-inv` `associate--r+`
1×	`pow-to-exp` `rem-log-exp` `pow-exp` `log-pow` `associate--r-`

Counts

4 → 120

Calls

4 calls:

5.0ms	(/ -1/16 (pow x 5))
15.0ms	(/ 1/8 (* (* x x) x))
59.0ms	(log (- (/ -1/16 (pow x 5)) (- (/ 1/2 x) (/ 1/8 (* (* x x) x)))))
89.0ms	(- (/ -1/16 (pow x 5)) (- (/ 1/2 x) (/ 1/8 (* (* x x) x))))

series354.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(/ -1/16 (pow x 5))
68.0ms	(/ 1/8 (* (* x x) x))
158.0ms	(log (- (/ -1/16 (pow x 5)) (- (/ 1/2 x) (/ 1/8 (* (* x x) x)))))
66.0ms	(- (/ -1/16 (pow x 5)) (- (/ 1/2 x) (/ 1/8 (* (* x x) x))))

simplify1.6s

Counts

132 → 132

Iterations

Iter	Nodes
done	5006
2	2203
1	612
0	264

prune514.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ x (- x (- (/ 1/8 (* (* x x) x)) (/ 1/2 x))))
0.1b	(* (* x x) x)
0.5b	(/ 1/8 (* (* x x) x))
10.0b	(log (+ x (- x (- (/ 1/8 (* (* x x) x)) (/ 1/2 x)))))

rewrite984.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 92

Calls

4 calls:

321.0ms	(+ x (- x (- (/ 1/8 (* (* x x) x)) (/ 1/2 x))))
16.0ms	(* (* x x) x)
22.0ms	(/ 1/8 (* (* x x) x))
622.0ms	(log (+ x (- x (- (/ 1/8 (* (* x x) x)) (/ 1/2 x)))))

series350.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(+ x (- x (- (/ 1/8 (* (* x x) x)) (/ 1/2 x))))
55.0ms	(* (* x x) x)
84.0ms	(/ 1/8 (* (* x x) x))
163.0ms	(log (+ x (- x (- (/ 1/8 (* (* x x) x)) (/ 1/2 x)))))

simplify1.6s

Counts

104 → 104

Iterations

Iter	Nodes
done	5004
2	1449
1	366
0	158

prune297.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes184.0ms

Accuracy

99.2% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 31.6b

bsearch140.0ms

Steps

Iters	Range		Point
11	4.21785760657603e-35	57.56933376468871	0.9540314055762552
9	-34.11472770615283	-3.67231414207575e-08	-1.0840635159626253

simplify11.0ms

Iterations

Iter	Nodes
done	36
1	36
0	30

end0.0ms

sample4.6s

Algorithm

intervals

Results

2.4s	2352×	body	1280	valid
776.0ms	1515×	body	640	valid
674.0ms	786×	body	2560	valid
286.0ms	773×	body	320	valid
204.0ms	2138×	body	80	valid
84.0ms	436×	body	160	valid