Details

sample44.0ms

Algorithm

intervals

Results

12.0ms	192×	body	80	valid
6.0ms	27×	body	640	valid
4.0ms	13×	body	1280	valid
2.0ms	13×	body	320	valid
1.0ms	11×	body	160	valid

simplify1.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
6	1686
5	419
4	152
3	74
2	35
1	16
0	8

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.0b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ y (+ 1.0 y))
0.0b	(* (- 1.0 x) (/ y (+ 1.0 y)))
2.8b	(- 1.0 (* (- 1.0 x) (/ y (+ 1.0 y))))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

37×	`*-un-lft-identity`
28×	`add-sqr-sqrt`
25×	`times-frac`
21×	`add-cube-cbrt`
18×	`associate-r`
10×	`add-cbrt-cube` `add-exp-log`
7×	`distribute-lft-out`
5×	`pow1` `associate-l` `add-log-exp`
4×	`associate-/r*` `associate-/r/`
3×	`flip3--` `flip--` `associate-/l*`
2×	`frac-times` `cbrt-undiv` `flip3-+` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `flip-+` `div-inv` `unswap-sqr`
1×	`clear-num` `sub-neg` `frac-2neg` `diff-log` `pow-prod-down` `associate-r/` `-commutative` `distribute-lft-out--` `difference-of-squares`

Counts

3 → 88

Calls

3 calls:

17.0ms	(/ y (+ 1.0 y))
62.0ms	(* (- 1.0 x) (/ y (+ 1.0 y)))
5.0ms	(- 1.0 (* (- 1.0 x) (/ y (+ 1.0 y))))

series252.0ms

Counts

3 → 9

Calls

3 calls:

62.0ms	(/ y (+ 1.0 y))
63.0ms	(* (- 1.0 x) (/ y (+ 1.0 y)))
126.0ms	(- 1.0 (* (- 1.0 x) (/ y (+ 1.0 y))))

simplify1.6s

Counts

97 → 97

Iterations

Iter	Nodes
done	5001
2	2479
1	424
0	157

prune401.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- 1.0 x) (/ (/ y (sqrt (+ 1.0 y))) (sqrt (+ 1.0 y))))
0.0b	(/ (/ y (sqrt (+ 1.0 y))) (sqrt (+ 1.0 y)))
0.1b	(/ y (sqrt (+ 1.0 y)))
5.1b	(- 1.0 (* (- 1.0 x) (/ (/ y (sqrt (+ 1.0 y))) (sqrt (+ 1.0 y)))))

rewrite260.0ms

Algorithm

rewrite-expression-head

Rules

724×	`times-frac`
552×	`*-un-lft-identity`
421×	`sqrt-prod`
368×	`add-sqr-sqrt`
342×	`add-cube-cbrt`
195×	`associate-r`
104×	`distribute-lft-out`
36×	`sqrt-div` `associate-/r/`
30×	`associate-/l*`
20×	`add-cbrt-cube` `add-exp-log`
18×	`flip3-+` `flip-+` `div-inv`
14×	`associate-/r*`
7×	`cbrt-undiv` `div-exp` `unswap-sqr`
6×	`pow1` `add-log-exp`
5×	`associate-l`
3×	`flip3--` `prod-exp` `cbrt-unprod` `flip--`
2×	`frac-times` `clear-num` `frac-2neg` `associate-*l/`
1×	`sub-neg` `diff-log` `pow-prod-down` `associate-r/` `-commutative` `distribute-lft-out--` `difference-of-squares` `associate-/l/`

Counts

4 → 524

Calls

4 calls:

120.0ms	(* (- 1.0 x) (/ (/ y (sqrt (+ 1.0 y))) (sqrt (+ 1.0 y))))
47.0ms	(/ (/ y (sqrt (+ 1.0 y))) (sqrt (+ 1.0 y)))
21.0ms	(/ y (sqrt (+ 1.0 y)))
4.0ms	(- 1.0 (* (- 1.0 x) (/ (/ y (sqrt (+ 1.0 y))) (sqrt (+ 1.0 y)))))

series376.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* (- 1.0 x) (/ (/ y (sqrt (+ 1.0 y))) (sqrt (+ 1.0 y))))
47.0ms	(/ (/ y (sqrt (+ 1.0 y))) (sqrt (+ 1.0 y)))
171.0ms	(/ y (sqrt (+ 1.0 y)))
102.0ms	(- 1.0 (* (- 1.0 x) (/ (/ y (sqrt (+ 1.0 y))) (sqrt (+ 1.0 y)))))

simplify809.0ms

Counts

536 → 536

Iterations

Iter	Nodes
done	5001
1	1387
0	497

prune1.7s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize22.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (/ 1.0 y) (- x (/ (* 1.0 x) y)))
0.0b	(- x (/ (* 1.0 x) y))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity` `add-log-exp`
4×	`add-sqr-sqrt`
2×	`pow1` `associate-+r+` `sum-log` `sub-neg` `flip3--` `add-cbrt-cube` `diff-log` `frac-add` `add-exp-log` `add-cube-cbrt` `flip--` `distribute-lft-out` `distribute-lft-out--`
1×	`+-commutative` `associate-+r-` `flip3-+` `flip-+` `difference-of-squares`

Counts

2 → 33

Calls

2 calls:

55.0ms	(+ (/ 1.0 y) (- x (/ (* 1.0 x) y)))
12.0ms	(- x (/ (* 1.0 x) y))

series82.0ms

Counts

2 → 6

Calls

2 calls:

34.0ms	(+ (/ 1.0 y) (- x (/ (* 1.0 x) y)))
48.0ms	(- x (/ (* 1.0 x) y))

simplify595.0ms

Counts

39 → 39

Iterations

Iter	Nodes
done	5000
2	1057
1	208
0	70

prune126.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.1b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (- 1.0 (* (- 1.0 x) (/ y (+ y 1.0)))))
0.0b	(* (- 1.0 x) (/ y (+ y 1.0)))
2.8b	(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))
3.3b	(log (exp (- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))))

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
18×	`associate-r`
16×	`add-cube-cbrt`
13×	`times-frac`
9×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
7×	`pow1`
6×	`exp-prod`
5×	`log-prod` `associate-l`
4×	`exp-sum` `log-pow`
3×	`sub-neg` `flip3--` `flip--` `distribute-lft-out`
2×	`frac-times` `exp-diff` `diff-log` `associate-*l/` `prod-exp` `associate-/r/` `cbrt-unprod` `unswap-sqr` `rem-exp-log`
1×	`cbrt-undiv` `log-div` `flip3-+` `div-exp` `rem-log-exp` `pow-prod-down` `associate-r/` `-commutative` `flip-+` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 88

Calls

4 calls:

17.0ms	(exp (- 1.0 (* (- 1.0 x) (/ y (+ y 1.0)))))
59.0ms	(* (- 1.0 x) (/ y (+ y 1.0)))
4.0ms	(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))
12.0ms	(log (exp (- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))))

series413.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(exp (- 1.0 (* (- 1.0 x) (/ y (+ y 1.0)))))
57.0ms	(* (- 1.0 x) (/ y (+ y 1.0)))
108.0ms	(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))
113.0ms	(log (exp (- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))))

simplify2.1s

Counts

100 → 100

Iterations

Iter	Nodes
done	5001
2	2797
1	509
0	185

prune596.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.1b

regimes365.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.3b against oracle of 0.2b and baseline of 23.1b

bsearch115.0ms

Steps

Iters	Range		Point
8	2205.5689030668646	131076869.41239427	70729809.48992495
7	-22.8286883066892	-0.10952899301968014	-1.0200493385609686

simplify5.0ms

Iterations

Iter	Nodes
done	28
1	28
0	21

end0.0ms

sample1.2s

Algorithm

intervals

Results

460.0ms	6102×	body	80	valid
151.0ms	745×	body	640	valid
113.0ms	516×	body	320	valid
92.0ms	354×	body	1280	valid
31.0ms	283×	body	160	valid