Details

sample62.0ms

Algorithm

intervals

Results

22.0ms	54×	body	1280	valid
12.0ms	51×	body	640	valid
6.0ms	149×	body	80	valid
4.0ms	28×	body	320	valid
3.0ms	87×	body	80	nan
1.0ms	8×	body	160	valid

simplify115.0ms

Counts

1 → 1

Iterations

Useful iterations: 4 (9.0ms)

Iter	Nodes	Cost
0	15	6
1	24	6
2	51	6
3	108	6
4	310	4
5	792	4
6	4192	4
7	5002	4
done	5002	4

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.0b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ x (+ x y))
4.6b	(pow (/ x (+ x y)) x)

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

34×	`*-un-lft-identity`
24×	`times-frac`
20×	`add-sqr-sqrt` `add-cube-cbrt`
18×	`unpow-prod-down`
7×	`add-exp-log` `distribute-lft-out`
4×	`associate-/r*` `associate-/r/` `add-cbrt-cube`
3×	`pow1` `pow-unpow` `associate-/l*`
2×	`expm1-log1p-u` `flip3-+` `div-exp` `pow-exp` `flip-+` `log1p-expm1-u` `div-inv` `add-log-exp`
1×	`cbrt-undiv` `pow-to-exp` `pow-pow` `frac-2neg` `clear-num` `sqr-pow`

Counts

2 → 70

Calls

2 calls:

10.0ms	(/ x (+ x y))
12.0ms	(pow (/ x (+ x y)) x)

series282.0ms

Counts

2 → 6

Calls

2 calls:

46.0ms	(/ x (+ x y))
236.0ms	(pow (/ x (+ x y)) x)

simplify42.0ms

Counts

76 → 76

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	320	413
1	1304	399
2	5002	398
done	5002	398

prune163.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.8b

localize5.0ms

Local error

Found 1 expressions with local error:

0.0b	(/ (exp (* -1 y)) x)

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `times-frac`
3×	`associate-/r` `add-cbrt-cube` `associate-/l`
2×	`add-exp-log`
1×	`pow1` `cbrt-undiv` `exp-neg` `expm1-log1p-u` `frac-2neg` `mul-1-neg` `div-exp` `clear-num` `log1p-expm1-u` `div-inv` `associate-/l/` `add-log-exp`

Counts

1 → 30

Calls

1 calls:

9.0ms

(/ (exp (* -1 y)) x)

series20.0ms

Counts

1 → 3

Calls

1 calls:

20.0ms

(/ (exp (* -1 y)) x)

simplify51.0ms

Counts

33 → 33

Iterations

Useful iterations: 2 (13.0ms)

Iter	Nodes	Cost
0	118	194
1	313	179
2	1512	177
3	5001	177
done	5001	177

prune75.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.8b

localize9.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt (/ (exp (* -1 y)) x)) (cbrt (/ (exp (* -1 y)) x)))
0.4b	(cbrt (/ (exp (* -1 y)) x))
0.4b	(cbrt (/ (exp (* -1 y)) x))
0.4b	(cbrt (/ (exp (* -1 y)) x))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

103×	`cbrt-prod`
81×	`add-sqr-sqrt`
69×	`times-frac`
57×	`add-cube-cbrt` `*-un-lft-identity`
16×	`swap-sqr` `associate-r` `associate-l`
11×	`pow1`
9×	`pow1/3` `unswap-sqr`
7×	`cbrt-div` `div-inv`
6×	`add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-times` `pow-plus` `associate-r/` `associate-l/` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 152

Calls

4 calls:

28.0ms	(* (cbrt (/ (exp (* -1 y)) x)) (cbrt (/ (exp (* -1 y)) x)))
3.0ms	(cbrt (/ (exp (* -1 y)) x))
3.0ms	(cbrt (/ (exp (* -1 y)) x))
3.0ms	(cbrt (/ (exp (* -1 y)) x))

series316.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(* (cbrt (/ (exp (* -1 y)) x)) (cbrt (/ (exp (* -1 y)) x)))
73.0ms	(cbrt (/ (exp (* -1 y)) x))
73.0ms	(cbrt (/ (exp (* -1 y)) x))
74.0ms	(cbrt (/ (exp (* -1 y)) x))

simplify51.0ms

Counts

164 → 164

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	331	1775
1	1173	1706
2	5001	1624
done	5001	1624

prune464.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.8b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (pow (/ (sqrt x) (sqrt (+ x y))) x) (pow (/ (sqrt x) (sqrt (+ x y))) x))
0.1b	(/ (sqrt x) (sqrt (+ x y)))
0.1b	(/ (sqrt x) (sqrt (+ x y)))

rewrite247.0ms

Algorithm

rewrite-expression-head

Rules

450×	`sqrt-prod`
415×	`add-sqr-sqrt`
400×	`times-frac`
354×	`unpow-prod-down`
331×	`*-un-lft-identity`
199×	`add-cube-cbrt`
98×	`swap-sqr`
58×	`distribute-lft-out`
52×	`associate-r` `associate-l`
49×	`unswap-sqr`
39×	`add-exp-log`
18×	`sqr-pow`
16×	`pow-exp` `prod-exp`
14×	`associate-/r*`
12×	`sqrt-div` `associate-/r/` `associate-/l*`
10×	`div-exp`
9×	`add-cbrt-cube`
8×	`pow-to-exp`
6×	`flip3-+` `flip-+` `div-inv`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `sqrt-undiv` `frac-2neg` `clear-num`
1×	`pow2` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod`

Counts

3 → 426

Calls

3 calls:

176.0ms	(* (pow (/ (sqrt x) (sqrt (+ x y))) x) (pow (/ (sqrt x) (sqrt (+ x y))) x))
13.0ms	(/ (sqrt x) (sqrt (+ x y)))
17.0ms	(/ (sqrt x) (sqrt (+ x y)))

series369.0ms

Counts

3 → 9

Calls

3 calls:

237.0ms	(* (pow (/ (sqrt x) (sqrt (+ x y))) x) (pow (/ (sqrt x) (sqrt (+ x y))) x))
69.0ms	(/ (sqrt x) (sqrt (+ x y)))
63.0ms	(/ (sqrt x) (sqrt (+ x y)))

simplify69.0ms

Counts

435 → 435

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	956	5506
1	5001	5194
done	5001	5194

prune745.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.8b

regimes74.0ms

Accuracy

87.7% (1.4b remaining)

Error of 1.9b against oracle of 0.4b and baseline of 12.2b

bsearch70.0ms

Steps

Iters	Range		Point
7	3.250284779123594e-16	2.925089333066609e-14	2.852199015031174e-14
9	-1418669.5161722333	-0.15939393977811658	-7.006483848542437

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	16
1	31	16
done	31	16

end0.0ms

sample1.8s

Algorithm

intervals

Results

641.0ms	1481×	body	1280	valid
367.0ms	1490×	body	640	valid
204.0ms	4783×	body	80	valid
141.0ms	836×	body	320	valid
84.0ms	2967×	body	80	nan
47.0ms	472×	body	160	valid