Details

sample99.0ms

Algorithm

intervals

Results

32.0ms	46×	body	1280	valid
20.0ms	49×	body	640	valid
11.0ms	149×	body	80	valid
8.0ms	27×	body	320	valid
5.0ms	87×	body	80	nan
2.0ms	12×	body	160	valid

simplify1.1s

Counts

1 → 1

Iterations

Useful iterations: 2 (8.0ms)

Iter	Nodes	Cost
0	8	11
1	15	11
2	24	9
3	51	9
4	148	9
5	485	9
6	1979	9
done	5000	9

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.2b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (pow (/ x (+ x y)) x) x)
0.0b	(/ x (+ x y))
7.8b	(pow (/ x (+ x y)) x)

rewrite125.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
118×	`*-un-lft-identity`
90×	`unpow-prod-down`
80×	`add-sqr-sqrt` `add-cube-cbrt`
25×	`associate-/l*`
19×	`distribute-lft-out`
16×	`add-exp-log`
12×	`associate-/r/`
7×	`div-exp` `associate-/r*` `add-cbrt-cube` `div-inv`
6×	`flip3-+` `flip-+`
5×	`sqr-pow`
4×	`pow1` `pow-exp`
3×	`pow-unpow` `add-log-exp`
2×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `clear-num`
1×	`pow-pow`

Counts

3 → 172

Calls

3 calls:

71.0ms	(/ (pow (/ x (+ x y)) x) x)
16.0ms	(/ x (+ x y))
14.0ms	(pow (/ x (+ x y)) x)

series583.0ms

Counts

3 → 9

Calls

3 calls:

167.0ms	(/ (pow (/ x (+ x y)) x) x)
65.0ms	(/ x (+ x y))
350.0ms	(pow (/ x (+ x y)) x)

simplify1.6s

Counts

181 → 181

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	276	2881
1	648	2711
2	2817	2657
done	5000	2654

prune591.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.5b

localize34.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
1.2b	(pow (/ (cbrt x) (cbrt (+ x y))) x)
1.9b	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

61×	`unpow-prod-down`
51×	`cbrt-prod`
48×	`*-un-lft-identity`
43×	`times-frac`
36×	`add-sqr-sqrt` `add-cube-cbrt`
20×	`add-exp-log`
14×	`cbrt-div`
10×	`associate-/r/`
7×	`flip3-+` `pow-exp` `flip-+`
6×	`pow1` `pow-unpow` `distribute-lft-out`
5×	`div-exp`
4×	`frac-times` `prod-exp` `add-cbrt-cube` `add-log-exp`
2×	`pow-to-exp` `pow-pow` `pow1/3` `associate-r/` `associate-l/` `div-inv` `sqr-pow`

Counts

4 → 116

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
42.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
40.0ms	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

series1.4s

Counts

4 → 12

Calls

4 calls:

327.0ms	(cbrt x)
281.0ms	(cbrt x)
376.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
379.0ms	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

simplify1.7s

Counts

128 → 128

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	295	2319
1	964	2162
2	3078	2028
done	5000	1978

prune593.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
1.2b	(pow (/ (cbrt x) (cbrt (+ x y))) x)
3.4b	(log (/ (cbrt x) (cbrt (+ x y))))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

96×	`cbrt-prod`
85×	`*-un-lft-identity`
84×	`times-frac`
61×	`add-sqr-sqrt` `add-cube-cbrt`
48×	`unpow-prod-down` `log-prod`
12×	`distribute-lft-out`
10×	`add-exp-log`
6×	`pow1`
4×	`cbrt-div` `associate-/r/` `add-cbrt-cube` `add-log-exp`
3×	`pow-unpow`
2×	`flip3-+` `pow1/3` `div-exp` `rem-log-exp` `pow-exp` `flip-+` `div-inv`
1×	`pow-to-exp` `log-div` `pow-pow` `log-pow` `sqr-pow`

Counts

4 → 144

Calls

4 calls:

2.0ms	(cbrt x)
2.0ms	(cbrt x)
34.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
9.0ms	(log (/ (cbrt x) (cbrt (+ x y))))

series919.0ms

Counts

4 → 12

Calls

4 calls:

284.0ms	(cbrt x)
230.0ms	(cbrt x)
316.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
89.0ms	(log (/ (cbrt x) (cbrt (+ x y))))

simplify1.5s

Counts

156 → 156

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	274	2485
1	795	2317
2	2459	2241
done	5000	2235

prune886.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize11.0ms

Local error

Found 1 expressions with local error:

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

rewrite26.0ms

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` `associate-/l/`
1×	`pow1` `cbrt-undiv` `neg-sub0` `exp-neg` `frac-2neg` `exp-diff` `div-exp` `clear-num` `div-inv` `add-log-exp`

Counts

1 → 29

Calls

1 calls:

25.0ms

(/ (exp (- y)) x)

series38.0ms

Counts

1 → 3

Calls

1 calls:

38.0ms

(/ (exp (- y)) x)

simplify3.2s

Counts

32 → 32

Iterations

Useful iterations: 3 (805.0ms)

Iter	Nodes	Cost
0	64	299
1	125	289
2	488	271
3	3657	267
done	5001	267

prune73.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes83.0ms

Accuracy

97% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 5.3b

bsearch235.0ms

Steps

Iters	Range		Point
9	0.004463962237743991	1051.5641664341613	2.134762495789531
8	-3.667948724445863e+96	-2.39912100600768e+92	-2.575795415940148e+92

simplify6.0ms

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	23	43
1	29	39
done	29	39

end0.0ms

sample3.8s

Algorithm

intervals

Results

1.2s	1516×	body	1280	valid
1.1s	1445×	body	640	valid
425.0ms	4875×	body	80	valid
255.0ms	2956×	body	80	nan
216.0ms	809×	body	320	valid
72.0ms	436×	body	160	valid