Details

sample26.0ms

Algorithm

intervals

Results

7.0ms	51×	body	1280	valid
5.0ms	43×	body	640	valid
4.0ms	132×	body	80	valid
1.0ms	19×	body	320	valid
1.0ms	11×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.5b

localize10.0ms

Local error

Found 3 expressions with local error:

0.3b	(cbrt (+ 1.0 x))
0.5b	(cbrt x)
3.0b	(- (cbrt (+ 1.0 x)) (cbrt x))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

64×	`cbrt-prod`
56×	`*-un-lft-identity`
42×	`prod-diff`
41×	`add-sqr-sqrt`
33×	`add-cube-cbrt`
9×	`distribute-lft-out`
7×	`fma-neg`
5×	`add-log-exp`
4×	`difference-of-squares`
3×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `distribute-lft-out--`
2×	`cbrt-div` `pow1/3`
1×	`sub-neg` `flip3-+` `flip3--` `diff-log` `flip-+` `flip--`

Counts

3 → 99

Calls

3 calls:

6.0ms	(cbrt (+ 1.0 x))
1.0ms	(cbrt x)
58.0ms	(- (cbrt (+ 1.0 x)) (cbrt x))

series1.0s

Counts

3 → 9

Calls

3 calls:

117.0ms	(cbrt (+ 1.0 x))
290.0ms	(cbrt x)
642.0ms	(- (cbrt (+ 1.0 x)) (cbrt x))

simplify947.0ms

Counts

108 → 108

Iterations

Iter	Nodes
done	5000
2	1428
1	460
0	194

prune431.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.3b

localize42.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ 1.0 x))
0.5b	(cbrt x)
2.6b	(log (exp (- (cbrt (+ 1.0 x)) (cbrt x))))
3.0b	(- (cbrt (+ 1.0 x)) (cbrt x))

rewrite176.0ms

Algorithm

rewrite-expression-head

Rules

117×	`cbrt-prod`
104×	`*-un-lft-identity`
84×	`prod-diff`
78×	`add-sqr-sqrt`
62×	`add-cube-cbrt`
47×	`log-prod`
44×	`exp-sum`
16×	`distribute-lft-out`
11×	`log-pow`
10×	`exp-prod`
8×	`difference-of-squares`
7×	`fma-neg`
6×	`distribute-lft-out--` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u`
2×	`cbrt-div` `sub-neg` `pow1/3`
1×	`log-div` `flip3-+` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `flip-+` `flip--`

Counts

4 → 168

Calls

4 calls:

3.0ms	(cbrt (+ 1.0 x))
1.0ms	(cbrt x)
99.0ms	(log (exp (- (cbrt (+ 1.0 x)) (cbrt x))))
61.0ms	(- (cbrt (+ 1.0 x)) (cbrt x))

series900.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(cbrt (+ 1.0 x))
326.0ms	(cbrt x)
218.0ms	(log (exp (- (cbrt (+ 1.0 x)) (cbrt x))))
220.0ms	(- (cbrt (+ 1.0 x)) (cbrt x))

simplify1.2s

Counts

180 → 180

Iterations

Iter	Nodes
done	5000
2	1875
1	605
0	315

prune743.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.3b

localize27.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt x)
0.5b	(cbrt x)
0.5b	(cbrt x)
20.3b	(- (cbrt (+ 1.0 x)) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x))))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

17×	`cbrt-prod`
15×	`*-un-lft-identity`
11×	`add-sqr-sqrt` `add-cube-cbrt`
7×	`fma-neg` `prod-diff`
6×	`add-log-exp`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u`
3×	`pow1/3`
2×	`distribute-lft-out`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 67

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)
67.0ms	(- (cbrt (+ 1.0 x)) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x))))

series1.0s

Counts

4 → 12

Calls

4 calls:

266.0ms	(cbrt x)
285.0ms	(cbrt x)
283.0ms	(cbrt x)
201.0ms	(- (cbrt (+ 1.0 x)) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x))))

simplify2.5s

Counts

79 → 79

Iterations

Iter	Nodes
done	5000
3	4861
2	966
1	286
0	120

prune471.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 7.3b

localize30.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (cbrt (+ 1.0 x)))
0.3b	(* (cbrt (+ 1.0 x)) (cbrt (+ 1.0 x)))
0.5b	(cbrt x)
29.6b	(fma (cbrt (* (cbrt (+ 1.0 x)) (cbrt (+ 1.0 x)))) (cbrt (cbrt (+ 1.0 x))) (- (cbrt x)))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

38×	`cbrt-prod`
31×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
16×	`cbrt-div`
15×	`add-cube-cbrt`
11×	`pow1`
9×	`swap-sqr`
8×	`pow1/3`
7×	`flip3-+` `associate-r` `associate-l` `flip-+` `distribute-lft-out`
6×	`add-exp-log`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

4 → 97

Calls

4 calls:

4.0ms	(cbrt (cbrt (+ 1.0 x)))
47.0ms	(* (cbrt (+ 1.0 x)) (cbrt (+ 1.0 x)))
1.0ms	(cbrt x)
1.0ms	(fma (cbrt (* (cbrt (+ 1.0 x)) (cbrt (+ 1.0 x)))) (cbrt (cbrt (+ 1.0 x))) (- (cbrt x)))

series897.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(cbrt (cbrt (+ 1.0 x)))
147.0ms	(* (cbrt (+ 1.0 x)) (cbrt (+ 1.0 x)))
278.0ms	(cbrt x)
331.0ms	(fma (cbrt (* (cbrt (+ 1.0 x)) (cbrt (+ 1.0 x)))) (cbrt (cbrt (+ 1.0 x))) (- (cbrt x)))

simplify1.1s

Counts

109 → 109

Iterations

Iter	Nodes
done	5001
2	2047
1	561
0	244

prune732.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 7.3b

regimes127.0ms

Accuracy

98% (0.4b remaining)

Error of 8.9b against oracle of 8.4b and baseline of 30.1b

bsearch133.0ms

Steps

Iters	Range		Point
9	5.1798647897020696e-05	160.65039477392645	0.04777649667975738
10	-83422883652835.42	-0.9341403346610884	-0.9906799218317324

simplify13.0ms

Iterations

Iter	Nodes
done	51
2	51
1	50
0	43

end0.0ms

sample1.5s

Algorithm

intervals

Results

626.0ms	1318×	body	640	valid
412.0ms	1679×	body	1280	valid
227.0ms	4079×	body	80	valid
100.0ms	600×	body	320	valid
23.0ms	324×	body	160	valid