Details

sample32.0ms

Algorithm

intervals

Results

7.0ms	46×	body	1280	valid
5.0ms	142×	body	80	valid
4.0ms	37×	body	640	valid
4.0ms	19×	body	320	valid
1.0ms	12×	body	160	valid

simplify6.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.9b

localize18.0ms

Local error

Found 3 expressions with local error:

0.3b	(cbrt (+ 1.0 x))
0.6b	(cbrt x)
2.8b	(- (cbrt (+ 1.0 x)) (cbrt x))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

15×	`cbrt-prod`
14×	`*-un-lft-identity`
13×	`add-sqr-sqrt`
5×	`add-cube-cbrt` `add-log-exp`
4×	`difference-of-squares`
3×	`pow1` `add-cbrt-cube` `add-exp-log` `distribute-lft-out--`
2×	`cbrt-div` `pow1/3` `distribute-lft-out`
1×	`sub-neg` `flip3-+` `flip3--` `diff-log` `flip-+` `flip--`

Counts

3 → 44

Calls

3 calls:

12.0ms	(cbrt (+ 1.0 x))
1.0ms	(cbrt x)
66.0ms	(- (cbrt (+ 1.0 x)) (cbrt x))

series647.0ms

Counts

3 → 9

Calls

3 calls:

136.0ms	(cbrt (+ 1.0 x))
305.0ms	(cbrt x)
207.0ms	(- (cbrt (+ 1.0 x)) (cbrt x))

simplify1.9s

Counts

53 → 53

Iterations

Iter	Nodes
done	5003
3	3717
2	948
1	313
0	131

prune243.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (- (cbrt (+ 1.0 x)) (cbrt x)) 3)
0.3b	(cbrt (+ 1.0 x))
0.6b	(cbrt x)
2.8b	(- (cbrt (+ 1.0 x)) (cbrt x))

rewrite158.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
32×	`*-un-lft-identity`
31×	`cbrt-prod`
12×	`difference-of-squares`
10×	`unpow-prod-down` `cube-prod`
9×	`add-cube-cbrt` `distribute-lft-out--`
6×	`add-log-exp`
5×	`pow1` `add-cbrt-cube` `add-exp-log`
4×	`distribute-lft-out`
3×	`pow-unpow`
2×	`cube-div` `cbrt-div` `flip3--` `pow1/3` `flip--`
1×	`cube-mult` `pow-to-exp` `sub-neg` `pow-pow` `flip3-+` `diff-log` `unpow3` `pow-exp` `flip-+` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 83

Calls

4 calls:

80.0ms	(pow (- (cbrt (+ 1.0 x)) (cbrt x)) 3)
6.0ms	(cbrt (+ 1.0 x))
1.0ms	(cbrt x)
64.0ms	(- (cbrt (+ 1.0 x)) (cbrt x))

series937.0ms

Counts

4 → 12

Calls

4 calls:

282.0ms	(pow (- (cbrt (+ 1.0 x)) (cbrt x)) 3)
135.0ms	(cbrt (+ 1.0 x))
268.0ms	(cbrt x)
251.0ms	(- (cbrt (+ 1.0 x)) (cbrt x))

simplify1.4s

Counts

95 → 95

Iterations

Iter	Nodes
done	5001
2	3273
1	808
0	256

prune498.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.6b

localize34.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (+ (cbrt x) (cbrt (+ 1.0 x))) (cbrt x))
0.6b	(cbrt x)
0.6b	(cbrt x)
12.4b	(cbrt (pow (/ (+ 1.0 0) (+ (* (cbrt (+ 1.0 x)) (cbrt (+ 1.0 x))) (* (+ (cbrt x) (cbrt (+ 1.0 x))) (cbrt x)))) 3))

rewrite184.0ms

Algorithm

rewrite-expression-head

Rules

88×	`cbrt-prod`
49×	`cbrt-div`
45×	`*-un-lft-identity`
43×	`flip3-+` `flip-+`
42×	`associate-*l/`
36×	`associate-/r/`
34×	`unpow-prod-down` `cube-prod`
32×	`frac-add`
30×	`add-sqr-sqrt`
26×	`add-cube-cbrt`
24×	`times-frac`
16×	`frac-times`
10×	`distribute-lft-out`
8×	`associate-*r/`
6×	`pow1` `associate-r` `associate-l` `add-exp-log`
5×	`add-cbrt-cube`
4×	`add-log-exp`
3×	`pow1/3`
2×	`div-inv` `unswap-sqr`
1×	`cube-div` `cube-mult` `unpow3` `pow-prod-down` `prod-exp` `*-commutative` `rem-cbrt-cube` `cbrt-unprod` `sqr-pow`

Counts

4 → 133

Calls

4 calls:

86.0ms	(* (+ (cbrt x) (cbrt (+ 1.0 x))) (cbrt x))
1.0ms	(cbrt x)
1.0ms	(cbrt x)
81.0ms	(cbrt (pow (/ (+ 1.0 0) (+ (* (cbrt (+ 1.0 x)) (cbrt (+ 1.0 x))) (* (+ (cbrt x) (cbrt (+ 1.0 x))) (cbrt x)))) 3))

series1.4s

Counts

4 → 12

Calls

4 calls:

274.0ms	(* (+ (cbrt x) (cbrt (+ 1.0 x))) (cbrt x))
311.0ms	(cbrt x)
282.0ms	(cbrt x)
563.0ms	(cbrt (pow (/ (+ 1.0 0) (+ (* (cbrt (+ 1.0 x)) (cbrt (+ 1.0 x))) (* (+ (cbrt x) (cbrt (+ 1.0 x))) (cbrt x)))) 3))

simplify795.0ms

Counts

145 → 145

Iterations

Iter	Nodes
done	5002
1	1702
0	513

prune880.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
0.3b	(* (cbrt x) (+ (cbrt (+ x 1.0)) (cbrt x)))
0.6b	(cbrt x)
0.6b	(cbrt x)

rewrite196.0ms

Algorithm

rewrite-expression-head

Rules

38×	`cbrt-prod` `*-un-lft-identity`
29×	`add-sqr-sqrt`
17×	`add-cube-cbrt`
13×	`pow1` `associate-r` `associate-l`
12×	`cbrt-div`
10×	`distribute-lft-out`
9×	`swap-sqr`
8×	`pow1/3` `add-exp-log`
7×	`flip3-+` `flip-+`
6×	`unswap-sqr`
5×	`add-cbrt-cube`
4×	`frac-times` `associate-*r/` `add-log-exp`
3×	`pow-prod-down`
2×	`associate-l/` `prod-exp` `pow-sqr` `-commutative` `pow-prod-up` `cbrt-unprod`
1×	`pow2` `distribute-rgt-in` `distribute-lft-in` `pow-plus`

Counts

4 → 104

Calls

4 calls:

64.0ms	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
124.0ms	(* (cbrt x) (+ (cbrt (+ x 1.0)) (cbrt x)))
1.0ms	(cbrt x)
1.0ms	(cbrt x)

series985.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
227.0ms	(* (cbrt x) (+ (cbrt (+ x 1.0)) (cbrt x)))
324.0ms	(cbrt x)
288.0ms	(cbrt x)

simplify1.5s

Counts

116 → 116

Iterations

Iter	Nodes
done	5001
2	2367
1	542
0	204

prune593.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.0b

regimes136.0ms

Accuracy

0% (0.5b remaining)

Error of 0.6b against oracle of 0.1b and baseline of 0.6b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	18
1	18
0	13

end0.0ms

sample1.3s

Algorithm

intervals

Results

529.0ms	1756×	body	1280	valid
255.0ms	1266×	body	640	valid
172.0ms	4028×	body	80	valid
78.0ms	644×	body	320	valid
71.0ms	306×	body	160	valid